10. Which equation has the largest value of Keq? $$ \begin{array}{ll} ext { A. } \quad \mathrm{N}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})} ightleftarrows 2 \mathrm{NO}_{(\mathrm{g})} & \Delta \mathrm{H}=21 \mathrm{~kJ} \ ext { B. } \quad \mathrm{C}_{2} \mathrm{H}_{6(\mathrm{~g})} ightleftarrows 2 \mathrm{C}_{(\mathrm{s})}+3 \mathrm{H}_{2(\mathrm{~g})} & \Delta \mathrm{H}+83 \mathrm{~kJ} \ ext { C. } \quad \mathrm{H}_{2(\mathrm{~g})}+1 / 2 \mathrm{O}_{2(\mathrm{~g})} ightleftarrows \mathrm{H}_{2} \mathrm{O}_{(\mathrm{g})} \ ext { D. } \quad \mathrm{Ca}_{(\mathrm{s})}+3 \mathrm{H}_{2} \mathrm{O}_{(\mathrm{l})} ightleftarrows \mathrm{Ca}(\mathrm{OH})_{2(\mathrm{aq})}+\mathrm{H}_{2(\mathrm{~g})} & \Delta \mathrm{H}=-240 \mathrm{~kJ} \ \end{array} $$

Question

10. Which equation has the largest value of Keq? $$ \begin{array}{ll}	ext { A. } \quad \mathrm{N}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})} ightleftarrows 2 \mathrm{NO}_{(\mathrm{g})} & \Delta \mathrm{H}=21 \mathrm{~kJ} \ 	ext { B. } \quad \mathrm{C}_{2} \mathrm{H}_{6(\mathrm{~g})} ightleftarrows 2 \mathrm{C}_{(\mathrm{s})}+3 \mathrm{H}_{2(\mathrm{~g})} & \Delta \mathrm{H}+83 \mathrm{~kJ} \ 	ext { C. } \quad \mathrm{H}_{2(\mathrm{~g})}+1 / 2 \mathrm{O}_{2(\mathrm{~g})} ightleftarrows \mathrm{H}_{2} \mathrm{O}_{(\mathrm{g})} \ 	ext { D. } \quad \mathrm{Ca}_{(\mathrm{s})}+3 \mathrm{H}_{2} \mathrm{O}_{(\mathrm{l})} ightleftarrows \mathrm{Ca}(\mathrm{OH})_{2(\mathrm{aq})}+\mathrm{H}_{2(\mathrm{~g})} & \Delta \mathrm{H}=-240 \mathrm{~kJ} \ \end{array} $$

UpStudy AI · Accepted Answer

**Step 1. Analyze the Given Reactions**

We are given four reactions with their ΔH values (when provided):

- **Reaction A:** 
  $$
  \mathrm{N}_2(\mathrm{g}) + \mathrm{O}_2(\mathrm{g}) \rightleftharpoons 2\,\mathrm{NO}(\mathrm{g}), \quad \Delta H = 21\,\mathrm{kJ}
  $$
  This reaction is endothermic. Typically, an endothermic reaction is less favorable at lower temperatures, so the equilibrium constant is not expected to be very large.

- **Reaction B:** 
  $$
  \mathrm{C}_2\mathrm{H}_6(\mathrm{g}) \rightleftharpoons 2\,\mathrm{C}(\mathrm{s}) + 3\,\mathrm{H}_2(\mathrm{g}), \quad \Delta H = +83\,\mathrm{kJ}
  $$
  This reaction is even more endothermic. Thus, it tends to favor the reactants at typical conditions, leading to a small equilibrium constant.

- **Reaction C:** 
  $$
  \mathrm{H}_2(\mathrm{g}) + \frac{1}{2}\mathrm{O}_2(\mathrm{g}) \rightleftharpoons \mathrm{H}_2\mathrm{O}(\mathrm{g})
  $$
  Although the value of $$\Delta H$$ is not explicitly given, the formation of water from $$\mathrm{H}_2$$ and $$\mathrm{O}_2$$ is well known to be highly exothermic. This large exothermicity typically means that the products (in this case, water vapor) are heavily favored, especially at lower temperatures, resulting in a very large equilibrium constant.

- **Reaction D:** 
  $$
  \mathrm{Ca}(\mathrm{s}) + 3\,\mathrm{H}_2\mathrm{O}(\mathrm{l}) \rightleftharpoons \mathrm{Ca(OH)}_2(\mathrm{aq}) + \mathrm{H}_2(\mathrm{g}), \quad \Delta H = -240\,\mathrm{kJ}
  $$
  Even though this reaction is very exothermic, it involves dissolution and precipitation processes (for example, the solubility of $$\mathrm{Ca(OH)}_2$$). The solubility limits often do not allow this reaction to proceed completely to products under standard conditions, so its equilibrium constant will not be as large as one might initially expect from the magnitude of $$\Delta H$$.

**Step 2. Determine Which Reaction has the Largest $$K_{eq}$$**

- Reactions A and B are endothermic, indicating that at typical conditions (unless at very high temperatures), they will not proceed substantially to the products, resulting in relatively small equilibrium constants.
  
- Reaction D, although very exothermic, involves a sparingly soluble product ($$\mathrm{Ca(OH)}_2$$) that limits the formation of products.

- Reaction C represents the formation of water vapor from its elements. The process is known to be highly exothermic and, under standard conditions, proceeds almost completely towards the formation of water. This results in a very large equilibrium constant.

**Final Answer**

$$
\textbf{C. } \quad \mathrm{H}_2(\mathrm{g}) + \frac{1}{2}\mathrm{O}_2(\mathrm{g}) \rightleftharpoons \mathrm{H}_2\mathrm{O}(\mathrm{g})
$$
Reaction C has the largest $$ K_{eq} $$.

Which equation has the largest value of Keq?

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