2.3.6 (HL)—Equilibrium calculations

Write the balanced reaction, record initial concentrations, express changes as coefficient multiples of x, and substitute the equilibrium row into Kc. Use a small-K approximation when justified; quadratic equations are not expected here.

Equilibrium reactions do not use the limiting-reactant idea: both directions remain possible, so calculate the equilibrium composition instead.

After using an approximation such as C₀ − x ≈ C₀, validate it by checking that x/C₀ is small, commonly below 5% for the stated course method. If the check fails, the approximation is not justified; revise the setup rather than treating equilibrium as a limiting-reactant completion.

Worked equilibrium example: for $\ce{2SO2(g) + O2(g) <=> 2SO3(g)}$ , $K=3.0$ , $[\ce{SO2}]_{eq}=0.12$ and $[\ce{SO3}]_{eq}=0.18\,\mathrm{mol\,dm^{-3}}$ . From $3.0=(0.18)^2/[x(0.12)^2]$ , $x=[\ce{O2}]_{eq}=0.75\,\mathrm{mol\,dm^{-3}}$ . Forming $0.18\,\mathrm{mol\,dm^{-3}}$ of $\ce{SO3}$ consumes $0.18$ of $\ce{SO2}$ and $0.090$ of $\ce{O2}$ , so their initial concentrations were $0.30$ and $0.84\,\mathrm{mol\,dm^{-3}}$ , respectively.

Representative question

[Maximum number: 3]

The equilibrium constant, $K_{\mathrm{c}}$ , for the reaction

\mathrm{CO}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{~g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{~g})+\mathrm{CO}_{2}(\mathrm{~g})

was found to be 10.0 at $420^{\circ} \mathrm{C}$ .
1.00 mol of CO(g) and 1.00 mol of $\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ are mixed in a $1.00 \mathrm{dm}^{3}$ container at $420^{\circ} \mathrm{C}$ . Calculate the equilibrium concentration of each component in the mixture, showing your working.

$\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{~g})+\mathrm{CO}_{2}(\mathrm{~g})$ $(1.00-x)(1.00-x) \quad x \quad x$ $K_{c}=10.0=\frac{x^{2}}{(1.00-x)^{2}} / \sqrt{10.0}=\frac{x}{(1.00-x)}$ ;
x=0.760 /(1.00-x)=0.240;
$[\mathrm{CO}]=0.240\left(\mathrm{moldm}^{-3}\right)$ and $\left[\mathrm{H}_{2} \mathrm{O}\right]=0.240\left(\mathrm{moldm}^{-3}\right)$ and $\left[\mathrm{H}_{2}\right]=0.760\left(\mathrm{moldm}^{-3}\right)$
and $\left[\mathrm{CO}_{2}\right]=0.760\left(\mathrm{~mol} \mathrm{dm}^{-3}\right)$ ;

Retrieve the route: define dynamic equilibrium, write K, interpret its magnitude, predict Le Châtelier shifts, compare Q with K, solve a RICE table, and connect K with ΔG.

Check closed-system and equal-rate language, exponents and direction, whether a change affects K, current versus equilibrium concentrations, stoichiometric x changes, and kelvin/unit consistency in ΔG calculations.

2.3.6 (HL)—Equilibrium calculations

RICE-Table Equilibrium Calculations

Solving for Equilibrium Composition

Assessment in practice

Extent of Chemical Change Summary

Question 1