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`
The expression of equilibrium constant is

Options

A. `K_(c)=([N_(2)][H_(2)]^(3))/([NH_(3)]^(2))`
B. `K_(c)=([N_(2)][H_(2)])/([NH_(3)])`
C. `K_(c)=([NH_(3)])/([N_(2)][H_(2)]^(3))`
D. `K_(c)=([NH_(3)]^(2))/([N_(2)][H_(2)]^(3))`

Explanation

To find the expression of the equilibrium constant \( K_c \) for the synthesis of ammonia given by the reaction:

\[ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \]

we can follow these steps:

### Step 1: Identify the Products and Reactants
In the given reaction, the products are ammonia (\( NH_3 \)), and the reactants are nitrogen (\( N_2 \)) and hydrogen (\( H_2 \)).

### Step 2: Write the General Expression for \( K_c \)
The equilibrium constant \( K_c \) is defined in terms of the concentrations of the products and reactants at equilibrium. The general expression for \( K_c \) for a reaction of the form:

\[ aA + bB \rightleftharpoons cC + dD \]

is given by:

\[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]

### Step 3: Apply the Stoichiometric Coefficients
For our specific reaction:

- The stoichiometric coefficient of \( NH_3 \) is 2.
- The stoichiometric coefficient of \( N_2 \) is 1.
- The stoichiometric coefficient of \( H_2 \) is 3.

### Step 4: Write the Expression for \( K_c \)
Using the stoichiometric coefficients, we can write the expression for \( K_c \) as follows:

\[ K_c = \frac{[NH_3]^2}{[N_2]^1 [H_2]^3} \]

### Step 5: Finalize the Expression
Thus, the expression for the equilibrium constant \( K_c \) for the synthesis of ammonia is:

\[ K_c = \frac{[NH_3]^2}{[N_2][H_2]^3} \]