Units, Dimensions, and Dimensional Analysis
Physical quantities are expressed as a numerical value and a unit; dimensions identify the underlying type of quantity.
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Physical quantities are expressed as a numerical value and a unit; dimensions identify the underlying type of quantity.
Scalars have magnitude only; vectors have magnitude and direction.
Vector sums are found component-wise or geometrically.
Position locates an object; distance is path length; displacement is final position minus initial position.
Speed is the magnitude of velocity; average velocity is displacement divided by elapsed time; instantaneous velocity is the slope of the position-time curve.
Acceleration is the rate of change of velocity.
For constant acceleration, displacement, velocity, acceleration, and time are related by standard kinematic equations.
Position-, velocity-, and acceleration-time graphs encode motion through slopes and signed areas.
An object maintains constant velocity unless acted on by a nonzero net external force.
The net external force equals mass times acceleration.
Interaction forces occur in equal-magnitude, opposite-direction pairs acting on different objects.
A free-body diagram isolates one object and shows all external forces acting on it.
Weight is gravitational force mg; the normal force is the perpendicular contact force and may differ from mg.
Friction opposes relative or impending sliding between surfaces.
Tension is a pulling force transmitted along a taut rope or cable.
The center of mass is the mass-weighted average position of a system.
On an incline, gravity is resolved into components parallel and perpendicular to the surface.
Translational equilibrium requires zero net force in every direction.
Torque measures a force’s tendency to rotate an object about an axis.
Rotational equilibrium requires zero net torque about any axis.
An object is statically stable when the vertical projection of its center of mass lies within its base of support and restoring behavior resists small perturbations.
Work is energy transferred by a force through displacement.
Mechanical advantage compares output force to input force and trades force for distance in an ideal machine.
Net work on an object equals its change in kinetic energy.
For a conservative force, work depends only on endpoints and can be represented by potential energy; nonconservative forces make mechanical energy path-dependent.
Kinetic energy is energy associated with translational motion.
Near Earth’s surface, gravitational potential-energy change is mgΔh.
An ideal spring exerts a restoring force proportional to displacement and stores elastic potential energy.
When only conservative forces do work, K+U remains constant.
Power is the rate of energy transfer or work.
Periodic motion repeats after a period; amplitude measures maximum displacement, frequency counts cycles per time, and phase specifies position within a cycle.
Simple harmonic motion occurs when restoring force is proportional and opposite to displacement.
The period of an ideal mass–spring oscillator depends on mass and spring stiffness.
For small angular displacements, a simple pendulum approximates SHM.
A transverse wave oscillates perpendicular to propagation; a longitudinal wave oscillates parallel to propagation.
Density is mass per unit volume: ρ = m/V.
Specific gravity is the ratio of a substance’s density to the density of water and is dimensionless.
Pressure is normal force per unit area: P = F/A.
In a static incompressible fluid, pressure increases with depth because of the weight of fluid above.
Absolute pressure is measured relative to vacuum; gauge pressure is measured relative to local atmospheric pressure.
A pressure change applied to a confined incompressible fluid is transmitted throughout the fluid.
A submerged object experiences an upward buoyant force equal to the weight of displaced fluid.
A floating object is in vertical equilibrium when buoyant force equals its weight.
Apparent weight is the support force measured while buoyancy reduces the required support.
Volume flow rate is the volume passing a cross-section per unit time.
For steady incompressible flow through a single stream tube, volume flow rate is conserved.
In a branching circulation with approximately conserved total flow, average speed is inversely related to the total cross-sectional area at that level.
Viscosity quantifies a fluid’s resistance to shear and flow.
For steady laminar flow of a Newtonian fluid through a long cylindrical tube, flow depends strongly on radius.
Fluid resistances combine analogously to electrical resistors under steady-flow models.
Laminar flow consists of orderly layers with a parabolic speed profile in an ideal tube.
Turbulence is irregular mixing that becomes more likely with high speed, large diameter, high density, and low viscosity.
Along a streamline in ideal steady incompressible nonviscous flow, pressure, kinetic, and gravitational energy per volume trade off.
The Venturi effect is the pressure decrease associated with increased speed through a constriction in ideal flow.
A Pitot tube estimates flow speed by comparing stagnation pressure with static pressure.
Surface tension is energy per unit area or force per unit length associated with a liquid interface.
Curved interfaces require a pressure difference related to surface tension and radius.
Capillary action arises from surface tension plus adhesive and cohesive interactions in narrow tubes.
Arteries carry blood away from the heart under generally higher, more pulsatile pressure; veins return blood at lower pressure and act as capacitance vessels.
Net fluid flow is driven by a pressure difference and opposed by resistance.
Measured vascular pressure depends on reference level and hydrostatic height relative to the heart.
Compliance describes how volume changes with pressure: C = ΔV/ΔP.
Real blood flow loses mechanical energy to viscosity, turbulence, vessel deformation, and branching.
Kelvin temperature is an absolute thermodynamic scale used in gas laws.
Gas pressure results from molecular collisions with container walls.
A mercury barometer balances atmospheric pressure against the hydrostatic pressure of a mercury column.
At 0°C and 1 atm, one mole of an ideal gas occupies approximately 22.4 L.
An ideal gas is modeled as point particles with negligible volume, no intermolecular forces except elastic collisions, and random motion.
The ideal gas law relates pressure, volume, amount, and absolute temperature.
For fixed amount of ideal gas at constant temperature, pressure is inversely proportional to volume.
For fixed amount of ideal gas at constant pressure, volume is proportional to absolute temperature.
At fixed temperature and pressure, ideal-gas volume is proportional to moles.
For an ideal gas, average translational kinetic energy depends only on absolute temperature.
Boltzmann’s constant relates microscopic particle energy to absolute temperature.
Gas heat capacity depends on constraints because expansion at constant pressure requires work in addition to internal-energy change.
Real gases deviate from ideal behavior because molecules have finite volume and intermolecular attractions or repulsions.
The van der Waals equation corrects ideal-gas pressure for attractions and available volume for finite molecular size.
A gas component’s mole fraction is its mole count divided by total moles; its partial pressure is the pressure it would exert alone in the mixture volume at the same temperature.
For an ideal gas mixture, total pressure equals the sum of component partial pressures.
Electric charge is a conserved property measured in coulombs; ordinary matter carries integer multiples of the elementary charge e.
Conductors contain mobile charge carriers that redistribute under an electric field; insulators strongly restrict bulk charge motion.
Grounding connects an object to a large charge reservoir; induction redistributes charge without direct contact with the inducing body.
The electrostatic force between point charges is proportional to the product of charges and inversely proportional to squared separation.
The net electrostatic force is the vector sum of forces from all source charges.
Electric field is force per unit positive test charge: E = F/q.
Field lines visualize direction and relative magnitude of electric fields.
Electric potential is electric potential energy per unit charge; voltage is a potential difference.
Electrostatic potential energy depends on charge configuration.
Between large oppositely charged parallel plates, the field is approximately uniform away from edges.
Current is the rate of net charge flow through a cross-section.
Electromotive force is energy supplied per unit charge by a source; terminal voltage is the measured potential difference across its terminals.
Resistance quantifies opposition to current; an ohmic element obeys a linear voltage-current relation.
