When ' $\mathrm{X}$ ' $\mathrm{g}$ of graphite is completely burnt in a bomb calorimeter in excess of…
When ' $\mathrm{X}$ ' $\mathrm{g}$ of graphite is completely burnt in a bomb calorimeter in excess of $\mathrm{O}_2$ at $298 \mathrm{~K}$ and $1 \mathrm{~atm}$ pressure as given in the equation
$\mathrm{C}$ (graphite) $+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})$
The temperature of calorimeter raised from $298 \mathrm{~K}$ to $302 \mathrm{~K}$. If the heat capacity of the calorimeter and molar enthalpy change for the reaction at $1 \mathrm{~atm}$ and $298 \mathrm{~K}$ are $20.7 \mathrm{~kJ} \mathrm{~K}^{-1}$ and $-248.4 \mathrm{~kJ} \mathrm{~mol}^{-1}$, ' $\mathrm{X}^{\prime}$ in $\mathrm{g}$ is
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Solution
Heat released in the reaction with ' $\mathrm{X}$ ' g carbon $\mathrm{Q}=\mathrm{C}_{\mathrm{P}} \Delta \mathrm{T}=(20.7)(4)=82.8 \mathrm{~kJ}$
1 mole or $12 \mathrm{~g}$ of carbon (graphite) gives $248.4 \mathrm{~kJ}$ heat ' $\mathrm{X}$ ' g carbon gives $82.8 \mathrm{~kJ}$ heat
$\Rightarrow X=\frac{12 \times 82.8}{248.4}=4 \mathrm{~g}$