For a reaction,X_{2(g)} + Y_{2(g)} rightlefth | vedclass

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(A) Using the Gibbs-Helmholtz equation at $200 \ K$: $\Delta G = \Delta H - T \Delta S$. Substituting the values: $20 \ kJ \ mol^{-1} = \Delta H_{200}

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$20 \ kJ \ mol^{-1}$

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(A) Using the Gibbs-Helmholtz equation at $200 \ K$: $\Delta G = \Delta H - T \Delta S$. Substituting the values: $20 \ kJ \ mol^{-1} = \Delta H_{200} - (200 \ K) 	imes (-20 \ J \ K^{-1} \ mol^{-1} / 1000 \ J \ kJ^{-1})$. $20 = \Delta H_{200} + 4$,so $\Delta H_{200} = 16 \ kJ \ mol^{-1}$. Now,using Kirchhoff's law: $\Delta H_{T_2} = \Delta H_{T_1} + \int_{T_1}^{T_2} \Delta C_P \ dT$. $\Delta H_{400} = \Delta H_{200} + \Delta C_P 	imes (T_2 - T_1)$. $\Delta H_{400} = 16 \ kJ \ mol^{-1} + (20 \ J \ K^{-1} \ mol^{-1} / 1000 \ J \ kJ^{-1}) 	imes (400 \ K - 200 \ K)$. $\Delta H_{400} = 16 + (0.02 	imes 200) = 16 + 4 = 20 \ kJ \ mol^{-1}$.

Column $I$	Column $II$
$A$. $CO_{2(s)} \rightarrow CO_{2(g)}$	$p$. phase transition
$B$. $CaCO_{3(s)} \rightarrow CaO_{(s)} + CO_{2(g)}$	$q$. allotropic change
$C$. $2H_{(g)} \rightarrow H_{2(g)}$	$r$. $\Delta H$ is positive
$D$. $P_{(\text{white, solid})} \rightarrow P_{(\text{red, solid})}$	$s$. $\Delta S$ is positive
	$t$. $\Delta S$ is negative

For a reaction,$X_{2(g)} + Y_{2(g)} \rightleftharpoons 2XY_{(g)}$. If $\Delta G_r^o = 20 \ kJ \ mol^{-1}$ and $\Delta S_r^o = -20 \ J \ K^{-1} \ mol^{-1}$ at $200 \ K$. Calculate $\Delta H_r^o$ at $400 \ K$ (Given $\Delta_r C_P = 20 \ J \ K^{-1} \ mol^{-1}$).

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