Resistivity is a material property relating resistance to conductor geometry.
Series resistors carry the same current and their voltage drops add.
Parallel resistors share the same voltage and their currents add.
Kirchhoff’s rules express charge conservation at junctions and energy conservation around closed loops.
Electrical power is the rate of energy transfer in a circuit.
Capacitance measures charge stored per potential difference.
For large parallel plates in vacuum, capacitance increases with plate area and decreases with separation.
A charged capacitor stores electric potential energy in its field.
Series capacitors carry equal charge magnitude and their voltage differences add.
Parallel capacitors share the same voltage and their stored charges add.
A dielectric polarizes in an electric field, reducing the internal field produced by free charge and increasing capacitance.
Conductivity describes ease of charge transport; metals conduct mainly by electrons, while electrolytes conduct by mobile ions.
An ammeter measures current in series and ideally has negligible resistance; a voltmeter measures potential difference in parallel and ideally has very large resistance.
A magnetic field is a vector field that exerts forces on moving charges, currents, and magnetic dipoles.
The magnetic force on a charge is perpendicular to both its velocity and the magnetic field.
A charge moving perpendicular to a uniform magnetic field follows circular motion when magnetic force supplies centripetal force.
A current-carrying wire in a magnetic field experiences a force from the motion of its charge carriers.
Oxidation is loss of electrons and reduction is gain of electrons.
A redox reaction can be separated into oxidation and reduction half-reactions whose electrons cancel when combined.
The anode is the site of oxidation and the cathode is the site of reduction in both galvanic and electrolytic cells.
A galvanic cell converts the free energy of a spontaneous redox reaction into electrical work.
An electrolytic cell uses external electrical energy to drive a nonspontaneous redox reaction.
An electrolyte provides mobile ions that carry current through solution and maintain bulk charge balance.
A salt bridge permits ionic conduction between half-cells while limiting direct bulk mixing.
Standard reduction potentials rank tendencies for reduction under standard conditions.
Electrochemical potential is linked to reaction free energy and equilibrium.
The Nernst equation adjusts cell potential for nonstandard reaction conditions.
A concentration cell generates voltage from a concentration difference between otherwise similar half-cells.
The amount of substance produced or consumed at an electrode is proportional to total charge transferred.
Electrons flow through the external circuit from anode to cathode; ions move through electrolyte to maintain charge balance.
Electrode mass and ion concentration change according to oxidation or reduction stoichiometry.
A battery is one or more electrochemical cells that convert chemical energy and electrical energy.
A lead-storage battery is a rechargeable galvanic system using lead, lead dioxide, and sulfuric acid during discharge.
A nickel-cadmium battery is a rechargeable electrochemical cell using cadmium and nickel oxyhydroxide chemistry in alkaline electrolyte.
Myelin electrically insulates axonal membrane; Schwann cells form myelin in the peripheral nervous system.
Nodes of Ranvier are gaps in myelin with high densities of voltage-gated channels where action potentials are regenerated.
A membrane potential is an electrical potential difference created by charge separation and maintained ion gradients across a selectively permeable membrane.
A wave transfers energy through a propagating disturbance characterized by amplitude, wavelength, frequency, period, and speed.
In transverse waves, oscillation is perpendicular to propagation; in longitudinal waves, oscillation is parallel to propagation.
When waves overlap, the resultant displacement is the algebraic sum of individual displacements.
Standing waves result from interference of opposite-traveling waves and contain fixed nodes and antinodes.
Resonance is large-amplitude response when a periodic drive is near a system natural frequency.
Intensity is power transmitted per unit area. For an isotropic point source, intensity decreases as inverse square of distance.
Sound is a mechanical pressure wave produced by vibration and transmitted through matter.
Sound speed depends on elastic stiffness and density of the medium.
Sound intensity level expresses intensity on a logarithmic decibel scale.
Pitch is the perceptual correlate of frequency, while loudness relates mainly to intensity and auditory sensitivity.
Attenuation is reduction of wave intensity with distance because of geometric spreading, absorption, scattering, and reflection losses.
The Doppler effect is a change in observed frequency caused by relative motion between source and observer.
When ultrasound reflects from moving blood cells, Doppler shifting occurs on incidence and again on return.
A string fixed at both ends supports harmonics with nodes at both ends.
Air columns resonate according to displacement boundary conditions at open and closed ends.
Beats are periodic intensity variations produced by superposition of two nearby frequencies.
Ultrasound uses high-frequency sound pulses and returning echoes to image internal structures.
Shock waves form when a source moves at or above the wave speed and wavefronts pile up into a sharp pressure disturbance.
Electromagnetic radiation consists of oscillating electric and magnetic fields that propagate energy.
The electromagnetic spectrum is ordered by frequency, wavelength, and photon energy.
A photon carries quantized energy proportional to frequency.
Visible color corresponds to wavelength-dependent stimulation of visual receptors and selective reflection, transmission, or emission.
Polarization describes the orientation behavior of the electric-field oscillation of transverse light.
Incident light can be absorbed, transmitted, reflected, or scattered, with energy conserved across all channels.
Two coherent slits produce alternating bright and dark fringes from path-dependent interference.
A finite slit spreads light and produces a broad central maximum with weaker side maxima.
A diffraction grating uses many regularly spaced slits to create sharp wavelength-dependent maxima.
Reflections from the top and bottom of a thin film can interfere depending on optical path difference and phase shifts on reflection.
X-rays diffract from regularly spaced atomic planes because their wavelengths are comparable to interatomic distances.
Absorbance logarithmically relates incident and transmitted intensity and is proportional to concentration and path length under Beer-Lambert conditions.
Infrared absorption excites molecular vibrational modes that change dipole moment.
Vibrational frequency increases with bond stiffness and decreases with reduced mass.
A substance appears the complementary color of the visible wavelengths it preferentially absorbs.
UV-visible absorption promotes electrons between molecular orbitals, commonly involving pi and nonbonding electrons.
NMR detects transitions between nuclear spin states in an external magnetic field.
Chemically equivalent protons share an NMR signal; signal integration is proportional to the number of contributing protons.
Neighboring nonequivalent protons split signals through spin-spin coupling.
For specular reflection, angle of incidence equals angle of reflection, measured from the normal.
Refraction is direction change when light changes speed across an interface.
Dispersion is wavelength dependence of refractive index, causing different colors to refract by different amounts.
Total internal reflection occurs when light travels from higher to lower refractive index and incidence exceeds the critical angle.
A spherical mirror is characterized by center of curvature, radius, principal axis, and focal length.
Object distance, image distance, and focal length determine spherical-mirror images.
Converging lenses bring parallel rays to a real focus; diverging lenses spread them as if from a virtual focus.
The thin-lens equation relates focal length, object distance, and image distance.
Lens power is reciprocal focal length in meters.
For thin lenses in contact, optical powers add.
Aberrations are image defects because real optical systems do not focus all rays or wavelengths identically.
The cornea and lens focus light onto the retina; accommodation changes lens shape to alter optical power.
Refractive errors occur when the relaxed optical system focuses images in front of or behind the retina.
Optical instruments use lens combinations to increase angular size or resolve small or distant objects.
Water is a bent, polar molecule whose O-H bond dipoles produce a net molecular dipole.
