Question

The combustion of carbon monoxide is carried out in a closed, rigid and insulated vessel. 1 mol of CO, 0.5 mol of O₂ and 2 mol of N₂ 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 (\(\Delta u^\circ_R\)) for the combustion of carbon monoxide at 298 K is -282 kJ mol\(^{-1}\). At constant pressure, the molar heat capacities of N₂ and CO₂ are 33.314 J mol\(^{-1}\) K\(^{-1}\) and 58.314 J mol\(^{-1}\) K\(^{-1}\), respectively. Assume the heat capacities are independent of temperature, and the gases are ideal. Take R = 8.314 J mol\(^{-1}\) K\(^{-1}\). The final pressure in the vessel at the completion of the reaction is \(\underline{\hspace{1cm}}\) bar (round off to 1 decimal place).

Hint:

Use the ideal gas law and the reaction's energy change to find final pressure in a closed system.

Answer 1

Correct Answer: 8.9

At constant volume, the total change in internal energy \(\Delta U\) is the sum of the change in internal energy of the reactants and products: \[ \Delta U = \Delta u_R^\circ \times \text{mol of reactant}. \] Next, calculate change in internal energy per amount:
Final pressure can be found using the ideal gas law, where we can calculate the total number of moles and apply energy change for entropic effects. Final answer: 8.9 to 9.1 bar.