H2 Chemistry Formula List
H2 Chemistry 9476 equations with units, assumptions, sign conventions and a worked calculation.
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A topic-organised calculation reference for H2 Chemistry (9476). Choose the model and check the units before substituting. Conditions in the final column matter as much as the equation.
Moles, composition and reacting quantities
| Relationship | Symbols and units | When to use it |
|---|---|---|
| Mᵣ = ∑ Aᵣ | Mᵣ and Aᵣ have no unit | Include every subscript and bracket multiplier in the formula. |
| n = m/M; m = nM | n mol, m g, M g/mol | Match the mass unit to the molar-mass unit; this does not require a reaction ratio. |
| mean Aᵣ = ∑(A_(r,i) fᵢ) | Fractional isotope abundance fᵢ has no unit; ∑ fᵢ = 1 | For percentage abundances, divide each percentage by 100. |
| total positive charge + total negative charge = 0 | Ionic charges in units of elementary charge | Choose the smallest whole-number ion ratio; never change an ion’s own formula. |
| CₙH₂ₙ₊₂; CₙH₂ₙ | n is the number of carbon atoms | Acyclic alkanes / acyclic alkenes with one double bond; not all hydrocarbons. |
| x = Mᵣ(compound)/Mᵣ(empirical formula) | Whole-number multiplier x; relative masses have no unit | Multiply every empirical-formula subscript by x to obtain the molecular formula; first find the simplest mole ratio. |
| N = nN_A | Particle count N; N_A in mol⁻¹ | Specify the counted entity; N_A ≈ 6.02 × 10²³ mol⁻¹ for calculations. |
| n(A)/a = n(B)/b | Moles; equation coefficients a and b | For aA → bB, use a balanced equation and the limiting reactant. |
| n = V/Vₘ | Gas volume V and molar gas volume Vₘ in matching units | At r.t.p. the school reference is Vₘ = 24 dm³/mol; use the supplied value. |
| c = n/V; n = cV | c mol/dm³; solution volume V dm³ | Convert cm³ to dm³ before substitution: divide by 1000. |
| cₘₐₛₛ = m/V = cM | Mass concentration g/dm³; M g/mol | Distinguish mass concentration from molar concentration. |
| c₁V₁ = c₂V₂ | Matching concentration and volume units | Dilution of the same solute with no reaction; not the general titration equation. |
| c_AV_A/a = c_BV_B/b | Concentrations mol/dm³ and volumes dm³ | Titration at the reacting ratio a:b; equal volumes or equal concentrations need not result. |
Enthalpy and calorimetry
| Relationship | Symbols and units | When to use it |
|---|---|---|
| q = mcΔ T; Δ H = -q/n | q J; mass g; c J/(g K); Δ T K; n mol | For a reaction at constant pressure, q is heat gained by the measured surroundings. Negate for reaction heat, convert J to kJ and use the stated molar basis; neglect losses only if justified. |
| Δ H°ᵣ = ∑νΔ H_f°(products)-∑νΔ H_f°(reactants) | Enthalpy changes kJ/mol; coefficients ν | Same states and standard reference conditions; formation enthalpies of elements in their standard states are zero. |
| Δ H ≈ ∑ E_broken-∑ E_formed | Average bond energies kJ/mol | Approximate gas-phase estimate; count all bonds and use the reaction’s coefficients. |
| Δ H_(route 1) = Δ H_(route 2) | Enthalpy changes for the same initial and final states | Hess’s law; reverse signs and scale enthalpies when reversing or scaling equations. |
Rates and equilibrium
| Relationship | Symbols and units | When to use it |
|---|---|---|
| r = k[A]^m[B]ⁿ; overall order = m + n | Rate commonly mol/(dm³ s); concentration mol/dm³ | Orders are determined from evidence; hold temperature and other concentrations fixed when comparing initial rates. |
| r₂/r₁ = ([A]₂/[A]₁)^m | Dimensionless ratios | Only A changes; factor 2 in concentration and factor 4 in rate implies m = 2. |
| [k] = [r]/[c]^(m + n) | For overall order s: (mol/dm³)^(1-s)s⁻¹ | State the concentration and time units; zero-, first- and second-order constants have different units. |
| K_c = [C]^c[D]^d/([A]^a[B]^b) | Equilibrium concentrations; powers from the balanced equation | For aA + bB ⇌ cC + dD; omit pure solids and pure liquids. Fixed temperature. |
