The reaction quotient (Q) for the reaction `N_2(g) +3H_2(g) hArr 2NH_3(g)` is given by
`Q=([NH_3]^2)/([N_2][H_2]^3)`. The reaction will proceed from right to left if

Options

A. `Q=K_c`
B. `Q lt K_c`
C. `Q gt K_c`
D. `Q =0`

Answer

To determine the conditions under which the reaction will proceed from right to left for the reaction \( N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \), we need to analyze the reaction quotient \( Q \) and its relationship to the equilibrium constant \( K_c \).

### Step-by-Step Solution:

1. **Understanding the Reaction Quotient (Q)**:
The reaction quotient \( Q \) is defined as:
\[ Q = \frac{[NH_3]^2}{[N_2][H_2]^3} \]
This expression compares the concentrations of the products and reactants at any point in time.

2. **Equilibrium Constant (Kc)**:
At equilibrium, the reaction quotient \( Q \) becomes equal to the equilibrium constant \( K_c \):
\[ K_c = \frac{[NH_3]^2}{[N_2][H_2]^3} \]
The value of \( K_c \) is constant at a given temperature.

3. **Comparing Q and Kc**:
- If \( Q < K_c \): The reaction will proceed to the right (toward products) to reach equilibrium.
- If \( Q = K_c \): The system is at equilibrium, and no net change will occur.
- If \( Q > K_c \): The reaction will proceed to the left (toward reactants) to reach equilibrium.

4. **Condition for Right to Left Shift**:
For the reaction to proceed from right to left, we need:
\[ Q > K_c \]
This means that the concentration of products (in this case, \( NH_3 \)) is too high compared to the concentration of reactants (\( N_2 \) and \( H_2 \)), leading the system to shift back to the left to decrease the concentration of \( NH_3 \).

### Conclusion:
The reaction will proceed from right to left if the reaction quotient \( Q \) is greater than the equilibrium constant \( K_c \).