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Mole Calculations

Every mole calculation follows the same path: convert what you know into moles, use the mole ratio from the balanced equation, then convert back into what you want. Gases: $n=\frac{V}{24}$ ( $\mathrm{dm^3}$ at room temperature and pressure). Solutions: $n=c\times V$ ( $V$ in $\mathrm{dm^3}$ ). Percentage yield $=\frac{\text{actual}}{\text{theoretical}}\times100$ .

Relative Masses and the Mole

Relative formula mass $M_r$ is the sum of the relative atomic masses in a formula. A mole is the amount of substance containing $6.02\times10^{23}$ particles (the Avogadro constant); one mole has a mass in grams equal to $M_r$ . So $n=\frac{m}{M_r}$ . The empirical formula is the simplest whole-number ratio of atoms, found by dividing each mass by $A_r$ and simplifying.

Reacting Quantities and Titrations

Every calculation runs through moles: mass ( $n=\frac{m}{M}$ ), solution ( $n=cV$ , $V$ in dm³), gas ( $n=\frac{V}{24.0}$ dm³ at r.t.p.). Use the balanced equation's mole ratio to link substances. The limiting reagent is used up first and sets the yield. Titrations find unknown concentrations. In a back titration, an excess of reagent is added and the leftover is titrated; subtracting gives the amount that reacted. Percentage yield $=\frac{\text{actual}}{\text{theoretical}}\times100$ .

The Ideal Gas Equation

One mole contains $N_A=6.02\times10^{23}$ particles. An ideal gas obeys $pV=nRT$ , where $n$ is the number of moles, $R=8.31$ J mol⁻¹ K⁻¹ and $T$ is in kelvin. Equivalently $pV=NkT$ , with $N$ molecules and the Boltzmann constant $k=\dfrac R{N_A}=1.38\times10^{-23}$ J K⁻¹. Boyle's law, Charles's law and the pressure law are special cases.

The Mole, Formulae and Equations

Relative masses are measured against one-twelfth of a carbon-12 atom. One mole contains $6.02\times10^{23}$ particles (the Avogadro constant, $L$ ), and has a mass in grams equal to $M_r$ : $n=\frac{m}{M}$ . Empirical formulae come from composition by mass (or combustion data); the molecular formula is a whole-number multiple matching $M_r$ . Equations balance atoms and charge; ionic equations omit spectator ions. Water of crystallisation is found from mass lost on heating. Atom economy $=\frac{M_r\text{ of desired product}}{\sum M_r\text{ of all products}}\times100$ .

Ionisation Energies

The first ionisation energy is the energy needed to remove one mole of electrons from one mole of gaseous atoms: $\mathrm{X(g)\rightarrow X^+(g)+e^-}$ . It depends on nuclear charge, distance of the outer electron from the nucleus and shielding. Across a period it generally increases (more protons, similar shielding); down a group it decreases (further away, more shielding). Dips occur at Group 13 (new p subshell, higher energy) and Group 16 (spin-pair repulsion). Successive ionisation energies show big jumps when an inner shell is broken into.

Kp, Ksp and Partition

For gas equilibria, partial pressure $p_A=x_A\times P_\text{total}$ , where mole fraction $x_A=n_A/n_\text{total}$ . $K_p$ uses partial pressures: for $\mathrm{N_2O_4\rightleftharpoons2NO_2}$ , $K_p=\frac{p_{\mathrm{NO_2}}^2}{p_{\mathrm{N_2O_4}}}$ . Only temperature changes $K_p$ . The solubility product $K_{sp}$ for a sparingly soluble salt, e.g. $K_{sp}=[\mathrm{Ag^+}][\mathrm{Cl^-}]$ ; a precipitate forms if the ionic product exceeds $K_{sp}$ . Adding a common ion lowers solubility. The partition coefficient $K_{pc}=\frac{[X]_\text{solvent 1}}{[X]_\text{solvent 2}}$ describes how a solute distributes between two immiscible solvents.

Electrolysis Calculations

Charge $Q=It$ (coulombs = amps × seconds). The Faraday constant $F=96\,500$ C mol⁻¹ is the charge on 1 mol of electrons, and $F=Le$ (Avogadro constant × electron charge). Moles of electrons $=Q/F$ ; then use the half-equation: $\mathrm{Cu^{2+}+2e^-\rightarrow Cu}$ needs 2 mol e⁻ per mol Cu. Products in aqueous electrolysis are predicted from E⦵: at the cathode, the ion with the more positive E⦵ is reduced (Cu²⁺, Ag⁺ before H₂O); at the anode, concentrated halide gives halogen, otherwise O₂ forms. The Avogadro constant can be found by electrolysis: $L=F/e$ .

Entropy and Gibbs Free Energy

Entropy ( $S$ ) measures the number of ways particles and their energy can be arranged; units J K⁻¹ mol⁻¹. $S$ increases from solid → liquid → gas, with more moles of gas, with dissolving and with temperature. $\Delta S=\sum S(\text{products})-\sum S(\text{reactants})$ . Gibbs free energy: $\Delta G=\Delta H-T\Delta S$ (convert $\Delta S$ to kJ). A reaction is feasible when $\Delta G\le0$ . If $\Delta H$ and $\Delta S$ have the same sign, feasibility depends on temperature; the switch occurs at $T=\Delta H/\Delta S$ . A feasible reaction may still be slow (high activation energy): kinetic vs thermodynamic stability.

