One reaction used to produce small quantities of pure $\mathrm{H}_{2}$ is

$$\mathrm{CH}_{3} \mathrm{OH}(g) \rightleftharpoons \mathrm{CO}(g)+2 \mathrm{H}_{2}(g)$$

(a) Determine $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for the reaction at 298 $\mathrm{K}$ .

(b) Assuming that these values are relatively independent of temperature, calculate $\Delta G^{\circ}$ at $28^{\circ} \mathrm{C}, 128^{\circ} \mathrm{C},$ and $228^{\circ} \mathrm{C}$ .

(c) What is the significance of the different values of $\Delta G^{\circ} ?$

(d) At what temperature (in $\mathrm{K} )$ does the reaction become spontaneous?

## Discussion

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(a) Write the chemical equations that correspond to $\Delta G_{f}^{\circ}$ for $\mathrm{NH}_{3}(g)$ and for $\mathrm{CO}(g) .$ (b) For which of these formation reactions will the value of $\Delta G_{f}^{\circ}$ be more positive (less negative) than $\Delta H_{f}^{\circ} ?(\mathbf{c})$ In general, under which condition is $\Delta G_{f}^{\circ}$ more positive (less negative) than $\Delta H_{f}^{\circ} ?$ (i) When the temperature is high, (ii) when the reaction is reversible, (iii) when $\Delta S_{f}^{\circ}$ is negative.