Question

${N_2} + 3{H_2} \rightleftharpoons 2N{H_3}$ Starting with one mole of nitrogen and 3 moles of hydrogen, at equilibrium 50% of each had reacted. If the equilibrium pressure is P, the partial pressure of hydrogen at equilibrium would be:
(A) P/2
(B) P/3
(C) P/4
(D) P/6

Answer 1

Hint: Try to recall that partial pressure of a gas is equal to the product of the total pressure and mole fraction of gas and mole fraction is the ratio of number of moles of a substance to total moles. Now, by using this you can easily find the correct option from the given ones.
Complete answer:

• The equilibrium reaction is : ${N_2} + 3{H_2} \rightleftharpoons 2N{H_3}$
  Initial moles of nitrogen, ${N_2}$= 1
  Initial moles of hydrogen,${H_2}$=3
  We are given that at equilibrium 50% of each reactant had reacted
  So, number of moles of nitrogen dissociated, {N_2}$$$${\text{ = }}\dfrac{{{\text{50}}}}{{{\text{100}}}}{\text{ \times 1 = 0}}{\text{.5mole}}
  Number of moles of hydrogen dissociated, {H_2}$$$${\text{ = }}\dfrac{{{\text{50}}}}{{{\text{100}}}}{\text{ \times 3 = 1}}{\text{.5mole}}.
  Therefore, amount of {N_2}$$$, $$${H_2}$$$ and $$$N{H_3} at equilibrium will be
  ${N_2} = 1 - 0.5 = 0.5mole$
  ${H_2} = 3 - 1.5 = 1.5mole$
  Since, 1 mole of ${N_2}$ on dissociation gives 2 mole of $N{H_3}$
  So, 0.5 mole of ${N_2}$ gives$2 \times 0.5 = 1mole{\text{ of }}N{H_3}$.
  Number of moles of hydrogen left at equilibrium= 1.5 mole
  Total number of moles at equilibrium$= 0.5 + 1.5 + 1 = 3mole$
  Mole fraction of hydrogen $= \dfrac{{number{\text{ of moles of hydrogen}}}}{{total{\text{ number of moles at equilibrium}}}} = \dfrac{{1.5}}{3} = 0.5$
  Also, given total pressure at equilibrium is P
  Partial pressure of hydrogen $= mole{\text{ fraction of hydrogen}} \times {\text{total pressure at equilibrium}}$

$$\\\ {\text{ = }}\left( {0.5} \right) \times P \\\ or,\dfrac{P}{2} \\\$$

Therefore, from the above calculation, we can say that option A is the correct option to the given question.
Note:

• It should be remembered to you that the law of mass action states that the rate at which a substance reacts is directly proportional to its active mass and hence the rate of a chemical reaction is directly proportional to the product of the active masses of the reactants.
• Also, you should remember that equilibrium constant of a reaction is constant at constant temperature and does not depend upon the concentration of reactants.