For the reaction `2SO_(2)(g)+O_(2)(g)=2SO_(3)(g)` `deltaH=-57.2kJmol^(-1)` and `K_(C)=1.7xx10^(16)` ltbr. Which of the following statements is INCORRECT?
A
The equilibrium constant is large suggestive of reaction going to completion and so no catalyst is required.
B
The equilibrium will shift in forward direction as the pressure increases.
C
The equilibrium constant decreases as the temperatue increases
D
The addition of inert gas at constant volume will not affect the equilibrium constant.
Text Solution
AI Generated Solution
The correct Answer is:
To solve the problem, we need to analyze the given reaction and the statements provided. The reaction is:
\[ 2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g) \]
with the enthalpy change (\(\Delta H\)) of \(-57.2 \, \text{kJ/mol}\) indicating that the reaction is exothermic. The equilibrium constant (\(K_C\)) is given as \(1.7 \times 10^{16}\).
### Step-by-Step Solution:
1. **Understanding the Reaction**:
- The reaction involves the conversion of sulfur dioxide (\(SO_2\)) and oxygen (\(O_2\)) into sulfur trioxide (\(SO_3\)).
- Since \(\Delta H\) is negative, the reaction releases heat, confirming it is exothermic.
2. **Analyzing the Statements**:
- We need to evaluate each statement to identify which one is incorrect.
3. **Statement 1**: "Equilibrium constant is large, so the reaction is going to be complete, so no catalyst is needed."
- A large equilibrium constant (\(K_C\)) indicates that at equilibrium, the concentration of products is much greater than that of reactants. However, it does not imply that the reaction goes to completion. It simply means that the forward reaction is favored. Catalysts are not required for the reaction to proceed; they only speed up the attainment of equilibrium. Thus, this statement is **incorrect**.
4. **Statement 2**: "The equilibrium will shift in the forward direction as the pressure increases."
- According to Le Chatelier's principle, increasing pressure shifts the equilibrium toward the side with fewer moles of gas. In this reaction, there are 3 moles of gas on the reactants' side (2 from \(SO_2\) and 1 from \(O_2\)) and 2 moles on the products' side (\(SO_3\)). Therefore, increasing pressure will shift the equilibrium to the right (forward direction), making this statement **correct**.
5. **Statement 3**: "The equilibrium constant decreases as the temperature increases."
- For an exothermic reaction, increasing the temperature shifts the equilibrium to the left (backward direction) to absorb the added heat. This means that the concentration of reactants increases relative to products, which results in a decrease in the equilibrium constant (\(K_C\)). Hence, this statement is **correct**.
6. **Statement 4**: "The addition of inert gas at constant volume will not affect the equilibrium constant."
- The equilibrium constant is dependent only on temperature. Adding an inert gas at constant volume does not change the partial pressures of the reactants and products, thus it does not affect the equilibrium constant. This statement is **correct**.
### Conclusion:
The incorrect statement is **Statement 1**.