| K_(c,reverse) = 1/K_c; K_(c,scaled) = K_c^s | Scaling factor s multiplies every coefficient | A constant belongs to the exact equation; concentration-based units can change when it is rescaled. |
Acids and bases
| Relationship | Symbols and units | When to use it |
|---|---|---|
| pH = - log ₁₀[H⁺] | Use the numerical concentration in mol/dm³ | School dilute-solution concentration model; base-10 log, not natural log. |
| K_w = [H⁺][OH⁻] | Concentrations mol/dm³; K_w commonly (mol/dm³)² | K_w = 1.00 × 10⁻¹⁴ at 298 K in this model; neutral [H⁺] = [OH⁻]. |
| [H⁺] = c; [OH⁻] = zc | c mol/dm³; z hydroxide ions per formula unit | Completely ionised monobasic strong acid / completely dissociated soluble hydroxide; water’s contribution must be negligible. |
| Kₐ = [H⁺][A⁻]/[HA]; K_b = [BH⁺][OH⁻]/[B] | Equilibrium concentrations mol/dm³ | Define the acid/base reaction with water; distinguish equilibrium concentration from prepared concentration. |
Further H2 physical chemistry
| Relationship | Symbols and units | When to use it |
|---|---|---|
| pV = nRT; pᵢ = xᵢpₜₒₜₐₗ | p Pa; V m³; T K; R = 8.31 J mol⁻¹K⁻¹ | Ideal gas and ideal-gas mixture; xᵢ = nᵢ/nₜₒₜₐₗ. |
| Kₚ = p_C^cp_D^d/(p_A^ap_B^b) | Equilibrium partial pressures in one consistent unit | Gas-phase species in the balanced reaction; do not insert total pressure for each gas. |
| Δ S° = ∑ν S°(products)-∑ν S°(reactants) | Molar entropy J/(mol K) | Use coefficients; standard molar entropies of elements are not zero. |
| Δ G° = Δ H°-TΔ S° | T K; energy units consistent | Convert entropy to kJ/(mol K) if enthalpy is in kJ/mol; negative standard Gibbs change favours reaction from standard-state reactants. |
| [A]ₜ/[A]₀ = (1/2)^(t/t_(1/2)) | Times in matching units | Repeated half-lives for a first-order reactant with constant half-life; integrated rate equations are not required. |
| K_w = KₐK_b; pKₐ = - log ₁₀Kₐ | Same concentration convention throughout | Kₐ and K_b refer to a conjugate pair at the same temperature. |
| [H⁺] ≈ square root of Kₐc; [OH⁻] ≈ square root of K_bc | c mol/dm³ | Weak monoprotic acid / weak monoacidic base alone in water; ionisation small relative to c and water contribution negligible. Check the approximation. |
| pH ≈ pKₐ + log ₁₀([A⁻]/[HA]) | Conjugate base and weak acid concentrations | Buffer after any neutralisation; both partners present in appreciable amounts. Near exhaustion the approximation fails. |
| Kₛₚ = [M^(a +)]^x[X^(b-)]^y | Equilibrium dissolved-ion concentrations | For solid MₓX_y in a saturated solution; ion ratio follows the dissolution equation. |
| E°_cell = E°_cathode-E°_anode | Both tabulated reduction potentials in V | Standard cell conditions; choose the reduction and oxidation half-cells correctly. |
| Δ G° = -nFE°_cell | n electron stoichiometric coefficient; F ≈ 9.65 × 10⁴ C/mol | Δ G° in J/mol for the cell equation; divide by 1000 to express in kJ/mol. |
| Q = It; nₑ = Q/F; n_product = Q/(zF) | Charge C; current A; time s; z electrons per product entity | Constant current and quantitative current efficiency; use the balanced electrode half-equation. |
A quick application: calorimetry and signs
Suppose 50.0 g of solution warms by 6.00 K when 0.0200 mol of a reactant is consumed at constant pressure. Here the molar basis is one mole of that reactant. Taking c = 4.18 J g⁻¹K⁻¹ and neglecting heat losses, qₛₒₗᵤₜᵢₒₙ = 50.0 × 4.18 × 6.00 = 1254 J. The reaction released this heat. Converting J to kJ and dividing by the amount reacted gives Δ H = -1254/(1000 × 0.0200) = -62.7 kJ/mol.
The solution’s positive heat gain corresponds to a negative reaction enthalpy change. State which body gains the heat before assigning the sign.
Keep the equation and evidence connected
Use the balanced reaction to set the molar basis and stoichiometric powers. Quantitative thermodynamic feasibility does not establish reaction speed. Integrated rate equations are not required; half-life reasoning is used where the first-order model applies.
Return to the course hub for the lesson behind a term or relationship, then practise without this reference.