Question

Nitrogen gas $ \left( {{N_2}} \right) $ reacts with hydrogen gas $ \left( {{H_2}} \right) $ to from ammonia $ \left( {N{H_3}} \right) $ . At $ {200^0}C $ in a closed container, $ 1.05 $ atm of nitrogen gas is mixed with $ 2.02 $ atm of hydrogen gas. At equilibrium the total pressure is $ 2.02 $ atm. What is the partial pressure of hydrogen gas at equilibrium?

Answer 1

Hint: By writing the balanced chemical equation and ICE table the partial pressure of the reactants and products will be determined. After equating the sum of partial pressures of reactants and products with the total mixture gives the change of partial pressure. By substituting the value in partial pressure of hydrogen gives the partial pressure of hydrogen gas at equilibrium.

Complete answer:
Given that a mixture of nitrogen gas and hydrogen gas were reacted to form ammonia. The partial pressure was already given.
The balanced chemical equation will be as follows:
 $ {N_2} + 3{H_2} \to 2N{H_3} $

initial	$ 1.05 $	$ 2.02 $	$ 0 $
change	$ - x $	$ - 3x $	$ + 2x $
equilibrium	$ 1.05 - x $	$ 2.02 - 3x $	$ + 2x $

The above values are the partial pressures of the reactants and product at equilibrium.
Given that the total pressure is $ 2.02 $ atm
Thus, the partial pressure of the hydrogen gas, nitrogen gas and ammonia at equilibrium will be equal to the total pressure at equilibrium.
 $ 1.05 - x + 2.02 - 3x + 2x = 2.02 $
By simplification the value of will be
 $ 1.05 - 2x = 0 \Rightarrow x = 0.525 $
Substitute the value of in the partial pressure of hydrogen gas
 $ {P_{{H_2}}} = 2.02 - 3\left( {0.525} \right) = 0.44atm $
Thus, the partial pressure of hydrogen gas at equilibrium is $ 0.44atm $

Note:
According to Dalton’s law of partial pressure, the sum of the partial pressure of the gases at equilibrium in a closed container is equal to the total pressure of a mixture. Thus, the partial pressures must be calculated according to a balanced chemical equation.