Reversible Reactions and Equilibrium

A reversible reaction can go both ways ( $\rightleftharpoons$ ). In a closed system it reaches dynamic equilibrium: forward and backward rates are equal, so concentrations stay constant. Changing conditions shifts the equilibrium to oppose the change: higher pressure favours fewer gas moles; higher temperature favours the endothermic direction. The Haber process ( $\mathrm{N_2+3H_2\rightleftharpoons2NH_3}$ ) uses about $450\,^\circ\mathrm{C}$ , $200$ atm and an iron catalyst as a compromise between yield and rate.

Syllabus topics

Topic	Board	Paper	Lesson
Mole calculations	Cambridge 5070	Multiple Choice	Available
Relative masses and the mole	Cambridge 5070	Multiple Choice	Available
Mole calculations	Cambridge 5070	Theory	Available
Relative masses and the mole	Cambridge 5070	Theory	Available
Mole calculations	Cambridge 0620	Extended	Available
Relative masses and the mole	Cambridge 0620	Extended	Available
Mole calculations	Cambridge 0620	Core	Available
Relative masses and the mole	Cambridge 0620	Core	Available
Mole calculations	Edexcel 4CH1	Paper 1 (core content)	Available
Relative masses and the mole	Edexcel 4CH1	Paper 1 (core content)	Available
Mole calculations	Edexcel 4CH1	Paper 2 (all content)	Available
Relative masses and the mole	Edexcel 4CH1	Paper 2 (all content)	Available
The mole and equations	Cambridge 9701	Multiple Choice	Available
The mole and equations	Cambridge 9701	AS Level Structured Questions	Available
The mole and equations	Edexcel YCH11	Unit 1: Structure, Bonding and Introduction to Organic Chemistry	Available
The mole and equations	AQA 7405	Paper 1: Physical and inorganic chemistry	Available

Questions

ID	Question	Topic	Marks	Difficulty
SA-AC-MO-001	Calculate the number of molecules in 0.25 mol of water. Enter the number.…	A Level Chemistry: the mole, formulae and equations Relative masses, the mole and Avogadro constant	2	L1 Foundation
SA-AC-MO-012	The Avogadro constant is…	A Level Chemistry: the mole, formulae and equations Relative masses, the mole and Avogadro constant	1	L1 Foundation
SA-OC-MO-007	One mole of any substance contains…	Chemistry: relative masses and the mole Moles, mass and molar mass	1	L1 Foundation
SA-OC-MO-012	The number of moles in a sample is found by…	Chemistry: relative masses and the mole Moles, mass and molar mass	1	L1 Foundation
SA-AC-MO-006	Relative atomic mass is defined relative to…	A Level Chemistry: the mole, formulae and equations Relative masses, the mole and Avogadro constant	1	L1 Foundation
SA-9702-IG1-003	A gas at constant temperature is compressed from 3.0 litres at 100 kPa to 1.2 litres. Calculate the new pressure.…	Physics: the mole and the ideal gas equation pV = nRT = NkT and the gas laws	1	L1 Foundation
SA-9702-IG1-004	Calculate the number of molecules in 2.5 mol of gas, in units of 10^24. (N_A=6.0210^23 mol⁻¹)…	Physics: the mole and the ideal gas equation The mole, Avogadro constant and number of particles	1	L1 Foundation
SA-9702-IG1-009	For a fixed mass of ideal gas at constant pressure, volume is proportional to…	Physics: the mole and the ideal gas equation pV = nRT = NkT and the gas laws	1	L1 Foundation
SA-9702-IG1-002	A sealed rigid cylinder holds gas at 200 kPa and 27 °C. It's heated to 127 °C. Calculate the new pressure.…	Physics: the mole and the ideal gas equation pV = nRT = NkT and the gas laws	1	L1 Foundation
SA-9702-IG1-012	One mole of any substance contains…	Physics: the mole and the ideal gas equation The mole, Avogadro constant and number of particles	1	L1 Foundation
SA-9702-IG1-006	Real gases behave most like an ideal gas at…	Physics: the mole and the ideal gas equation pV = nRT = NkT and the gas laws	1	L1 Foundation
SA-OC-MO-003	How many moles are in 36 g of water, H_2O? (M_r=18)…	Chemistry: relative masses and the mole Moles, mass and molar mass	2	L1 Foundation
SA-OC-MO-001	Calculate M_r of H_2SO_4. (A_r: H 1, S 32, O 16)…	Chemistry: relative masses and the mole Relative formula mass and percentage composition	1	L1 Foundation
SA-OC-MO-002	Calculate M_r of Ca(OH)_2. (A_r: Ca 40, O 16, H 1)…	Chemistry: relative masses and the mole Relative formula mass and percentage composition	1	L1 Foundation
SA-AC-MC-012	How many moles of solute are in 200\ cm^3 of 0.150\ mol dm^-3 solution?…	A Level Chemistry: reacting masses, gases, solutions and titrations Solutions and titration calculations	1	L1 Foundation