When $2.0 \mathrm{~g}$ sucrose is oxidised forming $\mathrm{CO}_2(\mathrm{~g})$ and $\mathrm{H}_2…

When $2.0 \mathrm{~g}$ sucrose is oxidised forming $\mathrm{CO}_2(\mathrm{~g})$ and $\mathrm{H}_2 \mathrm{O}_{(\ell)}$ the internal energy changes by $24 \mathrm{~kJ}$. Calculate the value of $\Delta \mathrm{H}$ at $298 \mathrm{~K}$ in $\mathrm{kJ} / \mathrm{mol}$. (Molar mass of sucrose $=342 \mathrm{~g} \mathrm{~mol}^{-1}$ )
  1. $-140.3 \mathrm{~J}$
  2. $2014 \mathrm{~J}$
  3. $-5612 \mathrm{~J}$
  4. $8208 \mathrm{~J}$

Solution

$\begin{aligned} & \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(\mathrm{~s})+12 \mathrm{O}_2(\mathrm{~g}) \rightarrow 12 \mathrm{CO}_2(\mathrm{~g})+11 \mathrm{H}_2 \mathrm{O}(\mathrm{c}) \\ & \Delta \mathrm{ng}=12-12=0 \\ & \Delta \mathrm{H}=\Delta \mathrm{E}+\Delta \mathrm{ngRT} \\ & =24 \mathrm{~kJ} \\ & \Delta \mathrm{H} \text { for } 2 \text { g sucrose }=-\frac{24}{342} \times 2 \\ & =0.1403 \mathrm{~kJ} \\ & =-140.3 \mathrm{~J}\end{aligned}$

Asked in: MHT CET 2022 (06 Aug Shift 2)

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