Hydrogen bonding is a strong intermolecular attraction between a hydrogen covalently bound to an electronegative atom and a lone pair on another electronegative atom.
Cohesion is attraction among water molecules; adhesion is attraction between water and another surface; surface tension reflects the energetic cost of increasing a liquid surface.
Water requires substantial energy to change temperature or vaporize because energy is used to disrupt hydrogen-bond networks.
Ice forms an open hydrogen-bonded lattice and is less dense than liquid water, so ice floats. Liquid water reaches maximum density near 4 degrees C.
Water can act as a Bronsted-Lowry acid by donating a proton or as a base by accepting a proton.
Nonpolar solutes aggregate in water largely because aggregation reduces ordered water exposure and increases solvent entropy.
At equilibrium, evaporation and condensation rates are equal; vapor pressure reflects escaping tendency and rises with temperature.
A solution is a homogeneous mixture in which solute particles are dispersed at molecular or ionic scale in a solvent.
Solvation stabilizes separated solute particles through solvent interactions; hydration is solvation by water.
Solubility is favored when solute-solvent interactions can replace disrupted solute-solute and solvent-solvent interactions.
Molarity is moles of solute per liter of final solution.
Molality is moles solute per kilogram solvent; mole fraction is component moles divided by total moles; mass percent is component mass divided by total solution mass times 100%.
Dilution adds solvent without changing moles of conserved solute.
Electrolytes produce mobile ions in solution and conduct electricity; nonelectrolytes remain largely molecular.
An unsaturated solution can dissolve more solute; a saturated solution is in dynamic equilibrium with undissolved solute; a supersaturated solution contains more dissolved solute than equilibrium permits.
Solubility depends on solute-solvent interactions, temperature, pressure for gases, and chemical reactions such as ionization or complexation.
At fixed temperature and dilute conditions, dissolved gas concentration is proportional to its partial pressure above the solution.
Colligative properties depend primarily on the number of dissolved particles, not their chemical identity, in ideal dilute solutions.
For an ideal solution, a component partial vapor pressure equals its liquid mole fraction times its pure-component vapor pressure.
A nonvolatile solute raises the boiling point because the solution must reach a higher temperature for its vapor pressure to equal external pressure.
A solute lowers the freezing point by stabilizing the liquid solution relative to pure solvent solid.
Osmosis is net solvent movement through a selectively permeable membrane toward the side with greater effective concentration of nonpenetrating solute.
Osmotic pressure is the external pressure required to prevent net osmosis.
Osmolarity counts total dissolved particle concentration, while tonicity predicts sustained cell-volume effects from effectively nonpenetrating solutes.
An Arrhenius acid increases H3O+ in water; an Arrhenius base increases OH- in water.
A Bronsted-Lowry acid donates a proton; a base accepts a proton. Products differ from reactants by one proton in conjugate pairs.
A Lewis acid accepts an electron pair; a Lewis base donates an electron pair.
Water autoionizes to form hydronium and hydroxide, with Kw = [H3O+][OH-].
pH = -log[H3O+] and pOH = -log[OH-] for dilute solutions; at 25 degrees C, pH + pOH = 14.
Strong acids or bases ionize essentially completely in dilute aqueous solution; weak acids or bases establish equilibria with substantial unionized species.
Ka and Kb quantify acid and base ionization equilibria; larger K means greater strength, while pK = -log K reverses the ordering.
An ICE table organizes initial concentrations, equilibrium changes, and equilibrium concentrations for weak-electrolyte calculations.
Percent ionization is equilibrium ionized concentration divided by initial weak-acid concentration times 100%.
Polyprotic acids donate protons in sequential equilibria with generally decreasing Ka values.
Acid strength increases when the conjugate base is stabilized by electronegativity, resonance, induction, orbital character, or solvation and when the H-A bond is easier to break.
A buffer contains a weak acid and its conjugate base, or a weak base and its conjugate acid, and resists pH change by consuming added strong acid or base.
The Henderson-Hasselbalch equation relates buffer pH to pKa and the conjugate-base/acid ratio.
Buffer capacity is the amount of added acid or base a buffer can absorb before large pH change; effective buffering is strongest near pKa.
Neutralization first follows stoichiometric proton transfer between acid and base before any remaining weak species are treated by equilibrium.
A titration curve tracks pH as titrant is added and contains initial, buffer, equivalence, and excess-titrant regions depending on system.
At half-equivalence in a weak acid-strong base titration, moles HA equal moles A-, so pH = pKa.
An acid-base indicator is a weak acid/base pair whose forms have different colors; its transition range is centered near its pKa.
Ions from salts can react with water and alter pH depending on the strengths of their parent acids and bases.
Adding an ion already present in an equilibrium shifts that equilibrium to reduce further production of the ion.
Ksp is the equilibrium constant for dissolution of a sparingly soluble ionic solid, written from dissolved ion activities with stoichiometric exponents.
The ion product Qsp has the same form as Ksp but uses current concentrations; comparison predicts dissolution or precipitation direction.
Selective precipitation separates ions by adding a reagent so one salt exceeds Ksp before others.
Complex formation can lower free metal-ion concentration and thereby increase dissolution of a sparingly soluble salt.
A covalent bond forms when atoms share electron density, usually allowing valence shells to reach lower-energy arrangements.
Lewis structures represent valence electrons as bonds and lone pairs to track connectivity and electron count.
The octet rule is a useful main-group guideline, not an absolute law; H follows a duet, some electron-deficient species have incomplete octets, and third-period or heavier atoms can appear hypervalent in Lewis models.
Formal charge is an electron-bookkeeping value assigned by assuming equal sharing of bonding electrons.
Resonance contributors are alternative valid Lewis representations that differ only in electron placement, not atom connectivity.
The real electronic structure is a resonance hybrid with electron density delocalized over the atoms represented by valid contributors.
A Lewis acid accepts an electron pair, whereas a Lewis base donates an electron pair.
Electronegativity describes an atom’s tendency to attract shared electron density within a bond; unequal electronegativity produces bond polarity.
A polar covalent bond can be described as having partial ionic character because unequal sharing produces partial charges without complete electron transfer.
A bond dipole reflects separation of partial charge; the molecular dipole is the vector sum of all bond dipoles and relevant charge distributions.
A sigma bond results from head-on orbital overlap along the internuclear axis; a pi bond results from side-by-side overlap above and below that axis.
sp3 hybridization corresponds to four electron domains around a central atom and an ideal tetrahedral electron-domain geometry.
sp2 hybridization corresponds to three electron domains and an ideal trigonal-planar arrangement, leaving one unhybridized p orbital available for pi bonding.
sp hybridization corresponds to two electron domains and an ideal linear geometry, leaving two mutually perpendicular unhybridized p orbitals for pi bonding.
VSEPR predicts geometry by arranging electron domains around a central atom to minimize repulsion.
Nonbonding electron pairs generally occupy more angular space than bonding pairs and therefore compress adjacent bond angles.
Structural formulas encode atom connectivity, bond multiplicity, and often lone-pair or charge information using line, condensed, or skeletal representations.
For comparable atoms, increasing bond order generally shortens and strengthens a bond.
Rotation around a double bond is strongly restricted because rotating the bonded atoms would disrupt pi-orbital overlap.
