The entropy versus temperature plot for phases α and β at 1 bar pressure is given. S T and S 0 are entropies of the phases at temperatures T and 0 K , respectively. The transition temperature for α to β phase change is 600 K and C p , β - C p , α =1 J mol -1 K -1 . Assume ( C p , β - C p , α ) is independent of temperature in the range of 200 to 700 K . C p , α and C p , β are heat capacities of α and β phases, respectively. The value of enthalpy change, H β - H α ( . in . J mol -1 ) , at 300 K is \ \ \ \ .

Chemistry · Thermodynamics & Thermochemistry

JEE Advanced 2023 — Paper 2 — Question 44

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

The transition temperature for $\alpha$ to $\beta$ phase change is 600 K and $\mathrm{C}_{\mathrm{p}, \beta}-\mathrm{C}_{\mathrm{p}, \alpha}=1 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ . Assume

$\left(\mathrm{C}_{\mathrm{p}, \beta}-\mathrm{C}_{\mathrm{p}, \alpha}\right)$ is independent of temperature in the range of 200 to $700 \mathrm{~K} . \mathrm{C}_{\mathrm{p}, \alpha}$ and $\mathrm{C}_{\mathrm{p}, \beta}$ are heat

capacities of $\alpha$ and $\beta$ phases, respectively.

The value of enthalpy change, $\mathrm{H}_{\beta}-\mathrm{H}_{\alpha}\left(\right.$ in $\left.\mathrm{J} \mathrm{mol}^{-1}\right)$ , at 300 K is $\_\_\_\_$ .

Answer: 300

Numerical answer — enter this value.

Step-by-step solution

Transition : $\alpha \rightleftharpoons \beta ; \Delta \mathrm{G}=0$ So, $\Delta \mathrm{H}=\mathrm{T} \Delta \mathrm{S}$ $\Delta \mathrm{H}_{600}=600 \times 1 \because \Delta \mathrm{~S}=1$ $=600 \mathrm{~J} \mathrm{~mol}^{-1}$ From Krichoff's law $\Delta \mathrm{C}_{\mathrm{p}}=\frac{\Delta \mathrm{H}_{600}-\Delta \mathrm{H}_{300}}{600-300}$ $1=\frac{600-\Delta \mathrm{H}_{300}}{300}$ $\Delta \mathrm{H}_{300}=300 \mathrm{~J} \mathrm{~mol}^{-1}$

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Exam: JEE Advanced 2023
Paper: Paper 2
Subject: Chemistry
Chapter: Thermodynamics & Thermochemistry
Topic: Entropy Change in Different Processes

The entropy versus temperature plot for phases alpha and beta at 1 bar pressure is given. S T and S 0 are entropies of the phases at…

Answer: 300

Step-by-step solution

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