In the reaction,
` N_2(g) +3H_2(g) hArr 2NH_3(g)`
the value of the equilibrium constant depends on

Options

A. volume of the reaction vessel
B. total pressure of the system
C. the initial concentration of nitrogen and hydrogen
D. the temperature

Answer

To determine what the equilibrium constant (K) depends on in the reaction:

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

we can follow these steps:

### Step 1: Write the expression for the equilibrium constant (K)
The equilibrium constant for the reaction can be expressed in terms of the partial pressures of the gases involved:

\[ K_p = \frac{(P_{NH_3})^2}{(P_{N_2})(P_{H_2})^3} \]

Where:
- \( P_{NH_3} \) is the partial pressure of ammonia,
- \( P_{N_2} \) is the partial pressure of nitrogen,
- \( P_{H_2} \) is the partial pressure of hydrogen.

### Step 2: Analyze the factors affecting K
The equilibrium constant \( K_p \) is derived from the concentrations (or partial pressures) of the reactants and products at equilibrium. However, it is important to note that:

- The value of \( K \) is constant at a given temperature.
- Changes in concentration or pressure do not affect the value of \( K \) at equilibrium; they only shift the position of equilibrium.

### Step 3: Identify the correct dependency
From the analysis, we can conclude that the equilibrium constant \( K \) depends only on temperature. This is supported by the Van't Hoff equation, which states that the equilibrium constant is a function of temperature:

\[ K = A e^{-\frac{\Delta H^\circ}{RT}} \]

Where:
- \( A \) is the pre-exponential factor,
- \( \Delta H^\circ \) is the standard enthalpy change of the reaction,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin.

### Conclusion
Thus, the value of the equilibrium constant \( K \) for the reaction \( N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \) depends on **temperature**.

### Final Answer
The equilibrium constant depends on **temperature** (Option D).

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