Covalent bonding can produce discrete molecules or extended network solids; discrete molecular substances have identifiable individual molecules, whereas network solids are continuous covalent lattices.
Chemical nomenclature provides a standardized way to communicate molecular composition, connectivity, substituent position, and stereochemical descriptors.
Isomers share a molecular formula but differ in atom connectivity or three-dimensional arrangement.
Constitutional isomers have the same molecular formula but different atom connectivity.
Conformational isomers (conformers) differ by rotation about single sigma bonds or other low-energy geometric changes without breaking covalent bonds.
Stereoisomers have the same molecular formula and connectivity but differ in three-dimensional arrangement.
A molecule is chiral if it is not superimposable on its mirror image; a common source is a tetrahedral atom bonded to four different substituent groups.
Enantiomers are nonsuperimposable mirror-image stereoisomers.
Diastereomers are stereoisomers that are not mirror images of one another.
A meso compound contains stereogenic centers but is achiral because an internal symmetry element makes the molecule superimposable on its mirror image.
R/S nomenclature assigns absolute configuration at a stereogenic center using Cahn-Ingold-Prelog priority rules.
E/Z nomenclature describes alkene geometry when each double-bond carbon has two different substituents, using CIP priority on each carbon.
Cis-trans isomerism describes relative placement of comparable substituents on opposite sides or the same side of a rigid unit such as certain alkenes or rings.
A chiral sample can rotate plane-polarized light; the sign of rotation is an experimental property independent of the R/S naming convention.
Specific rotation normalizes observed optical rotation for path length and concentration under specified conditions.
A racemic mixture contains equal amounts of two enantiomers and has zero net optical rotation; enantiomeric excess measures imbalance between them.
Relative configuration compares stereochemical relationships without necessarily specifying absolute R/S configuration; Fischer projections are a common 2D convention for displaying such relationships.
London dispersion forces arise from instantaneous fluctuations in electron density that induce temporary dipoles in neighboring particles.
Polarizability is the ease with which an electron cloud can be distorted to create an induced dipole.
Dipole-dipole interactions are attractions between the partially positive region of one polar molecule and the partially negative region of another.
Hydrogen bonding is a particularly strong directional dipole interaction involving an H covalently attached to a highly electronegative atom and a lone-pair acceptor, classically N, O, or F in MCAT contexts.
Molecular samples often experience multiple intermolecular forces simultaneously; the observed property reflects their combined effect rather than a single categorical label.
Stronger intermolecular attractions generally raise boiling point and enthalpy of vaporization while lowering vapor pressure at a given temperature.
Melting point depends on both interaction strength and how efficiently molecules pack into an ordered solid lattice.
Stronger cohesive intermolecular attractions often increase viscosity and surface tension, although molecular shape, temperature, and entanglement can also matter.
Solubility is favored when new solute-solvent interactions can adequately compensate for the interactions disrupted within the pure solute and pure solvent.
Ion-dipole attraction occurs between a full ionic charge and the partial charges of a polar molecule and is central to hydration of ions in water.
A solute placed in two immiscible phases distributes between them according to its relative intermolecular interactions with each phase at equilibrium.
Liquid-liquid extraction separates compounds by allowing them to partition between immiscible solvents, followed by physical separation of the phases.
A separatory funnel permits controlled mixing and separation of immiscible liquid phases; layer position depends primarily on density, not on whether a phase is organic or aqueous.
Acid-base extraction changes a compound’s protonation state so that neutral and ionic forms have different phase preferences.
For a fixed total amount of extracting solvent, several smaller extractions can remove more solute than one single extraction because each step re-establishes the partition equilibrium.
An extraction workup may wash a retained phase to remove impurities, back-extract a solute into the opposite phase, and remove residual water from an organic phase with a drying agent before solvent removal.
An emulsion is a persistent dispersion of droplets of one liquid in another that can delay clean separation of nominally immiscible phases.
Distillation separates volatile liquids because the vapor above a liquid mixture is enriched in components with greater volatility under the operating conditions.
Simple distillation performs essentially one major vaporization-condensation step and is most effective when component volatilities differ substantially or when separating a volatile solvent from nonvolatile material.
Fractional distillation improves separation of liquids with closer volatilities by creating many effective vaporization-condensation equilibrations along a fractionating column.
Vacuum distillation lowers external pressure so liquids boil at lower temperatures, enabling distillation of high-boiling or thermally sensitive compounds.
During distillation, head temperature provides information about the composition of vapor reaching the condenser and can guide collection of separate fractions.
An azeotrope is a mixture composition at which vapor and liquid have the same composition under specified conditions, limiting further separation by ordinary distillation.
Chromatography separates mixture components by differential interaction with a stationary phase and a moving mobile phase.
Chromatographic selectivity arises from differences in adsorption, partitioning, charge, size, affinity, or other analyte interactions, depending on the stationary and mobile phases.
Column chromatography passes a mobile phase through a packed stationary phase so analytes separate into bands and are collected in sequential fractions.
In common normal-phase chromatography, the stationary phase is polar (often silica) and the mobile phase is less polar, so more strongly polar or hydrogen-bonding analytes are often retained more strongly.
Gas-liquid chromatography uses a gaseous mobile phase and a nonvolatile liquid-like stationary phase coating; separation reflects volatility plus analyte interactions with the stationary phase.
HPLC drives a liquid mobile phase through a densely packed column at high pressure, enabling efficient separation and quantitative detection of compounds that need not be volatile.
Reversed-phase chromatography uses a relatively nonpolar stationary phase and a more polar mobile phase; hydrophobic analytes are often retained more strongly.
Paper chromatography separates analytes as a solvent front moves through paper, with migration determined by differential interactions with the stationary environment and mobile solvent.
TLC separates small samples on a thin stationary layer, commonly polar silica, as solvent rises by capillary action.
The retention factor normalizes analyte migration to solvent-front migration: Rf = distance traveled by solute / distance traveled by solvent front.
Chromatographic resolution describes how well neighboring components are separated; detector peak position can support identity and peak area can support quantity when response is calibrated.
Protein purification usually combines methods that exploit different properties such as size, charge, specific binding, and electrophoretic mobility.
Size-exclusion chromatography separates molecules by access to pores in stationary beads; larger molecules are excluded from more pores and therefore generally elute earlier.
Ion-exchange chromatography separates molecules by electrostatic attraction to charged stationary groups.
Affinity chromatography selectively retains a target through a specific reversible interaction with an immobilized ligand.
Electrophoresis separates charged species by their motion in an electric field through a supporting medium; mobility depends on net charge, size/shape, and matrix conditions.
SDS-PAGE denatures proteins and coats polypeptide chains with a roughly uniform negative charge-to-mass ratio, so migration through the gel depends primarily on polypeptide size.
Reducing SDS-PAGE includes a reducing reagent that cleaves disulfide bonds, whereas nonreducing SDS-PAGE leaves disulfide linkages intact even though proteins are otherwise denatured by SDS.
Native PAGE separates proteins without the strong denaturation and uniform charge imposed by SDS, so mobility reflects a combination of native charge, size, shape, and oligomeric state.
Isoelectric focusing separates amphoteric molecules in a pH gradient according to isoelectric point (pI); a protein migrates until it reaches the pH at which its net charge is approximately zero.
