`N_(2)+3H_(2) Leftrightarrow 2NH_(3)` in this equilibrium system if the pressure is increased at `25^(@)C` then the value of K will

Options

A. Increases
B. Decreases
C. Remains the same
D. Depends on the nature of the reactants

Answer

To solve the question regarding the effect of increased pressure on the equilibrium constant \( K \) for the reaction

\[ N_2 + 3H_2 \leftrightarrow 2NH_3 \]

we can follow these steps:

### Step 1: Understand the Reaction
The given reaction involves the formation of ammonia (\( NH_3 \)) from nitrogen (\( N_2 \)) and hydrogen (\( H_2 \)). The balanced equation shows that 1 mole of nitrogen reacts with 3 moles of hydrogen to produce 2 moles of ammonia.

### Step 2: Write the Expression for the Equilibrium Constant
The equilibrium constant \( K_c \) for this reaction can be expressed as:

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

Where:
- \([NH_3]\) is the concentration of ammonia,
- \([N_2]\) is the concentration of nitrogen,
- \([H_2]\) is the concentration of hydrogen.

### Step 3: Analyze the Effect of Pressure
According to Le Chatelier's principle, if the pressure of a gaseous equilibrium system is increased, the system will shift in the direction that produces fewer moles of gas.

In this reaction:
- Reactants: \( 1 \, N_2 + 3 \, H_2 = 4 \, \text{moles of gas} \)
- Products: \( 2 \, NH_3 = 2 \, \text{moles of gas} \)

Since there are 4 moles of gas on the reactant side and 2 moles of gas on the product side, an increase in pressure will shift the equilibrium to the right, favoring the production of ammonia.

### Step 4: Determine the Effect on the Equilibrium Constant \( K_c \)
However, it is crucial to note that the equilibrium constant \( K_c \) is only affected by changes in temperature. The value of \( K_c \) remains constant regardless of changes in pressure or volume.

Thus, even though the equilibrium position shifts to the right with increased pressure, the actual value of \( K_c \) does not change.

### Conclusion
Therefore, the value of \( K \) (or \( K_c \)) remains the same when the pressure is increased at \( 25^\circ C \).

### Final Answer
The value of \( K \) will remain the same.

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