To solve the problem, we need to analyze the effect of a sudden decrease in pressure on the equilibrium of the reaction:
\[ 2NO(g) + Cl_2(g) \rightleftharpoons 2NOCl(g) \]
### Step-by-Step Solution:
1. **Identify the Reaction and Initial Conditions**:
- The reaction is \( 2NO(g) + Cl_2(g) \rightleftharpoons 2NOCl(g) \).
- Initially, we have an equilibrium mixture of the gases involved.
2. **Effect of Doubling the Volume**:
- When the volume of the container is doubled, the pressure of the gas mixture decreases. According to the ideal gas law, pressure is inversely proportional to volume (\( P \propto \frac{1}{V} \)).
- Therefore, if the volume is doubled, the pressure will decrease.
3. **Le Chatelier's Principle**:
- According to Le Chatelier's Principle, if a system at equilibrium is subjected to a change in conditions (like pressure), the system will adjust to counteract that change.
- In this case, since the pressure has decreased, the equilibrium will shift towards the side with more moles of gas to increase the pressure.
4. **Counting Moles**:
- On the left side (reactants), we have \( 2 \, \text{moles of NO} + 1 \, \text{mole of Cl}_2 = 3 \, \text{moles} \).
- On the right side (products), we have \( 2 \, \text{moles of NOCl} = 2 \, \text{moles} \).
- Since there are more moles of gas on the reactant side (3 moles vs. 2 moles), the equilibrium will shift to the left (towards the reactants).
5. **Changes in Concentration**:
- As the equilibrium shifts to the left, the concentration of \( NO \) and \( Cl_2 \) will increase, while the concentration of \( NOCl \) will decrease.
6. **Effect on Equilibrium Constant \( K_c \)**:
- The equilibrium constant \( K_c \) is only affected by changes in temperature. Since the temperature remains constant in this scenario, \( K_c \) will not change.
### Conclusion:
- After the system returns to equilibrium:
- The concentration of \( NO \) will increase.
- The concentration of \( Cl_2 \) will increase.
- The concentration of \( NOCl \) will decrease.
- The value of \( K_c \) will remain the same.
### Final Answer:
- The number of moles of chlorine will increase, and the number of moles of \( NOCl \) will decrease. The value of \( K_c \) will remain unchanged.
