When $1.00 \;g$ ethanol $C_2H_6O(l)$ is burnt in a bomb calorimeter at $25^oC$, $29.62 \;kJ$ heat are produced. The products of this combustion are $H_2O(l)$ and $CO_2(g)$ Calculate $\Delta U^o$ and $\Delta H^o $ for the combustion of ethanol. (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)
$\Delta U$ is the heat received at constant volume, therefore: For $1.00 \; g$ ethanol: $\Delta U$ $ =$ $\color{red}-\color{black}29620 \;J$
$\color{red}1\color{black}C_2H_6O(l)$ $+$ $\color{blue}3\color{black}O_2(g)$ $\longrightarrow$ $\color{blue}2\color{black}CO_2(g)$ $+$ $3H_2O(l)$ For one mole (stoichiometry!)= $46 \;g$ d'éthanol: $\Delta U^o$ $= $ $ -29620\cdot 46\approx 1362000 \;J$
$\Delta H^o$ $=$ $\Delta U^o$ $+$ $\Delta n RT$ $=$ $-1362000$ $+$ $\color{blue}(2-3)\color{black}\cdot 8.3 \cdot 298$ $\approx$ $-1364500 \; J$ (Liquids are neglected when variations of volume are calculated!)