Calculate $\Delta U^o$ for the following reactions: a) Complete combustion of one mole octane $C_8H_{18}(l)$ at $25^oC$, where $\Delta H^o$ $=$ $-5471kJ$ b) $3NO_2(g)$ $+H_2O(l)$ $\longrightarrow$ $2HNO_3(l)$ $+$ $NO(g)$ $\Delta H^o$ $=$ $-71.53\;kJ$ (o = standard means that the thermodynamic parameters are to be calculated in stoichiometric proportion, that means that each species must have the same number of moles as given by the equation and that the reaction has to be complete)
a) $C_8H_{18}(l)$ $+$ $\frac{25}{2}O_2(g)$ $\longrightarrow$ $8CO_2(g)$ $+$ $9H_2O(l)$ $\Delta U^o$ $=$ $\Delta H^o$ $-$ $\Delta n RT$ $=$ $-5471$ $-$ $(8$ $-$ $\frac{25}{2})\cdot 8.3\cdot \color{red}10^{-3}\color{black}\cdot 298$ $\approx$ $ -5482 \color{red}k\color{black}\;J $
b) $\Delta U^o$ $=$ $\Delta H^o$ $-$ $\Delta n RT$ $=$ $-71,53-(1-3)\cdot 8.3\cdot\color{red}10^{-3}\color{black}\cdot 298$ $\approx$ $-66.58 \color{red}k\color{black}\;J $