Question

which of the following compounds would be most likely to decompose into its elements if it were left out on a lab bench? note the values given are for $\delta g_{\text{formation}}^{\circ}$ for each compound. $\ce{n2h4(l)}, \delta g^\circ f = +149.34\\,\text{kj/mol}$ $\ce{nh4no3(s)}, \delta g^\circ f = -183.87\\,\text{kj/mol}$ $\ce{hcn(s)}, \delta g^\circ f = +124.97\\,\text{kj/mol}$ $\ce{sno(s)}, \delta g^\circ f = -256.90\\,\text{kj/mol}$

Explanation:

Step1: Recall the meaning of $\Delta G^\circ_{\text{formation}}$

The standard Gibbs free energy of formation ($\Delta G^\circ_{\text{formation}}$) tells us about the spontaneity of the formation of a compound from its elements. A positive $\Delta G^\circ_{\text{formation}}$ means the formation of the compound from its elements is non - spontaneous, and the decomposition of the compound into its elements would be spontaneous (since the reverse reaction of a non - spontaneous reaction is spontaneous). A negative $\Delta G^\circ_{\text{formation}}$ means the formation of the compound from its elements is spontaneous, so the decomposition would be non - spontaneous.

Step2: Analyze each compound

• For $\ce{N2H4(l)}$, $\Delta G^\circ_{\text{f}}= + 149.34\space kJ/mol$ (positive, so decomposition into elements is spontaneous candidate).
• For $\ce{NH4NO3(s)}$, $\Delta G^\circ_{\text{f}}=-183.87\space kJ/mol$ (negative, decomposition non - spontaneous).
• For $\ce{HCN(s)}$, $\Delta G^\circ_{\text{f}} = + 124.97\space kJ/mol$ (positive, decomposition spontaneous candidate).
• For $\ce{SnO(s)}$, $\Delta G^\circ_{\text{f}}=-256.90\space kJ/mol$ (negative, decomposition non - spontaneous).

Step3: Compare the magnitudes of positive $\Delta G^\circ_{\text{formation}}$

The larger the positive value of $\Delta G^\circ_{\text{formation}}$, the more spontaneous the decomposition reaction (because $\Delta G$ for decomposition is $-\Delta G^\circ_{\text{formation}}$ of the compound). Since $149.34>124.97$, the decomposition of $\ce{N2H4(l)}$ is more spontaneous than that of $\ce{HCN(s)}$.

Answer:

$\ce{N2H4(l)},\Delta G^\circ_{\text{f}} = + 149.34\space kJ/mol$