dumb freaking chem equations

E = hν

Energy of a photon. Use when calculating the energy of light from its frequency (photoelectric effect, atomic emission, spectroscopy).

c = λν

Relationship between speed of light, wavelength, and frequency. Use to convert between wavelength and frequency of electromagnetic radiation.

F ∝ (q₁q₂)/r²

Coulomb’s Law. Use to compare electrostatic attraction/repulsion between charged particles (ions, protons, electrons) based on charge and distance.

E (energy)

Energy of radiation or particles. Often calculated using E = hν in atomic/quantum problems.

ν (frequency)

Number of wave cycles per second. Used when calculating photon energy or converting with wavelength using c = λν.

λ (wavelength)

Distance between wave peaks. Used when working with electromagnetic radiation or spectral lines.

h (Planck’s constant)

Constant relating photon energy and frequency in E = hν.

c (speed of light)

Constant (2.998×10⁸ m/s) used to relate wavelength and frequency of light.

q (charge)

Electric charge of particles used in Coulombic force calculations.

r (distance)

Distance between charged particles in Coulomb’s law problems.

P₁V₁/T₁ = P₂V₂/T₂

Combined gas law. Use when a gas changes conditions (pressure, volume, temperature) but moles stay constant.

PV = nRT

Ideal gas law. Use to calculate any missing variable (P, V, n, or T) for gases under ideal conditions.

Pₐ = Ptotal × Xₐ

Partial pressure equation. Use when determining the pressure contributed by a gas in a mixture using mole fraction.

Ptotal = Pₐ + Pᵦ + …

Dalton’s Law. Use to calculate total pressure of a mixture of gases by adding individual partial pressures.

n = m / M

Mole calculation from mass. Use to convert between grams and moles in stoichiometry problems.

D = m / V

Density equation. Use when calculating density or when solving gas problems involving molar mass and density.

KE = ½mv²

Kinetic energy of moving particles. Used conceptually in kinetic molecular theory and energy calculations.

M = n / Lsolution

Molarity. Use to calculate concentration of a solution in moles per liter.

A = εbc

Beer-Lambert Law. Use in spectroscopy to relate absorbance to concentration of a solution.

P (pressure)

Force per unit area exerted by gas particles. Appears in gas law calculations.

V (volume)

Amount of space occupied by a gas or solution. Used in gas law and molarity calculations.

T (temperature)

Measure of average kinetic energy. Must be in Kelvin for gas law equations.

n (moles)

Amount of substance used in stoichiometry and gas law calculations.

X (mole fraction)

Ratio of moles of a component to total moles in a mixture. Used in partial pressure calculations.

m (mass)

Amount of matter in grams. Used in density and mole conversions.

M (molar mass)

Mass of one mole of a substance. Used to convert between grams and moles.

D (density)

Mass per volume of a substance. Used to identify substances or relate gas properties.

R (gas constant)

Constant used in the ideal gas law. Value depends on units used.

[A]t − [A]₀ = −kt

Zero-order integrated rate law. Use when reaction rate is independent of reactant concentration.

ln[A]t − ln[A]₀ = −kt

First-order integrated rate law. Use when rate depends directly on concentration of one reactant.

1/[A]t − 1/[A]₀ = kt

Second-order integrated rate law. Use when rate depends on square of concentration or two reactants.

t½ = 0.693/k

Half-life for first-order reactions. Use to determine time for concentration to drop by half.

k (rate constant)

Constant describing speed of a reaction at a given temperature.

t (time)

Time elapsed during a reaction, used in kinetics equations.

Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ

Equilibrium constant using molar concentrations. Use to determine extent of reaction at equilibrium.

Kp = (Pc)ᶜ(Pd)ᵈ / (Pa)ᵃ(Pb)ᵇ

Equilibrium constant using gas pressures. Used for reactions involving gases.

Kw = [H₃O⁺][OH⁻]

Ion product of water. Used to relate hydronium and hydroxide concentrations in aqueous solutions.

pH = −log[H₃O⁺]

Measure of acidity. Use when determining acidity from hydronium concentration.

pOH = −log[OH⁻]

Measure of basicity. Use when calculating base strength from hydroxide concentration.

Ka = [H₃O⁺][A⁻]/[HA]

Acid dissociation constant. Use to determine strength of weak acids.

Kb = [OH⁻][HB⁺]/[B]

Base dissociation constant. Use to determine strength of weak bases.

pKa = −log Ka

Logarithmic measure of acid strength. Lower pKa indicates stronger acid.

pKb = −log Kb

Logarithmic measure of base strength.

Kw = Ka × Kb

Relationship between conjugate acid-base pairs.

pH = pKa + log([A⁻]/[HA])

Henderson-Hasselbalch equation. Use to calculate pH of buffer solutions.

q = mcΔT

Heat transfer equation. Used in calorimetry to calculate heat absorbed or released.

ΔH°reaction = ΣΔH°f(products) − ΣΔH°f(reactants)

Standard enthalpy change of reaction calculated from formation values.

ΔS°reaction = ΣS°products − ΣS°reactants

Standard entropy change of a reaction.

ΔG°reaction = ΣΔG°f(products) − ΣΔG°f(reactants)

Standard Gibbs free energy change calculated from formation energies.

ΔG° = ΔH° − TΔS°

Used to determine spontaneity of reactions based on enthalpy and entropy.

ΔG° = −RT ln K

Connects thermodynamics and equilibrium. Use to calculate equilibrium constant from free energy.

ΔG° = −nFE°

Relationship between Gibbs free energy and electrochemical cell potential.

I = q/t

Definition of electric current. Used when calculating current from charge flow.

Ecell = E°cell − (RT/nF) ln Q

Nernst equation. Used to calculate cell potential under nonstandard conditions.

F (Faraday constant)

Charge of one mole of electrons. Used in electrochemistry calculations.

Q (reaction quotient)

Determines direction a reaction will shift relative to equilibrium.