Answer :
To determine which change will cause the equilibrium constant [tex]\( K \)[/tex] to increase for the given reaction, we should consider the effects of temperature changes on an equilibrium system.
The reaction in question is:
[tex]\[ \text{Fe}_3 \text{O}_4(s) + \text{CO}(g) \leftrightarrow 3 \text{FeO}(s) + \text{CO}_2(g) \][/tex]
with a positive enthalpy change, [tex]\(\Delta H^{\circ} = +35.9 \, \text{kJ}\)[/tex].
### Step-by-Step Analysis:
1. Understand the Reaction Type:
- The reaction is endothermic, as indicated by the positive [tex]\(\Delta H^{\circ}\)[/tex]. This means the reaction absorbs heat.
2. Le Chatelier’s Principle:
- According to Le Chatelier’s Principle, if a system at equilibrium is subjected to a change in temperature, volume, or pressure, the system will adjust to counteract that change.
- In an endothermic reaction, increasing the temperature adds heat to the system. The equilibrium will shift to the right (toward products) to absorb this added heat.
3. Effect of Temperature on [tex]\( K \)[/tex]:
- For endothermic reactions, increasing the temperature increases the equilibrium constant [tex]\( K \)[/tex]. This is because the forward reaction is favored, leading to more products.
4. Evaluate the Options:
- A. Adding CO: This will shift the equilibrium position but does not change the value of [tex]\( K \)[/tex].
- B. Adding [tex]\( \text{CO}_2 \)[/tex]: This shifts the equilibrium to the left but does not change [tex]\( K \)[/tex].
- C. Decreasing Temperature: For an endothermic reaction, this will decrease [tex]\( K \)[/tex], making it less favorable to form products.
- D. Increasing Temperature: This will increase [tex]\( K \)[/tex] because the endothermic reaction is favored with more products formed.
Therefore, the change that will cause the equilibrium constant [tex]\( K \)[/tex] to increase is increasing the temperature, which is option D.
The reaction in question is:
[tex]\[ \text{Fe}_3 \text{O}_4(s) + \text{CO}(g) \leftrightarrow 3 \text{FeO}(s) + \text{CO}_2(g) \][/tex]
with a positive enthalpy change, [tex]\(\Delta H^{\circ} = +35.9 \, \text{kJ}\)[/tex].
### Step-by-Step Analysis:
1. Understand the Reaction Type:
- The reaction is endothermic, as indicated by the positive [tex]\(\Delta H^{\circ}\)[/tex]. This means the reaction absorbs heat.
2. Le Chatelier’s Principle:
- According to Le Chatelier’s Principle, if a system at equilibrium is subjected to a change in temperature, volume, or pressure, the system will adjust to counteract that change.
- In an endothermic reaction, increasing the temperature adds heat to the system. The equilibrium will shift to the right (toward products) to absorb this added heat.
3. Effect of Temperature on [tex]\( K \)[/tex]:
- For endothermic reactions, increasing the temperature increases the equilibrium constant [tex]\( K \)[/tex]. This is because the forward reaction is favored, leading to more products.
4. Evaluate the Options:
- A. Adding CO: This will shift the equilibrium position but does not change the value of [tex]\( K \)[/tex].
- B. Adding [tex]\( \text{CO}_2 \)[/tex]: This shifts the equilibrium to the left but does not change [tex]\( K \)[/tex].
- C. Decreasing Temperature: For an endothermic reaction, this will decrease [tex]\( K \)[/tex], making it less favorable to form products.
- D. Increasing Temperature: This will increase [tex]\( K \)[/tex] because the endothermic reaction is favored with more products formed.
Therefore, the change that will cause the equilibrium constant [tex]\( K \)[/tex] to increase is increasing the temperature, which is option D.
