Question

Two equations can be written for the dissolution of $\operatorname{Mg}(\mathrm{OH})_{2}(\mathrm{s})$ in acidic solution. $$\begin{array}{r} \mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{s})+2 \mathrm{H}^{+}(\mathrm{aq}) \rightleftharpoons \mathrm{Mg}^{2+}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \\ \Delta_{\mathrm{r}} G^{\circ}=-95.5 \mathrm{kJ} \mathrm{mol}^{-1} \end{array}$$ $$\begin{aligned} \frac{1}{2} \mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{s})+\mathrm{H}^{+}(\mathrm{aq}) \rightleftharpoons & \frac{1}{2} \mathrm{Mg}^{2+}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(1) \\ & \Delta_{\mathrm{r}} G^{\circ}=-47.8 \mathrm{kJ} \mathrm{mol}^{-1} \end{aligned}$$ (a) Explain why these two equations have different $\Delta_{\mathrm{r}} G^{\circ}$ values. (b) Will $K$ for these two equations be the same or different? Explain.

          Two equations can be written for the dissolution of $\operatorname{Mg}(\mathrm{OH})_{2}(\mathrm{s})$ in acidic solution.
$$\begin{array}{r}
\mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{s})+2 \mathrm{H}^{+}(\mathrm{aq}) \rightleftharpoons \mathrm{Mg}^{2+}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \\
\Delta_{\mathrm{r}} G^{\circ}=-95.5 \mathrm{kJ} \mathrm{mol}^{-1}
\end{array}$$
$$\begin{aligned}
\frac{1}{2} \mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{s})+\mathrm{H}^{+}(\mathrm{aq}) \rightleftharpoons & \frac{1}{2} \mathrm{Mg}^{2+}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(1) \\
& \Delta_{\mathrm{r}} G^{\circ}=-47.8 \mathrm{kJ} \mathrm{mol}^{-1}
\end{aligned}$$
(a) Explain why these two equations have different $\Delta_{\mathrm{r}} G^{\circ}$ values.
(b) Will $K$ for these two equations be the same or different? Explain.

Added by John B.

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