Question

For the reaction, $2 CO + O ^{2} \rightarrow 2 CO _{2} ; \Delta H =-560\, kJ$. Two moles of $CO$ and one mole of $O_{2}$ are taken in a container of volume $1 \,L$. They completely form two moles of $CO _{2}$, the gases deviate appreciably from ideal behaviour. If the pressure in the vessel changes from $70$ to $40 \,atm$, find the magnitude (absolute value) of $\Delta U$ at $500\, K$. ($1 \,L$ atm $=0.1 \,kJ$ )

Answer 1

From the definition of enthalpy, we have
$\Delta H =\Delta U +\Delta( pV )$
$\Delta H =\Delta U + V \Delta p + p \Delta V ($ at constant volume $\Delta V =0)$
$\Delta U =\Delta H - V \Delta p$
$=-560+1 \times 30 \times 0.1( Dp =40-70=30 atm )$
$=-557 \,kJ$