Chemistry Formula Sheet

1. Mole Concept and Concentration

Useful for stoichiometry, solution preparation and quantitative chemistry.

Number of moles

n = m / M

n = amount in mol; m = mass in g; M = molar mass in g mol⁻¹.

Number of particles

N = nNₐ

N is the number of specified particles; Nₐ is Avogadro's constant.

Molarity

C = n / V

n is solute amount in mol; V is solution volume in litres. Unit: mol L⁻¹.

Molality

m = n / mass of solvent (kg)

Amount of solute per kilogram of solvent. Unit: mol kg⁻¹.

Mass percentage

Mass % = (solute mass / solution mass) × 100

Solute and solution masses must use the same mass unit.

Dilution

C₁V₁ = C₂V₂

Applies when the amount of solute remains unchanged during dilution. Use consistent volume units.

Mole fraction

xᵢ = nᵢ / Σn

Mole fraction of component i equals its moles divided by total moles.

Percentage yield

% yield = (actual yield / theoretical yield) × 100

Compare actual product obtained with the theoretical maximum.

2. Atomic Structure

Core relationships for atoms, photons and electronic transitions.

Atomic number

Z = number of protons

In a neutral atom, proton number equals electron number.

Mass number

A = Z + number of neutrons

Mass number counts protons and neutrons in the nucleus.

Wave relationship

c = νλ

c = speed of light; ν = frequency; λ = wavelength.

Photon energy

E = hν = hc/λ

h is Planck's constant. Use SI units for energy in joules.

de Broglie wavelength

λ = h/p

For a non-relativistic particle, p = mv, giving λ = h/(mv).

3. Gases and States of Matter

These equations describe ideal gases and common gas-law relationships.

Ideal gas equation

PV = nRT

P = pressure; V = volume; n = moles; T = kelvin temperature.

Combined gas law

P₁V₁/T₁ = P₂V₂/T₂

Applies to a fixed amount of ideal gas between two states.

Boyle's law

P₁V₁ = P₂V₂

At constant temperature and fixed amount of gas.

Charles's law

V₁/T₁ = V₂/T₂

At constant pressure and fixed amount of gas.

Dalton's law

Ptotal = ΣPᵢ

Total pressure equals the sum of partial pressures for a gas mixture.

Gas density

ρ = PM / RT

For an ideal gas, M is molar mass and ρ is mass density. Keep units consistent.

Always use absolute temperature in kelvin for gas equations. For the ideal gas equation, R = 8.314 J mol⁻¹ K⁻¹ works with pressure in Pa and volume in m³.

4. Chemical Thermodynamics

Relationships for heat, work, enthalpy, entropy and spontaneity.

First law

ΔU = q + w

Chemistry sign convention: q is heat absorbed by the system; w is work done on the system.

Pressure-volume work

w = −PextΔV

For constant external pressure. Expansion gives negative work under this convention.

Enthalpy

H = U + PV

At constant pressure, with only pressure-volume work, heat transfer is qₚ = ΔH.

Calorimetry

q = mcΔT

m = mass; c = specific heat capacity; ΔT = temperature change.

Reaction enthalpy

ΔᵣH° = ΣνΔfH°(products) − ΣνΔfH°(reactants)

ν represents stoichiometric coefficients.

Gibbs free energy

ΔG = ΔH − TΔS

For a process at constant temperature and pressure. Negative ΔG indicates thermodynamic favourability.

Entropy and equilibrium

ΔG° = −RT ln K

Relates standard Gibbs energy change to the dimensionless thermodynamic equilibrium constant K.

5. Chemical Equilibrium

Use these expressions for reversible reactions at equilibrium.

Equilibrium constant

aA + bB ⇌ cC + dD
Kc = [C]ᶜ[D]ᵈ / ([A]ᵃ[B]ᵇ)

This concentration expression applies to the reaction as written; pure solids and pure liquids are omitted.

Reaction quotient

Q uses the same form as K

Compare Q with K to predict the direction of net reaction toward equilibrium.

Relation between Kp and Kc

Kp = Kc(RT)Δn

For ideal gases, Δn = gaseous product coefficients minus gaseous reactant coefficients. Use consistent conventions.

Strictly, thermodynamic equilibrium constants are defined using activities and are dimensionless. Kc and Kp are common textbook expressions using concentration or pressure conventions.

