The synthesis of ammonia is given as:
`N_(2)(g)+3H_(2)(g) hArr 2NH_(3)(g), DeltaH^(ɵ)=-92.6 kJ mol^(-1)` given `K_(c)=1.2` and temperature `(T)=375^(@)C`
Starting with `2` mol of each `(N_(2), H_(2) "and" NH_(3))` in `5.0 L` reaction vessel at `375^(@)C`, predict what is true for the reaction?

Options

A. The reaction is at equilibrium
B. The reaction proceed in forward direction.
C. The reaction proceed in backward direction
D. `Q_(c)` for the reaction is less then `K_(c)`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Write the balanced chemical equation and identify the reaction conditions.
The balanced chemical equation for the synthesis of ammonia is:
\[ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \]
Given:
- \(\Delta H^{\circ} = -92.6 \, \text{kJ mol}^{-1}\) (indicating that the reaction is exothermic)
- \(K_c = 1.2\)
- Temperature \(T = 375^\circ C\)

### Step 2: Calculate the initial concentrations of the reactants and products.
We start with 2 moles of each \(N_2\), \(H_2\), and \(NH_3\) in a 5.0 L reaction vessel.

- Concentration of \(N_2\):
\[ \text{Concentration of } N_2 = \frac{2 \, \text{mol}}{5.0 \, \text{L}} = 0.4 \, \text{mol/L} \]

- Concentration of \(H_2\):
\[ \text{Concentration of } H_2 = \frac{2 \, \text{mol}}{5.0 \, \text{L}} = 0.4 \, \text{mol/L} \]

- Concentration of \(NH_3\):
\[ \text{Concentration of } NH_3 = \frac{2 \, \text{mol}}{5.0 \, \text{L}} = 0.4 \, \text{mol/L} \]

### Step 3: Write the expression for the reaction quotient \(Q_c\).
The reaction quotient \(Q_c\) is given by the formula:
\[ Q_c = \frac{[NH_3]^2}{[N_2][H_2]^3} \]

Substituting the concentrations we calculated:
\[ Q_c = \frac{(0.4)^2}{(0.4)(0.4)^3} \]

### Step 4: Simplify the expression for \(Q_c\).
Calculating \(Q_c\):
\[ Q_c = \frac{0.16}{0.4 \times 0.064} = \frac{0.16}{0.0256} = 6.25 \]

### Step 5: Compare \(Q_c\) with \(K_c\) to predict the direction of the reaction.
Given \(K_c = 1.2\) and \(Q_c = 6.25\):
- Since \(Q_c > K_c\), the reaction will shift to the left (towards the reactants) to reach equilibrium.

### Conclusion
The reaction will proceed in the backward direction.