When 2,00 moles of $SO_2(g)$ react completely with 1,00 mole $O_2(g)$ to produce 2 moles $SO_3(g)$ at $25\;^oC$ and a constant pressure of $1,00\;atm$, $198\;kJ$ of heat are produced. Determine $\Delta H$ and $\Delta U$ of this transformation.
$\Delta H$ is the quantity of heat received at constant pressure: $\Delta H$ $= $ $\color{red}-\color{black}198000\;J$
$\color{blue}2\color{black}SO_2(g)$ $+$ $\color{blue}1\color{black}O_2(g)$ $\longrightarrow$ $\color{green}2\color{black}SO_3(g)$ We have: $\Delta H$ $=$ $\Delta U$ $+$ $\Delta n$ $RT$ ($R$ $=$ $ 8.3 \frac{J}{mol\cdot K}$ and $T$: Kelvin temperature) with : $\Delta n$ $=$ $\color{green}2\color{black}$ $-($ $\color{blue}2+1\color{black})$ $=$ $-1$
$\Delta U$ $=$ $\Delta H$ $-$ $\Delta n$ $RT$ $=$ $-198000$ $-$ $(-1\cdot 8.3 \cdot 298)$ $=$ $-198000$ $+$ $2480$ $\approx$ $-196500\; J$