Assuming ideal behaviour,
Question:

Assuming ideal behaviour, the magnitude of $\log \mathrm{K}$ for the following reaction at $25^{\circ} \mathrm{C}$ is $\mathrm{x} \times 10^{-1}$. The value of $x$ is ________________.(Integer answer)

$3 \mathrm{HC} \equiv \mathrm{CH}_{(\mathrm{g})} \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{6(\ell)}$

$\left[\right.$ Given $\left.: \Delta_{f} \mathrm{G}^{\circ}(\mathrm{HC} \equiv \mathrm{CH})=-2.04 \times 10^{5}\right] \mathrm{mol}^{-1} ; \Delta_{\mathrm{f}} \mathrm{G}^{\circ}\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)=-1.24 \times 10^{5} \mathrm{~J} \mathrm{~mol}^{-1}$$\left.\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]$

Solution:

(855)

$3 \mathrm{HC} \equiv \mathrm{CH}(\mathrm{g}) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{6}(\ell)$

$\Delta \mathrm{G}_{\mathrm{r}}^{\circ}=\Delta \mathrm{G}_{\mathrm{f}}^{\circ}\left[\mathrm{C}_{6} \mathrm{H}_{8}(\ell)\right]-3 \times \Delta \mathrm{G}_{\mathrm{f}}^{\circ}[\mathrm{HC} \equiv \mathrm{CH}]$

$=\left[-1.24 \times 10^{5}-3 \times\left(-2.04 \times 10^{5}\right)\right]$

$=4.88 \times 10^{5} \mathrm{~J} / \mathrm{mol}$

$\Delta \mathrm{G}_{\mathrm{r}}^{\circ}=-\mathrm{RT} \ln \left(\mathrm{K}_{\mathrm{eq}}\right)$

$\log \left(\mathrm{K}_{\mathrm{eq}}\right)=\frac{-\Delta \mathrm{G}^{\circ}}{2.303 \mathrm{RT}}$

$=\frac{-4.88 \times 10^{5}}{2.303 \times 8.314 \times 298}$

$=-8.55 \times 10^{1}=855 \times 10^{-1}$

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