The system `PCl_(5)(g) hArr PCl_(3)(g)+Cl_(2)(g)` attains equilibrium. If the equilibrium concentration of `PCl_(3)(g)` is doubled, the concentration of `Cl_(2)(g)` would become

Options

A. `1//4` its original value
B. `1//2` its original value
C. Twice its original value
D. Unpredictable

Explanation

To solve the problem, we need to analyze the equilibrium reaction:

\[ \text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g) \]

1. **Understanding the Initial Condition**:
- Let the initial equilibrium concentrations be:
- \([PCl_5] = a\)
- \([PCl_3] = b\)
- \([Cl_2] = c\)

2. **Effect of Doubling \([PCl_3]\)**:
- According to the problem, the concentration of \([PCl_3]\) is doubled. Thus, the new concentration of \([PCl_3]\) becomes \(2b\).

3. **Le Chatelier's Principle**:
- Le Chatelier's Principle states that if a system at equilibrium is disturbed, the system will shift in a direction that counteracts the disturbance.
- In this case, increasing the concentration of \([PCl_3]\) will disturb the equilibrium, causing the reaction to shift to the left (towards the formation of \([PCl_5]\)) to reduce the concentration of \([PCl_3]\).

4. **Change in Concentrations**:
- Let \(x\) be the amount of \([PCl_3]\) and \([Cl_2]\) that reacts to restore equilibrium.
- The new concentrations will be:
- \([PCl_3] = 2b - x\)
- \([Cl_2] = c - x\)
- \([PCl_5] = a + x\)

5. **Establishing New Equilibrium**:
- At the new equilibrium, the concentrations of \([PCl_3]\) and \([Cl_2]\) will adjust such that the equilibrium constant \(K\) remains the same. The equilibrium constant expression is:
\[ K = \frac{[PCl_3][Cl_2]}{[PCl_5]} \]
- Since we do not have specific values for \(a\), \(b\), and \(c\), we cannot determine the exact values of \(x\), \([Cl_2]\), or \([PCl_5]\) after the shift.

6. **Conclusion**:
- The concentration of \([Cl_2]\) will decrease, but the exact new concentration cannot be determined without additional information. Therefore, the answer is that the concentration of \([Cl_2]\) becomes unpredictable.