6. Acids and Bases

Key equations for pH, weak-acid equilibria and neutralisation.

pH

pH = −log₁₀[H₃O⁺]

The simple concentration form is an approximation; rigorous pH is defined using hydrogen-ion activity.

pOH

pOH = −log₁₀[OH⁻]

The concentration form is commonly used for dilute aqueous solutions.

Water ion product

Kw = [H₃O⁺][OH⁻]

At 25°C, Kw is approximately 1.0 × 10⁻¹⁴.

pH and pOH

pH + pOH = pKw

At 25°C in dilute aqueous solutions, pKw is approximately 14.

Acid dissociation constant

Ka = [H₃O⁺][A⁻] / [HA]

For HA + H₂O ⇌ H₃O⁺ + A⁻, omitting liquid water from the expression.

Base dissociation constant

Kb = [BH⁺][OH⁻] / [B]

For B + H₂O ⇌ BH⁺ + OH⁻, omitting liquid water.

Henderson–Hasselbalch

pH = pKa + log₁₀([A⁻]/[HA])

Useful for buffer solutions when the approximation is appropriate.

7. Redox and Electrochemistry

Electron transfer, cell potential and electrical charge.

Charge transferred

Q = It

Q = charge in coulombs; I = current in amperes; t = time in seconds.

Faraday's constant

F ≈ 96485 C mol⁻¹

Charge per mole of electrons.

Electrochemical cell

E°cell = E°cathode − E°anode

Use standard reduction potentials for both electrodes.

Gibbs energy and cell potential

ΔG = −nFEcell

n = moles of electrons transferred per reaction as written.

Nernst equation at 25°C

E = E° − (0.05916 V / n) log₁₀ Q

For a cell reaction at 25°C, with Q the dimensionless reaction quotient under the chosen standard-state convention.

8. Solutions and Colligative Properties

Equations for vapour pressure, boiling point, freezing point and osmosis.

Henry's law

p = Kₕx

One common convention relating gas partial pressure to its mole fraction in solution. Other conventions exist.

Raoult's law

pA = xA pA°

Partial vapour pressure of a volatile component in an ideal solution.

Boiling-point elevation

ΔTb = iKbm

Kb = ebullioscopic constant; m = molality; i = van't Hoff factor.

Freezing-point depression

ΔTf = iKfm

Kf = cryoscopic constant; m = molality.

Osmotic pressure

π = iCRT

For dilute solutions: C = molar concentration; T = kelvin temperature.

Relative lowering of vapour pressure

(p° − p)/p° = xsolute

For an ideal solution containing a non-volatile solute.

9. Chemical Kinetics

Rate laws, integrated equations, half-life and temperature dependence.

General rate law

Rate = k[A]ᵐ[B]ⁿ

m and n are determined experimentally; overall order = m + n.

Zero-order integrated law

[A]t = [A]₀ − kt

For a zero-order reaction under the specified conditions.

First-order integrated law

ln([A]₀/[A]t) = kt

Equivalent to k = (2.303/t) log₁₀([A]₀/[A]t).

Second-order integrated law

1/[A]t = 1/[A]₀ + kt

For the rate law Rate = k[A]².

First-order half-life

t½ = 0.693/k

Independent of initial concentration for a first-order reaction.

Arrhenius equation

k = Ae⁻ᴱᵃ⁄ᴿᵀ

Ea = activation energy; R = gas constant; T = kelvin temperature.

Two-temperature Arrhenius form

ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂)

Assumes the same Arrhenius model and activation energy over the range.

10. Important Constants and Units

Check constants and units before substituting values into equations.

Quantity	Symbol	Common value or SI unit
Avogadro constant	Nₐ	6.02214076 × 10²³ mol⁻¹
Gas constant	R	8.314 J mol⁻¹ K⁻¹
Planck constant	h	6.62607015 × 10⁻³⁴ J s
Speed of light in vacuum	c	2.99792458 × 10⁸ m s⁻¹
Faraday constant	F	Approximately 96485 C mol⁻¹
Temperature	T	Kelvin (K)
Pressure	P	Pascal (Pa)
Energy	E, U, H	Joule (J)
Concentration	C	mol m⁻³ in SI; mol L⁻¹ commonly used

Numerical problem checklist: Convert temperature to kelvin where required, keep units consistent, check whether logarithms use ln or log₁₀, and confirm that the equation applies to the stated conditions.