Quantitative protein analysis measures concentration, amount, or activity using a calibrated signal rather than relying only on visual band intensity or purification labels.
For enzyme purification, specific activity is enzyme activity per unit total protein and often increases as contaminants are removed; yield tracks how much target activity remains.
After chromatographic separation, individual fractions can be assayed for target activity, protein amount, or identity before selected fractions are pooled.
A racemic mixture contains equal amounts of two enantiomers and is optically inactive because their equal and opposite rotations cancel.
A racemate can be resolved by reacting its enantiomers with a single-enantiomer resolving agent to form diastereomeric derivatives or salts with different physical properties, separating them, and regenerating the original enantiomers.
Chiral chromatography uses a chiral stationary phase or chiral selector so two enantiomers form transient diastereomeric interactions of different strength and can have different retention.
Enantiomeric purity can be assessed by a chiral separation or, when specific rotation of the pure enantiomer is known and other assumptions hold, by optical rotation and enantiomeric excess.
A nucleoside is a nitrogenous base attached to a pentose sugar; a nucleotide is a nucleoside with one or more phosphate groups.
Purines contain fused two-ring heterocycles; pyrimidines contain a single six-membered heterocycle.
Nucleic acids polymerize through phosphodiester linkages connecting the 3′ hydroxyl of one sugar to the 5′ phosphate of the next nucleotide.
DNA uses deoxyribose and thymine; RNA uses ribose and usually uracil. The 2′-OH of RNA increases its chemical reactivity relative to DNA.
Canonical DNA pairing places A with T and G with C through complementary hydrogen-bonding patterns; RNA commonly pairs A with U.
Heating, extreme pH, or low ionic strength can disrupt noncovalent interactions between strands without cleaving the covalent backbone; complementary strands can reanneal under suitable conditions.
Single-stranded RNA can form intramolecular base-paired stems, hairpins, loops, and other folded structures.
Nucleic acids store sequence information, but RNA can also act structurally, catalytically, and in regulation; nucleotides can participate in energy transfer and signaling.
Polymerization forms phosphodiester bonds using activated nucleotide substrates; hydrolysis cleaves covalent linkages by reaction with water, often accelerated by acid, base, or enzymes.
An α-amino acid contains an amino group, carboxyl group, hydrogen, and side chain attached to the α carbon.
Biological proteins use predominantly L-amino acids; most L-amino acids have S configuration at the α carbon, with cysteine as the common R exception because sulfur changes CIP priority.
Amino acids can carry both positive and negative charges simultaneously; their net charge depends on pH relative to relevant pKa values.
Side chains are commonly grouped as nonpolar, polar uncharged, acidic, basic, aromatic, or special-case residues according to dominant chemical behavior.
The isoelectric point pI is the pH at which the average net charge of a molecule is zero.
Two cysteine thiols can be oxidized to form a disulfide bond, producing a cystine linkage; reduction reverses the process.
A peptide bond is an amide linkage formed between the carboxyl group of one amino acid and the amino group of another with loss of water in the net condensation description.
Resonance delocalization gives the C-N peptide bond partial double-bond character, making the peptide unit approximately planar and restricting rotation about C-N.
Hydrolysis cleaves peptide bonds by addition of water; acids, bases, or proteases can catalyze the process.
Proteins can bind ligands, ions, nucleic acids, membranes, or other proteins through shape and chemical complementarity without catalyzing a reaction.
Antibodies and many immune receptors use protein surfaces to recognize specific molecular features.
Motor proteins couple chemical free-energy changes, typically nucleotide hydrolysis, to directed conformational changes and mechanical work.
Protein chemical behavior emerges from amino-acid sequence, side-chain chemistry, backbone constraints, and three-dimensional environment; changes in any can alter binding or reactivity.
Fatty acids contain a hydrocarbon chain and terminal carboxylic acid; chain length and unsaturation strongly affect physical properties.
Triacylglycerols are glycerol triesters of fatty acids and serve as dense, hydrophobic energy-storage molecules.
Saponification is base-promoted ester hydrolysis of fats or oils, producing glycerol and carboxylate salts (“soap”).
Glycerophospholipids contain a glycerol backbone, fatty acyl chains, phosphate, and often a polar head group, creating amphipathic molecules suited to membranes.
Sphingolipids use a sphingosine-related backbone and typically contain an amide-linked fatty acid; head groups determine subclasses and biological roles.
Waxes are esters of long-chain fatty acids with long-chain alcohols, producing highly hydrophobic protective materials.
Steroids share a characteristic four-fused-ring carbon skeleton; substitutions control properties and signaling functions.
Vitamins A, D, E, and K are fat-soluble molecules whose hydrophobic character affects absorption, transport, storage, and biochemical roles.
Prostaglandins are locally acting lipid mediators derived from polyunsaturated fatty-acid precursors.
Lipid reactivity often reflects ester, amide, phosphate, or alkene functional groups; hydrolysis susceptibility depends on the linkage and conditions.
Hydrophobicity, amphipathicity, chain packing, and functional-group chemistry determine whether lipids favor storage droplets, bilayers, barriers, or signaling roles.
Monosaccharides are polyhydroxy aldehydes or ketones classified by carbonyl type and carbon number, such as aldose/ketose and triose/pentose/hexose.
D/L sugar designation is assigned by the configuration of the highest-numbered stereocenter relative to glyceraldehyde in a Fischer projection.
Epimers are diastereomers that differ in configuration at exactly one stereocenter among several.
Monosaccharides cyclize when an internal hydroxyl attacks the carbonyl, forming a hemiacetal for aldoses or hemiketal for ketoses.
α and β anomers differ at the newly created anomeric stereocenter; they can interconvert through the open-chain form in solution when the anomeric center is free.
Cyclic sugars commonly form six-membered pyranoses or five-membered furanoses; six-membered rings often adopt chair conformations that minimize unfavorable interactions.
A glycosidic bond forms when an anomeric carbon is converted from a hemiacetal/hemiketal into an acetal/ketal linkage to another group; hydrolysis reverses the linkage under suitable conditions.
Disaccharides contain two monosaccharides joined by a glycosidic bond; a free hemiacetal anomeric carbon provides a reducing end capable of ring opening.
Polysaccharides are carbohydrate polymers whose linkage type and branching determine shape, solubility, and biological role.
Sugars with carbonyl groups can interconvert through enediol/enolate-like intermediates under suitable acid/base conditions, allowing aldose-ketose or epimerization chemistry.
Aldehydes contain a terminal carbonyl carbon bonded to at least one hydrogen; ketones contain an internal carbonyl bonded to two carbon groups.
The C=O bond is strongly polarized, making the carbonyl carbon electrophilic and oxygen nucleophilic/basic; carbonyl compounds accept hydrogen bonds but aldehydes/ketones lack O-H donors.
Nucleophiles attack the electrophilic carbonyl carbon, converting trigonal-planar sp2 carbon toward tetrahedral geometry; proton transfers then generate product-specific functionality.
Addition of alcohol to a carbonyl gives a hemiacetal/hemiketal; under acid-catalyzed conditions with excess alcohol, acetals/ketals can form with two OR groups on the former carbonyl carbon.
