H3 Chemistry Formula List

A reference for H3 Chemistry (9813): the additional spectroscopy, stereochemistry and mechanism content, followed by the H2 foundations examined with H3. The three-topic H3 roadmap keeps its own course progress; the H2 material remains part of the examined foundation.

Course hub · Definitions

Spectroscopy and molecular orbitals

NMR, isotope patterns and stereochemistry

Rate-law patterns

A quick application: absorbance

A species has ε = 150 dm³mol⁻¹cm⁻¹ at the selected wavelength. A 1.00 cm cell gives A = 0.600. Then c = A/(ε l) = 0.600/(150 × 1.00) = 4.00 × 10⁻³ mol/dm³. If the measured solution was diluted by a factor of 10.0, its original concentration was 0.0400 mol/dm³.

Do not use a calibration or absorption constant from a different wavelength. The dilution correction belongs after finding the measured solution’s concentration.

H2 foundations examined with H3

Open the H2 formula reference

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.

H3 stopping point

Use the supplied Data Booklet for characteristic IR absorptions. Quantitative LCAO and mathematical steady-state treatment are not required. The NMR energy discussion is qualitative; Fischer projections, fac/mer identification and solvent effects in the SN1/SN2 comparison are outside the specified additional scope.

Return to the H3 course hub for spectra, structures and mechanism reasoning.