Chemistry Formula and Concept Reference

n = m / M

Meaning and units: n in mol; m in g; M in g mol⁻¹.

Check: Use the molar mass of the specified substance, not a coefficient.

N = n Nₐ

Meaning and units: Nₐ = 6.02214076 × 10²³ mol⁻¹ (exact).

Check: Count the specified atoms, molecules, ions, or formula units.

M = n / V

Meaning and units: M in mol L⁻¹; n in mol; V in L.

Check: Use solution volume, not solvent volume.

M₁V₁ = M₂V₂

Meaning and units: Applies when the solute amount is conserved.

Check: Added solvent changes concentration, not moles of solute.

ρ = m / V

Meaning and units: Use consistent mass and volume units.

Check: For displacement, subtract initial from final volume.

% yield = 100 × actual yield / theoretical yield

Meaning and units: Use the same mass or mole units for both yields.

Check: Calculate theoretical yield from the limiting reactant.

% error = 100 × |measured − accepted| / |accepted|

Meaning and units: Reference value must be nonzero.

Check: Keep the signed error separately when direction matters.

PV = nRT

Meaning and units: Use an R value consistent with pressure and volume units; T in K.

Check: Do not insert temperature in °C.

P₁V₁ = P₂V₂

Meaning and units: Fixed n and T for ideal gases.

Check: State the fixed-temperature assumption.

V₁/T₁ = V₂/T₂

Meaning and units: Fixed n and P; temperatures in K.

Check: Absolute temperature is required.

q = mcΔT

Meaning and units: c = specific heat; ΔT = T_final − T_initial.

Check: Distinguish heat gained by solution from heat released by reaction.

q_rxn = −q_surroundings

Meaning and units: Only when additional heat exchanges are negligible or accounted for.

Check: An assumption, not a universal identity for every calorimeter.

pH = −log₁₀(a_H⁺)

Meaning and units: Activity-based definition; [H⁺] approximation in dilute solutions.

Check: pH is not universally equal to −log concentration in nonideal media.

pOH = −log₁₀(a_OH⁻)

Meaning and units: At 25 °C in dilute aqueous solution, pH + pOH ≈ 14.00.

Check: The value 14.00 depends on temperature and conventions.

pH ≈ pKₐ + log₁₀([A⁻]/[HA])

Meaning and units: Useful buffer approximation under appropriate conditions.

Check: Not reliable when the weak acid/base has been essentially consumed.

R_f = distance of spot / distance of solvent front

Meaning and units: Measure both from the same baseline; 0 ≤ Rf ≤ 1 for normal TLC.

Check: A spot position alone does not establish compound identity.

A = εℓc

Meaning and units: A unitless; ℓ in cm; c consistent with ε.

Check: Requires an appropriate linear concentration range.

y = mx + b; x = (y − b) / m

Meaning and units: For nonzero slope, within the validated calibration range.

Check: Avoid extrapolating far outside standards.

t₁/₂ = ln(2)/k

Meaning and units: For a genuine first-order process; k in reciprocal time.

Check: Other reaction orders have different half-life relationships.

N = N₀(1/2)^(t/t₁/₂)

Meaning and units: Applies to populations with constant decay probability.

Check: Use the same units for t and t₁/₂.

ΔG = ΔH − TΔS

Meaning and units: At fixed T, with consistent energy units.

Check: Interpret spontaneous tendency under the stated conditions.

Q = ∏ a_products^ν / ∏ a_reactants^ν

Meaning and units: Activities raised to stoichiometric coefficients; pure solids/liquids omitted.

Check: Use balanced stoichiometric coefficients.

E°cell = E°cathode − E°anode

Meaning and units: Values are reduction potentials.

Check: Do not multiply electrode potentials by coefficients.

DBE = (2C + 2 + N − H − X)/2

Meaning and units: Neutral closed-shell formulas of C,H,N and halogens; O,S ignored.

Check: Count halogens as H; check if formula assumptions apply.

FC = valence e⁻ − nonbonding e⁻ − ½(bonding e⁻)

Meaning and units: Bookkeeping for a specified Lewis structure.

Check: Sum of formal charges equals overall species charge.

ṽ = 1 / λ

Meaning and units: Use cm for λ to obtain cm⁻¹.

Check: A single IR band rarely proves compound identity.

area % = 100 × Aᵢ / ΣAⱼ

Meaning and units: Uncorrected detector-response fraction for integrated peaks.

Check: Not necessarily mass fraction, mole fraction or purity without response factors.