Primary amines condense with aldehydes or ketones to form imines (C=N) after addition and dehydration under suitable conditions.
Secondary amines react with aldehydes or ketones containing α hydrogens to form enamines, featuring C=C adjacent to nitrogen.
Hydride reagents deliver nucleophilic H− equivalent to the carbonyl carbon, reducing aldehydes to primary alcohols and ketones to secondary alcohols.
Cyanide adds to a carbonyl carbon and protonation yields a cyanohydrin bearing OH and CN on the same carbon, extending the carbon skeleton by one carbon.
Aldehydes are readily oxidized to carboxylic acids under common oxidizing conditions; ketones resist analogous oxidation without carbon-carbon bond cleavage.
Hydrogens on carbons adjacent to carbonyls are relatively acidic because deprotonation forms resonance-stabilized enolate ions.
Carbonyl compounds with α hydrogens can interconvert with enol forms; passage through a planar enol/enolate intermediate can erase stereochemical information at an α stereocenter and cause racemization.
An enolate or enol attacks another carbonyl to form a new C-C bond and β-hydroxy carbonyl; dehydration can produce an α,β-unsaturated carbonyl. Retro-aldol cleaves the corresponding C-C bond.
Enolate distribution can depend on base, temperature, reversibility, and substitution: kinetic products form faster, while thermodynamic products are more stable at equilibrium. Carbonyl electrophilicity also depends on steric and electronic substituent effects.
Alcohols contain an sp3 carbon bonded to OH; the hydroxyl group enables hydrogen bonding and gives weak acidity.
Primary alcohols can oxidize to aldehydes and further to carboxylic acids; secondary alcohols oxidize to ketones; tertiary alcohols lack the necessary carbinol hydrogen for simple analogous oxidation without bond cleavage.
Alcohol substitution requires converting OH into a better leaving group, often by protonation or derivatization; mechanism depends on substrate, nucleophile, solvent, and conditions.
Protecting groups temporarily convert a reactive OH into a less reactive derivative so another reaction can occur selectively, followed by deprotection.
Mesylation or tosylation converts an alcohol into a sulfonate ester that is a much better leaving group while retaining the C-O bond during activation.
Under suitable acidic and heated conditions, alcohols can eliminate water to form alkenes; competition with substitution depends on structure and conditions.
Hydroxyl groups in carbohydrates, serine/threonine residues, sterols, and metabolites alter hydrogen bonding, acidity, and derivatization chemistry.
Carboxylic acids contain a carboxyl group whose conjugate base is resonance-stabilized, making them substantially more acidic than typical alcohols.
Acyl derivatives react when a nucleophile adds to the carbonyl carbon to form a tetrahedral intermediate, followed by elimination of a leaving group to restore C=O.
Carboxylic acids and alcohols can form esters under suitable conditions; intramolecular ester formation yields lactones.
Amides are carboxylic-acid derivatives with nitrogen attached to the acyl carbon; cyclic amides are lactams. Peptide bonds are biological amides.
Acid anhydrides contain two acyl groups linked through oxygen and are relatively reactive acyl-transfer agents.
Acyl-substitution reactivity reflects leaving-group ability and resonance donation; a common MCAT ordering among listed derivatives is anhydrides > esters ≈ carboxylic acids (condition-dependent) > amides, with activated derivatives being more reactive.
Electron-withdrawing groups can increase acyl electrophilicity, while steric hindrance can reduce nucleophilic approach; resonance donation from substituents decreases electrophilicity.
Strong reducing agents can lower the oxidation state of carboxylic acids and many derivatives, often producing alcohols; exact products depend on substrate and reagent.
Decarboxylation removes a carboxyl-derived carbon as CO2, often favored when the resulting intermediate/product is stabilized, as in β-keto acids.
The α (2-) carbon next to a carboxyl group can undergo substitution when its C-H acidity is enhanced and appropriate activation conditions generate an enol/enolate-like intermediate.
Transesterification exchanges the alkoxy group of an ester with another alcohol under suitable acid/base catalysis while retaining the acyl carbon framework.
Amide hydrolysis cleaves the C-N acyl bond to give carboxylic-acid/carboxylate and amine/ammonium products depending on pH; it is slower than comparable ester hydrolysis because of amide resonance stabilization.
Four-membered β-lactam rings distort normal amide geometry and reduce resonance stabilization, making the carbonyl unusually reactive toward nucleophilic attack.
Peptide bonds, lipid esters, phospholipid linkages, and cyclic lactams/lactones can be analyzed with the same acyl-substitution framework while respecting linkage-specific differences.
Phenols are aromatic alcohol-like compounds whose conjugate phenoxide ions are resonance-stabilized, making phenols more acidic than typical aliphatic alcohols.
Hydroquinone/quinone pairs undergo reversible two-electron, two-proton redox chemistry in many biological electron-transfer systems.
Biological molecules frequently contain aromatic heterocycles with ring heteroatoms, including purines, pyrimidines, porphyrin-like systems, and many cofactors/drugs.
Fused or extended aromatic systems delocalize π electrons across multiple rings, influencing planarity, absorption, redox behavior, and molecular interactions.
Across biomolecules, reactivity can often be predicted by identifying electrophiles, nucleophiles, leaving groups, resonance stabilization, acid-base state, steric effects, and redox-active centers.
Atomic number Z is the number of protons in the nucleus and uniquely identifies the element.
Mass number A is protons plus neutrons for one nuclide; atomic weight is the abundance-weighted average isotopic mass for an element.
Nuclear composition sets Z and A, while net ionic charge reflects the difference between proton and electron counts.
Isotopes are atoms of the same element with the same proton number but different neutron numbers.
Nuclear binding reflects attractive strong-force interactions that stabilize nucleons at short range against proton-proton electrostatic repulsion.
Mass defect is the difference between the mass of separated nucleons and the mass of the bound nucleus; the difference corresponds to binding energy.
Unstable nuclei transform spontaneously toward more stable nuclear configurations through radioactive decay.
Alpha decay emits a 4He nucleus, decreasing parent mass number by 4 and atomic number by 2.
In beta-minus decay a neutron converts to a proton while an electron and antineutrino are emitted; A is unchanged and Z increases by 1.
Beta-plus decay converts a proton to a neutron with positron emission; electron capture also converts a proton to a neutron. In both, A is unchanged and Z decreases by 1.
Gamma emission releases a high-energy photon from an excited nucleus without changing its proton or neutron numbers.
Nuclear equations conserve total nucleon number and electric charge across reactants and products.
Half-life is the time required for the number of undecayed nuclei, activity, or another proportional decay measure to fall to one half its previous value.
Radioactive populations obey first-order exponential decay N=N0e^(-λt), with λ related to half-life by λ=ln2/t1/2.
Activity is the number of nuclear decays per unit time and, for a fixed isotope, is proportional to the number of undecayed nuclei: A=λN.
First-order radioactive decay becomes linear when ln(N) or ln(activity) is plotted versus time, with slope -λ.
Mass spectrometry separates or detects gas-phase ions according to mass-to-charge ratio (m/z), producing peaks that reflect ionic species and isotopic composition.
Ionized molecules can fragment into characteristic charged pieces; isotope abundances can create predictable neighboring peak patterns.
