Question 1 – Thermodynamics, equilibria & electrochemistry

(a) Laser gas mixture

(i) Mole fractions

• $\chi_{\mathrm{HCl}} = 0.136 / 5.296 = 0.0257$
• $\chi_{\mathrm{H_2}} = 0.500 / 5.296 = 0.0944$
• $\chi_{\mathrm{Ne}} = 4.660 / 5.296 = 0.8799$

(ii) Partial pressures at $138.0\;\text{kPa}$

• $p_{\mathrm{HCl}} = 3.54\;\text{kPa}$
• $p_{\mathrm{H_2}} = 13.0\;\text{kPa}$
• $p_{\mathrm{Ne}} = 121.4\;\text{kPa}$

Equations $p_i=\chi_i P_{\text{tot}}$

Slip-ups forgetting total moles, rounding mole fractions too early, mixing bar and kPa

(b) Combustion of hexadecane

(i) $\Delta_\mathrm f H^\circ[\mathrm{C_{16}H_{34}(l)}] = -4.55\times10^{2};\text{kJ mol}^{-1}$

(ii) $\Delta U = \Delta H -\Delta n_\mathrm{gas}RT = -1.07\times10^{4};\text{kJ mol}^{-1}$

Equations: Hess: $\Delta_\mathrm r H^\circ=\sum n\Delta_\mathrm f H^\circ(\text{prod})-\sum n\Delta_\mathrm f H^\circ(\text{reac})\\\Delta U=\Delta H-\Delta n_\mathrm{gas}RT$

Slip-ups sign of Δn, using 8.314 J mol⁻¹ K⁻¹ but forgetting to convert to kJ.

(c) Entropy change for $\mathrm{I_2(g)}$ heating $298.15\ \rightarrow\ 473.15\;\text{K}$