0.6 moles of `PCl_(5)`, 0.3 mole of `PCl_(3)` and 0.5 mole of `Cl_(2)` are taken in a 1 L flask to obtain the following equilibrium ,
`PCl_(5(g))rArrPCl_(3(g))+Cl_(2(g))` If the equilibrium constant `K_(c)` for the reaction is 0.2 Predict the direction of the reaction.

Options

A. a. Forward direction
B. b. Backward direction
C. c. Direction of the reaction cannot be predicted
D. d. Reaction does not move in any direction.

Explanation

To determine the direction of the reaction given the equilibrium constant \( K_c \) and the initial concentrations of the reactants and products, we can follow these steps:

### Step 1: Write the balanced chemical equation
The balanced chemical equation for the reaction is:
\[ PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g) \]

### Step 2: Identify the initial concentrations
From the problem, we have the following initial concentrations:
- Concentration of \( PCl_5 = 0.6 \, \text{mol/L} \)
- Concentration of \( PCl_3 = 0.3 \, \text{mol/L} \)
- Concentration of \( Cl_2 = 0.5 \, \text{mol/L} \)

### Step 3: Calculate the reaction quotient \( Q_c \)
The reaction quotient \( Q_c \) is calculated using the formula:
\[ Q_c = \frac{[PCl_3][Cl_2]}{[PCl_5]} \]
Substituting the values:
\[ Q_c = \frac{(0.3)(0.5)}{0.6} \]
Calculating the numerator:
\[ 0.3 \times 0.5 = 0.15 \]
Now substituting back:
\[ Q_c = \frac{0.15}{0.6} = 0.25 \]

### Step 4: Compare \( Q_c \) with \( K_c \)
Given that the equilibrium constant \( K_c = 0.2 \), we compare it with \( Q_c \):
- \( Q_c = 0.25 \)
- \( K_c = 0.2 \)

### Step 5: Determine the direction of the reaction
Since \( Q_c > K_c \) (0.25 > 0.2), the reaction will shift to the left (toward the reactants) to reach equilibrium.

### Conclusion
The direction of the reaction is backward (to the left).

### Summary
The final answer is that the reaction will shift in the backward direction.

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