The reaction n2 + 3h2 2nh3 takes place at 450°c .1 mole of n2 and 2 moles of h2 are mixed in a 1 litr vessel and 1mole of nh3 at equilibrium .then kc for the above reaction is

To determine the equilibrium constant \( K_c \) for the reaction \( N_2 + 3H_2 \rightleftharpoons 2NH_3 \) at 450°C, we first need to analyze the initial conditions and the changes that occur as the system reaches equilibrium.

Initial Conditions

We start with 1 mole of \( N_2 \) and 2 moles of \( H_2 \) in a 1-liter vessel. This gives us the following initial concentrations:

• Concentration of \( N_2 \) = 1 mole / 1 L = 1 M
• Concentration of \( H_2 \) = 2 moles / 1 L = 2 M
• Concentration of \( NH_3 \) = 0 M (since it hasn't been produced yet)

Change in Concentrations

As the reaction proceeds towards equilibrium, let \( x \) be the amount of \( N_2 \) that reacts. According to the stoichiometry of the reaction:

• For every 1 mole of \( N_2 \) that reacts, 3 moles of \( H_2 \) react and 2 moles of \( NH_3 \) are produced.

Thus, at equilibrium, the changes in concentrations will be:

• Concentration of \( N_2 \) = \( 1 - x \)
• Concentration of \( H_2 \) = \( 2 - 3x \)
• Concentration of \( NH_3 \) = \( 0 + 2x = 2x \)

Equilibrium Condition

We know from the problem that at equilibrium, the concentration of \( NH_3 \) is 1 M. Therefore, we can set up the equation:

2x = 1

From this, we find:

x = 0.5

Equilibrium Concentrations

Now we can substitute \( x \) back into our expressions for the equilibrium concentrations:

• Concentration of \( N_2 \) = \( 1 - 0.5 = 0.5 \) M
• Concentration of \( H_2 \) = \( 2 - 3(0.5) = 2 - 1.5 = 0.5 \) M
• Concentration of \( NH_3 \) = \( 2(0.5) = 1 \) M

Calculating Kc

The equilibrium constant \( K_c \) for the reaction is given by the expression:

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

Substituting the equilibrium concentrations into this expression:

Kc = \frac{(1)^2}{(0.5)(0.5)^3}

Calculating the denominator:

(0.5)^3 = 0.125

So, we have:

Kc = \frac{1}{(0.5)(0.125)} = \frac{1}{0.0625} = 16

Final Result

Thus, the equilibrium constant \( K_c \) for the reaction at 450°C is 16. This value indicates the extent to which the reaction favors the formation of products at equilibrium under the given conditions.