Calculations

n = m / Mr

n = m / Mr underpins nearly every calculation — get this automatic and the rest follow.

moles = conc x volume

Convert cm^3 to dm^3, then start from the solution whose concentration and volume are both known.

mass → moles → ratio → mass

Mass doesn't go straight to mass — you cross the 'moles bridge' using the balanced equation.

actual / theoretical x 100

Actual over theoretical. An apparent yield above 100% means the measured 'product' is not a pure, dry product or the calculation/measurement is wrong.

Mr(product) / Mr(reactants) x 100

It's about the balanced equation, not the experiment — desired product over the reactant mass.

Mr = sum of Ar values

One missed subscript changes every later answer, so expand the formula before adding.

weighted isotope mean

The abundances are weights: multiply first, add, then divide by the total abundance.

reactant mass = product mass

In a closed system the totals on both sides must match; identify the missing term before subtracting.

element mass / Mr x 100

Count every atom of the chosen element, then compare its total Ar contribution with the whole Mr.

c = mass / volume

This concentration is mass per solution volume, so no moles or Mr are needed.

c = moles / volume

Convert mass to moles first, then divide by the solution volume in dm3.

V = n x 24 at RTP

At room temperature and pressure, each mole occupies 24 dm3 or 24 000 cm3.

smallest n/coefficient limits

The smaller mass is not automatically limiting; compare available moles with the equation ratio.

rate = amount / time

Rate is a change divided by the time interval, with both quantities carrying units.

rate = tangent gradient

An instantaneous rate is the gradient of a tangent, not the gradient between arbitrary curve points.

Rf = spot / solvent

Both distances start at the pencil baseline, and the solvent front always goes underneath the fraction.

broken - formed

Breaking takes energy; making releases it. Keep that order in the subtraction.

volumes follow coefficients

At the same temperature and pressure, gas volumes follow the balanced equation's mole ratio.

Kc = [products] / [reactants]

Products over reactants, each raised to its balancing number — and the units come from the powers.

pH = -log₁₀[H+]

For a strong monoprotic acid [H+] equals the acid concentration — then it's just -log.

q = m c dT ; dH = -q / n

q = m c dT gives the energy; divide by the moles reacted and flip the sign for exothermic.

pV = nRT

pV = nRT only works in SI units — pascals, cubic metres and kelvin — so convert first.

mass → moles → ratio

Percentages become masses out of 100 g; masses become moles; only then can you simplify the ratio.

cV → ratio → c

The aliquot volumes belong to different chemicals; attach each volume to its concentration before using the ratio.

Kp from partial pressures

Only gaseous species appear, and every partial pressure is raised to its equation coefficient.

[H+] = sqrt(Ka[HA])

A weak acid is only partly dissociated, so use Ka before taking the negative logarithm.

[H+] = Ka[acid]/[salt]

Use the weak-acid equilibrium with the acid and conjugate-base concentrations after any neutralisation.

[OH-] = Kw/[H+]

Convert pH to [H+] first, then use Kw to find [OH-].

Hess cycle to lattice enthalpy

Give every cycle arrow its sign; electron affinity is often already negative.

dG = dH - TdS

Entropy is commonly in J/K/mol while enthalpy is in kJ/mol; align the units before multiplying by temperature.

rate = k[A]^m[B]ⁿ

Orders come from rate data, not balancing coefficients, and k units follow from the final rate equation.

two-temperature Arrhenius

Temperatures must be kelvin and the reciprocal-temperature subtraction order must match the logarithm ratio.

Ecell = Epositive - Enegative

Keep both values as reduction potentials: more positive minus more negative.

broken - formed

Count bonds in the balanced gaseous equation, then subtract energy released making bonds from energy absorbed breaking them.

hydrate mole ratio

The mass lost is water; the mass left is anhydrous salt. Convert both to moles before finding x.