Bound electrons occupy discrete allowed energy states rather than a continuum.
The principal quantum number n labels major electron shells and is related to orbital energy and characteristic size, especially in hydrogen-like atoms.
An orbital can contain at most two electrons with opposite spin, and subshells contain characteristic numbers of orbitals (s:1, p:3, d:5, f:7).
No two electrons in the same atom can have the same set of four quantum numbers; two electrons sharing an orbital must have opposite spins.
The ground state is the lowest-energy allowed electron configuration; an excited state has one or more electrons promoted to higher-energy states.
Electron configurations describe occupation of atomic orbitals using shell/subshell notation such as 1s2 2s2 2p6.
Atomic absorption and emission lines arise from transitions between discrete electronic energy levels, with photon energy equal to the level difference.
The Bohr model treats hydrogenic electron states as quantized energy levels; for hydrogen En is proportional to -1/n^2.
Position and momentum cannot both be known with arbitrarily small uncertainty; their uncertainties obey a lower-bound relation.
Species with one or more unpaired electrons are paramagnetic; species with all electrons paired are diamagnetic.
Effective nuclear charge is the net attractive nuclear charge experienced by an electron after shielding by other electrons is considered.
In the photoelectric effect, electrons are emitted from a material only when incident photon frequency exceeds a threshold; excess photon energy becomes electron kinetic energy.
Valence electrons are the outer electrons most directly involved in bonding, ion formation, and periodic chemical behavior.
Excitation promotes an electron to a higher bound state, whereas ionization removes it from the bound atom or molecule.
Elements in a main-group column share similar valence-electron configurations and therefore show related chemical behavior.
Alkali metals are Group 1 metals with one valence electron and a strong tendency to form +1 ions and react as reducing metals.
Alkaline earth metals are Group 2 metals with two valence electrons and commonly form +2 ions.
Group 16 main-group elements have six valence electrons and include oxygen and sulfur, which commonly participate in two-bond or -2 oxidation-state patterns while also showing covalent chemistry.
Halogens are Group 17 nonmetals with seven valence electrons, high electronegativity, and a tendency to gain one electron or form one covalent bond.
Noble gases have filled valence shells in the basic main-group model and are comparatively unreactive, monatomic gases under ordinary conditions.
Transition metals occupy the d block and often show multiple oxidation states and complex-ion behavior; representative elements are the main-group s/p-block elements.
Metals generally have lower ionization energies and form cations/conductive solids, whereas nonmetals more often gain/share electrons and are poorer bulk conductors.
Atomic radius generally increases down a group as shells are added and decreases across a period as effective nuclear charge rises.
Cations are generally smaller than their neutral atoms and anions larger; within an isoelectronic series, more protons produce a smaller ion.
Ionization energy is the energy required to remove an electron from a gaseous species; successive removals generally require more energy, with large jumps after valence electrons are exhausted.
Electron affinity describes the energy change associated with adding an electron to a gaseous atom; favorable electron gain is generally stronger for many right-side nonmetals than for metals.
Electronegativity is an atom’s tendency to attract shared electron density in a bond; it generally increases across a period and decreases down a group.
Periodic trends arise from the combined effects of principal shell, shielding, and effective nuclear charge.
Molar mass is the mass per mole of a substance, obtained by summing atomic masses according to formula composition.
An empirical formula gives the simplest whole-number atom ratio; a molecular formula gives the actual atom counts and is an integer multiple of the empirical formula.
Chemical calculations commonly require consistent SI/metric prefixes and scientific notation for mass, volume, concentration, energy, and amount.
Mass percent is component mass divided by total sample mass times 100%.
One mole contains Avogadro’s number of specified entities, approximately 6.02×10^23.
Density is mass per unit volume, ρ=m/V.
Oxidation number is a bookkeeping assignment used to track electron transfer and redox changes.
An oxidizing agent accepts electrons and is reduced; a reducing agent donates electrons and is oxidized.
In disproportionation, the same reactant species is simultaneously oxidized and reduced to products with higher and lower oxidation states.
Balanced chemical equations encode conservation of atoms and fixed mole ratios among reactants and products.
Equation balancing chooses coefficients so each element and total charge are conserved without altering chemical formulas.
Redox equations require conservation of atoms and charge; half-reaction balancing explicitly accounts for electrons and, when needed, H2O/H+/OH-.
The limiting reactant is consumed first according to stoichiometric ratios and therefore caps the amount of product that can form.
Theoretical yield is the maximum product predicted from the limiting reactant; percent yield compares actual to theoretical yield.
Multi-step stoichiometric reasoning combines formula mass, concentration or gas/sample information, balanced coefficients, limiting reagent, and yield.
Enzymes are classified according to the chemical transformation they catalyze, such as oxidation-reduction, group transfer, hydrolysis, addition/removal, isomerization, or bond formation.
Enzymes accelerate reactions by lowering the activation free-energy barrier through an alternative catalytic pathway; they do not change overall ΔG, ΔG°, or the equilibrium constant.
Enzyme specificity arises from complementary chemical and three-dimensional interactions between the active site and particular substrates or substrate features.
The active site is the localized region where substrate binding and catalytic chemistry occur through specific noncovalent and sometimes transient covalent interactions.
In induced fit, substrate binding promotes conformational changes that improve catalytic alignment and stabilize productive interactions.
Enzymes can accelerate reactions through acid-base catalysis, covalent catalysis, metal-ion catalysis, proximity/orientation effects, electrostatic stabilization, and preferential transition-state stabilization.
Cofactors are nonprotein components required for some enzyme activities; coenzymes are organic cofactors, many derived from vitamins, while metal ions are common inorganic cofactors.
For a simple Michaelis–Menten enzyme at fixed enzyme concentration, initial velocity rises hyperbolically with substrate concentration and approaches Vmax as active sites become saturated.
The Michaelis–Menten relation is v0=Vmax[S]/(Km+[S]) for the standard simple model.
Km is the substrate concentration at which a simple Michaelis–Menten enzyme operates at half Vmax; under specific kinetic assumptions it can inversely reflect apparent substrate affinity.
Vmax is the maximal initial velocity at substrate saturation and is proportional to total active enzyme concentration for a fixed catalytic turnover rate.
The turnover number kcat is the maximal number of substrate molecules converted per active enzyme site per unit time, with Vmax=kcat[E]T.
kcat/Km is a useful measure of catalytic performance at low substrate concentration, combining turnover and apparent substrate handling.
A classical competitive inhibitor competes with substrate for the active site, increasing apparent Km while leaving Vmax unchanged in the simple model; high substrate can overcome inhibition.
An ideal uncompetitive inhibitor binds the enzyme–substrate complex, decreasing both apparent Km and Vmax by the same factor in the simple model.
Mixed inhibitors bind free enzyme and enzyme–substrate complex with different affinities, lowering Vmax and shifting apparent Km; pure noncompetitive inhibition is the special case with unchanged Km.
A double-reciprocal plot graphs 1/v versus 1/[S], with y-intercept 1/Vmax, x-intercept -1/Km, and slope Km/Vmax for the simple model.
Cooperative substrate binding in multimeric/allosteric proteins can produce sigmoidal velocity or binding curves rather than simple hyperbolic Michaelis–Menten behavior.
