Question

What is the value of the equilibrium constant for the following reaction if the equilibrium concentrations of nitrogen, hydrogen, and ammonia are $1M,2M,$ and $15M$ respectively?
$N_2\left(g\right)+3H_2\left(g\right)\leftrightharpoons 2N{H}_3\left(g\right)$

• A. $0.035$
• B. $7.5$
• C. $28$
• D. $380$

Answer 1

Answer: (C)

$28$

The equilibrium constant of a particular reaction is expressed as the ratio of the concentrations of the products to the concentrations of the reactants, with their powers raised to their stoichiometric coefficients.

In the equation $N_2$ $+$ $3H_2$ $=$ $2N{H}_3$, the stoichiometric co-efficients of the reactants are $1$ and $3$ whereas, the stoichiometric coefficient of the product is $2$

Thus, equilibrium constant $k$ can be written as:

$k$ $=$ $[N{H}_3{]}^2$$/$$[N_2{]}^1$$[H_2{]}^3$

The concentrations of $N{H}_3$, $H_2$ and $N_2$ are $15M$, $2M$ and $1M$ respectively. Putting all these values in the equation we get,

$k$ $=$ $[15{]}^2$$/$$[1{]}^1$$[2{]}^3$

From this, the value of $k$ is obtained as $28.1$

Option $C$ is the correct answer.