The entropy versus temperature plot for phases α and β at 1 bar...

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 temperatures $T and 0K$ , respectively.

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

The transition temperature for $\alpha$ to $\beta$ phase change is 600K and ${C}_{p, \beta} - {C}_{p, \alpha} = 1J{mol}^{- 1}{K}^{- 1}$ . Assume $\left({C}_{p, \beta} - {C}_{p, \alpha}\right)$ is independent of temperature in the range of $200 to 700K . {C}_{p, \alpha} and {C}_{p, \beta}$ are heat capacities of $\alpha and \beta$ phases, respectively.

The value of enthalpy change,

{H}_{\beta} - {H}_{\alpha}

(in

{Jmol}^{- 1}

), at

300K

Correct answer

Step-by-step solution

According to Kirchhoff's law
${\Delta H}_{{T}_{2}} - {\Delta H}_{{T}_{1}} = n \times \left({C}_{p, \beta} - {C}_{p, \alpha}\right) ( {T}_{2} - {T}_{1} )$
${\Delta H}_{600} - {\Delta H}_{300} = 1 \times \left({C}_{p, \beta} - {C}_{p, \alpha}\right) ( 600 - 300 )$
Now, at transition temperature, $∆ G = 0$
${\Delta H}_{600} = {T \Delta S}_{600}$
$= 600 \times ( 6 - 5 )$
$600 - {\Delta H}_{300} = 1 \times 1 \times 300$
${\Delta H}_{300} = 600 - 300$
$= 300J{mol}^{- 1}$

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