Allosteric regulators bind sites distinct from the active site and alter enzyme conformation, activity, substrate response, or cooperativity.
Reversible covalent modification, commonly phosphorylation/dephosphorylation, can alter enzyme activity, localization, or interactions.
Enzyme activity depends on local conditions because ionization, binding, catalytic residue chemistry, and protein conformation vary with pH, temperature, ionic environment, and concentrations.
Biological reaction spontaneity and equilibrium are governed by Gibbs free energy; at equilibrium ΔG=0, and ΔG° is related to Keq.
Actual free-energy change depends on concentrations through ΔG=ΔG°+RT ln Q, so cellular conditions can make a reaction favorable or unfavorable relative to its standard value.
An unfavorable reaction can proceed when mechanistically coupled to a sufficiently favorable reaction so that the summed ΔG for the net process is negative.
ATP hydrolysis is strongly exergonic under typical cellular conditions because products are thermodynamically stabilized and cellular concentration ratios often favor hydrolysis.
ATP can transfer phosphoryl or other activated groups through enzyme-catalyzed coupling, creating intermediates whose subsequent reactions are more favorable or controllable.
Biological redox reactions can be separated into oxidation and reduction half-reactions that conserve electrons and charge.
Soluble electron carriers such as NAD+/NADH shuttle reducing equivalents between enzyme-catalyzed reactions.
Flavoproteins use flavin cofactors such as FAD/FADH2 or FMN/FMNH2 to participate in biological electron-transfer chemistry, often as tightly bound cofactors.
For a redox reaction, free energy and cell potential are related by ΔG=-nFE; favorable electron transfer under stated conditions corresponds to positive Ecell and negative ΔG.
Cells often couple reactions by forming an activated covalent intermediate whose formation is linked to ATP or another exergonic transformation.
Thermodynamics determines energetic favorability and equilibrium position; kinetics determines reaction rate and pathway. Enzymes primarily alter kinetics.
A thermodynamic system is the portion of the universe chosen for study, separated conceptually from surroundings by a boundary; systems may exchange energy and/or matter depending on type.
State functions such as U, H, S, G, P, V, and T depend only on the thermodynamic state, while heat q and work w depend on the process path.
The zeroth law establishes transitive thermal equilibrium and underlies the concept and measurement of temperature.
The first law expresses conservation of energy: the change in internal energy equals energy transferred as heat and work, with signs determined by convention.
For quasi-static expansion/compression, PV work is related to the integral of pressure with volume; at constant external pressure w=-PextΔV in the chemistry sign convention.
Area under a PV path represents work magnitude, and area enclosed by a complete PV cycle represents net work magnitude with direction setting sign.
The second law requires the entropy of an isolated universe/system total not to decrease for a spontaneous process; entropy measures energy dispersal/multiplicity and is often simplified as disorder.
For the same substance under comparable conditions, entropy generally follows gas > liquid > solid because accessible molecular configurations and dispersal increase.
Heat capacity C relates heat to temperature change for an object; specific heat c is heat capacity per unit mass, giving q=mcΔT when c is approximately constant.
Calorimetry infers heat transferred in a process from measured temperature changes and known heat capacities, using energy conservation.
Heat can transfer by conduction through microscopic interactions, convection through bulk fluid motion, or electromagnetic radiation without a material medium.
At constant pressure, an endothermic process has positive ΔH for the system and absorbs heat; an exothermic process has negative ΔH and releases heat.
Enthalpy H is a state function useful for constant-pressure heat; standard enthalpy of formation is the enthalpy change for forming one mole of compound from elements in standard states.
Because enthalpy is a state function, reaction enthalpies can be added after reversing/scaling component reactions to obtain a target reaction.
Average bond dissociation energies can estimate gas-phase reaction enthalpy as energy required to break reactant bonds minus energy released forming product bonds.
At constant temperature and pressure, Gibbs free energy combines enthalpy and entropy through ΔG=ΔH-TΔS and predicts thermodynamic direction.
For a specified direction, ΔG<0 is thermodynamically spontaneous, ΔG>0 favors the reverse direction, and ΔG=0 corresponds to equilibrium.
The signs of ΔH and ΔS determine whether increasing temperature makes a process more or less favorable through ΔG=ΔH-TΔS.
Thermal expansion describes dimensional change with temperature; for small changes, linear expansion can be modeled as ΔL=αL0ΔT and volumetric expansion analogously.
Latent heat is absorbed or released during phase change at approximately constant temperature; q=nΔHfus or nΔHvap (or mass-specific analogs) for the transition.
Heating curves combine sloped single-phase regions (q=mcΔT) with plateaus where added heat drives phase changes.
A phase diagram maps stable phases versus pressure and temperature and identifies coexistence lines, triple point, and critical point.
Reaction rate measures change in reactant or product concentration per unit time, with stoichiometric normalization when comparing species.
An empirical rate law relates reaction rate to reactant concentrations raised to experimentally determined orders, rate=k[A]^m[B]^n.
Reaction order with respect to a reactant is the exponent of its concentration in the empirical rate law; overall order is the sum of exponents.
The method of initial rates compares experiments that vary one reactant concentration while holding others fixed to infer rate-law exponents.
Units of k depend on overall reaction order so that the rate law yields concentration per time.
For ideal zero-order behavior, concentration changes linearly with time: [A]=[A]0-kt.
For an ideal first-order reaction, ln[A]=ln[A]0-kt and t1/2=ln2/k, independent of initial concentration.
For the simple rate law rate=k[A]^2, 1/[A]=1/[A]0+kt and half-life depends inversely on initial concentration.
In a multistep mechanism, the kinetically controlling slow step and preceding equilibria can determine the observed rate law; intermediates cancel from the overall reaction.
Activation energy is the energetic barrier between reactants and the transition-state region along a reaction pathway.
The transition state is a high-energy configuration near the top of the reaction coordinate that is traversed during conversion of reactants to products.
Reaction-coordinate diagrams display reactant/product energies, activation barriers, intermediates, and overall ΔH.
Raising temperature generally increases a reaction’s rate constant because a larger fraction of molecular encounters can overcome the activation barrier.
The Arrhenius equation k=Ae^(-Ea/RT) relates the rate constant to activation energy and absolute temperature.
Catalysts increase reaction rates by providing a lower-barrier pathway and are regenerated overall; they accelerate forward and reverse processes without changing Keq.
Under kinetic control, the faster-forming product can dominate; under thermodynamic control, the more stable product can dominate when equilibration is possible.
At dynamic equilibrium, forward and reverse reaction rates are equal, so macroscopic concentrations remain constant even though microscopic reactions continue.
For a balanced reaction, the equilibrium expression contains activities/concentrations of products over reactants raised to stoichiometric coefficients, omitting pure solids/liquids in standard simplified expressions.
The magnitude of K indicates the equilibrium product/reactant preference for the written reaction but does not reveal how quickly equilibrium is reached.
The reaction quotient Q has the same form as K but uses current conditions; comparison of Q to K predicts the direction of spontaneous composition change toward equilibrium.
When an equilibrium system is perturbed, it shifts in the direction that partially counteracts the imposed change, consistent with Q moving back toward K.
Standard free energy and equilibrium constant are related by ΔG°=-RT ln K.