In the reaction `N_(2)(g)+3H_(2)(g)hArr 2NH_(3)(g)`, the value of the equlibrium 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 value of the equilibrium constant depends on in the reaction:

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

we can analyze the factors affecting the equilibrium constant \( K \).

### Step-by-Step Solution:

1. **Understanding the Equilibrium Constant**:
The equilibrium constant \( K \) for the reaction can be expressed as:
\[ K = \frac{[NH_3]^2}{[N_2][H_2]^3} \]
where \([NH_3]\), \([N_2]\), and \([H_2]\) are the molar concentrations of ammonia, nitrogen, and hydrogen, respectively, at equilibrium.

2. **Factors Affecting \( K \)**:
The value of the equilibrium constant \( K \) is influenced by several factors, but it is important to distinguish between the factors that affect the position of equilibrium and those that affect the numerical value of \( K \).

3. **Temperature Dependence**:
- The equilibrium constant \( K \) is dependent on temperature. This is because the equilibrium position shifts with temperature changes, which can either favor the formation of products or reactants depending on whether the reaction is exothermic or endothermic.
- For an endothermic reaction (heat is absorbed), increasing the temperature will shift the equilibrium to the right, increasing the concentration of products and thus increasing \( K \).
- Conversely, for an exothermic reaction (heat is released), increasing the temperature will shift the equilibrium to the left, decreasing the concentration of products and thus decreasing \( K \).

4. **Independence from Other Factors**:
- The equilibrium constant does not depend on the concentration of reactants or products, the pressure of the system, or the volume of the reaction vessel. These factors can shift the position of equilibrium but do not change the value of \( K \) itself.

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

### Final Answer:
The value of the equilibrium constant \( K \) depends on **temperature**.

---