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JEE Advance - Chemistry (2023 - Paper 2 Online - No. 15)

The entropy versus temperature plot for phases $\alpha$ and $\beta$ at 1 bar pressure is given. $S_{\mathrm{T}}$ and $S_0$ are entropies of the phases at temperatures $\mathrm{T}$ and $0 \mathrm{~K}$, respectively.


The transition temperature for $\alpha$ to $\beta$ phase change is $600 \mathrm{~K}$ and $C_{\mathrm{p}, \beta}-C_{\mathrm{p}, \alpha}=1 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$. Assume $\left(C_{\mathrm{p}, \beta}-C_{\mathrm{p}, \alpha}\right)$ is independent of temperature in the range of 200 to $700 \mathrm{~K} . C_{\mathrm{p}, \alpha}$ and $C_{\mathrm{p}, \beta}$ are heat capacities of $\alpha$ and $\beta$ phases, respectively.
The entropy versus temperature plot for phases $\alpha$ and $\beta$ at 1 bar pressure is given. $S_{\mathrm{T}}$ and $S_0$ are entropies of the phases at temperatures $\mathrm{T}$ and $0 \mathrm{~K}$, respectively.


The transition temperature for $\alpha$ to $\beta$ phase change is $600 \mathrm{~K}$ and $C_{\mathrm{p}, \beta}-C_{\mathrm{p}, \alpha}=1 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$. Assume $\left(C_{\mathrm{p}, \beta}-C_{\mathrm{p}, \alpha}\right)$ is independent of temperature in the range of 200 to $700 \mathrm{~K} . C_{\mathrm{p}, \alpha}$ and $C_{\mathrm{p}, \beta}$ are heat capacities of $\alpha$ and $\beta$ phases, respectively.
The entropy versus temperature plot for phases $\alpha$ and $\beta$ at 1 bar pressure is given. $S_{\mathrm{T}}$ and $S_0$ are entropies of the phases at temperatures $\mathrm{T}$ and $0 \mathrm{~K}$, respectively.


The transition temperature for $\alpha$ to $\beta$ phase change is $600 \mathrm{~K}$ and $C_{\mathrm{p}, \beta}-C_{\mathrm{p}, \alpha}=1 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$. Assume $\left(C_{\mathrm{p}, \beta}-C_{\mathrm{p}, \alpha}\right)$ is independent of temperature in the range of 200 to $700 \mathrm{~K} . C_{\mathrm{p}, \alpha}$ and $C_{\mathrm{p}, \beta}$ are heat capacities of $\alpha$ and $\beta$ phases, respectively.
$$ \text { The value of enthalpy change, } \mathrm{H}_\beta-\mathrm{H}_\alpha \text { (in } \mathrm{J} \mathrm{mol}^{-1} \text { ), at } 300 \mathrm{~K} \text { is } $$ ________.
Answer
300

Explanation

As the phase transition temperature is $600 \mathrm{~K}$

So at $600 \mathrm{~K} \quad \Delta \mathrm{G}_{\mathrm{rxn}}^{\circ}=0$ So $\Delta \mathrm{H}^{\circ}{ }_{\text {reaction (600) }}=\mathrm{T} \Delta \mathrm{S}^{\circ}{ }_{\text {reaction (600) }}$

$\Delta \mathrm{H}^{\circ}{ }_{(600)}=600 \times 1=600 \mathrm{Joule} / \mathrm{mole}$

So $\Delta \mathrm{H}_{600}-\Delta \mathrm{H}_{300}=\Delta \mathrm{C}_{\mathrm{P}}\left(\mathrm{T}_2-\mathrm{T}_1\right)$

$\Delta \mathrm{H}_{600}-\Delta \mathrm{H}_{300}=1 \times 300$

$\Delta \mathrm{H}_{300}=\Delta \mathrm{H}_{600}-300=600-300=300$ Joule $/$ mole.

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