1.0 mol of pure dinitrogen gas at SATP conditions was put into a vessel of volume  $24.8m^3$ maintained at the temperature of 596.3K.The Pressure of the gas in the vessel is  $2\times {10}^{-y}$. What is the value  y? 

Volume of 1.0 mol of a gas at SATP  $\left(V_1\right)=24.8\times {10}^{-3}{m}^3$
Initial condition (SATP)     Final condition
$\begin{array}{l}{V}_1=24.8\times {10}^{-3}{m}^3\\ P_1=1bar\\ T_1=298.15K\end{array}$$\begin{array}{l}{V}_2=24.8m^3\\ P_2=?\\ T_2=596.3K\end{array}$               
According to the gas equation ,
$\begin{array}{l}\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}\\ P_2=\frac{P_1{V}_1\times T_2}{T_1\times V_2}=\frac{1.0\times 24.8\times {10}^{-3}\times 596.3}{298.15\times 24.8}=2\times {10}^{-3}bar\\ \therefore P_2=2\times {10}^{-3}bar\end{array}$