Observe the following reaction $\mathrm{ABO}_3(\mathrm{~s}) \xrightarrow{1000 \mathrm{~K}}…

Observe the following reaction $\mathrm{ABO}_3(\mathrm{~s}) \xrightarrow{1000 \mathrm{~K}} \mathrm{AO}(\mathrm{~s})+\mathrm{BO}_2(\mathrm{~g})$ $\Delta_{\mathrm{r}} \mathrm{H}$ for this reaction is $x \mathrm{~kJ} \mathrm{~mol}^{-1}$. What is its $\Delta_{\mathrm{r}} \mathrm{U}$ (in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) at the same temperature? $\left(\mathrm{R}=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right)$
  1. $x-8300$
  2. $x+8.3$
  3. $x+8300$
  4. $x-8.3$

Solution

$\Delta_{\mathrm{r}} \mathrm{H}=\Delta_{\mathrm{r}} \mathrm{U}+\Delta_{\mathrm{g}} R T$ $\begin{aligned} & \Delta_{\mathrm{r}} \mathrm{H}=\mathrm{x} \mathrm{kJ} \mathrm{mol}^{-1} \\ & \mathrm{R}=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} \\ & \Delta \mathrm{n}_{\mathrm{g}}=1 \\ & \mathrm{~T}=10^3 \mathrm{~K} \\ & \mathrm{x} \mathrm{kJ} \mathrm{mol}{ }^{-1}=\Delta_{\mathrm{r}} \mathrm{U}+\frac{1 \times 8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} \times 10^3 \mathrm{~K}}{10^3} \\ & \mathrm{x}=\Delta_{\mathrm{r}} \mathrm{U}+8.3 \qquad {\left[1 \mathrm{~kJ}=10^3 \mathrm{~J}\right]} \\ & \Delta_{\mathrm{r}} \mathrm{U}=\mathrm{x}-8.3 \end{aligned}$

Asked in: AP EAMCET 2024 (22 May Shift 2)

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