Question
Consider the following data for the reaction
$$X_{2}(\text{ }g) + Y_{2}(\text{ }g) \rightleftharpoons 2XY(g) $$at $600{\text{ }K}_{\text{. The}\text{~}\Delta_{r}G^{\ominus}}\left( inkJ{mol}^{- 1} \right)$ for the reaction is:
| Compound | $$\Delta_{f}H_{600\text{ }K}^{\Theta}$$ $$\left( kJ{mol}^{- 1} \right)$$ |
$$S_{600\text{ }K}^{\Theta}$$ $$\left( J{mol}^{- 1}{\text{ }K}^{- 1} \right)$$ |
|---|---|---|
| $$XY(g)$$ | 42 | 200 |
| $$X_{2}(\text{ }g)$$ | 8 | 140 |
| $$Y_{2}(\text{ }g)$$ | 80 | 250 |
$$\Delta_{f}H_{600\text{ }K}^{\Theta}$$
$$\left( kJ{mol}^{- 1} \right)$$
$$S_{600\text{ }K}^{\Theta}$$
$$\left( J{mol}^{- 1}{\text{ }K}^{- 1} \right)$$
Options
Solution
Sol. [Key Concept: $\Delta_{r}G = \Delta_{r}H - T\Delta_{r}S$ with $\Delta_{r}H = \sum\Delta_{f}H(prod) - \sum\Delta_{f}H(react)$ and $\Delta_{r}S$ likewise at $600$ K.]
$$\Delta_{r}G = \Delta_{r}H - T.\Delta_{r}S$$
$$\begin{matrix} \Delta_{r}H & \ = (2 \times 42 - 80 - 8) = - 4\text{ }kJ/mol \\ \Delta_{r}\text{ }S & \ = (400 - 250 - 140) = + 10\text{ }J/K.mol \\ \Delta_{r}G & \ = - 4000 - 600 \times (10) \\ & \ = - 10,000\text{ }J/mol = - 10\text{ }kJ/mol \end{matrix}$$
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