The combustion of carbon monoxide is carried out in a closed, rigid and insulated vessel. $1 \text{ mol}$ of $CO$, $0.5 \text{ mol}$ of $O_2$ and $2 \text{ mol}$ of $N_2$ 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 $( \Delta u ^\circ _R)$ for the combustion of carbon monoxide at $298\: K = -282 \text{ kJ mol}^{-1}$. At constant pressure, the molar heat capacities of $N_2$ and $CO_2$ are $33.314 \text{ J mol}^{-1} \: K^{-1}$ and $58.314 \text{ J mol}^{-1} \: K^{-1}$, respectively. Assume the heat capacities to be independent of temperature, and the gases are ideal. Take $R=8.314 \text{ J mol}^{-1} \: K^{-1}$.
The final pressure in the vessel at the completion of the reaction is ___________ bar (round off to $1$ decimal place).