GATE 2021 CH – Question 48
The combustion of carbon monoxide is carried out in a closed, rigid and insulated vessel. 1 mol of CO, 0.5 mol of $\mathrm O_2$ and 2 mol of $\mathrm N_2$ are taken initially at 1 bar and 298 K, and the combustion is carried out to completion. The standard molar internal energy change of reaction for the combustion of carbon monoxide at 298 K is −282 kJ/mol. At constant pressure, the molar heat capacities of $\mathrm N_2$ and $\mathrm{CO_2}$ are 33.314 and 58.314 J/(mol K), respectively. Assume the heat capacities to be independent of temperature, and the gases are ideal. Take R = 8.314 J/(mol K). The final pressure in the vessel at the completion of the reaction is _____ bar (round off to 1 decimal place).
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Correct answer: 8.96 to 9.04
Explanation
**Energy balance:** the rigid insulated vessel has no boundary work or heat loss, so its internal energy is conserved. Complete combustion leaves 1 mol of CO₂ and 2 mol of N₂. For ideal gases, $C_v=C_p-R$: these are 50 and 25 J/(mol K), respectively.
The released reaction energy raises the product temperature:
$$282000=[1(50)+2(25)](T_f-298),\qquad T_f=3118\ \mathrm K.$$
**Pressure:** volume is constant but the total moles decrease from 3.5 to 3. Therefore
$$P_f=P_i\frac{n_fT_f}{n_iT_i}=1\frac{3(3118)}{3.5(298)}=8.96836\ \mathrm{bar}.$$
Rounded as requested, **9.0 bar**.