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# ${N_2} + 3{H_2} \rightleftharpoons 2N{H_3}$ 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

Last updated date: 13th Jun 2024
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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.
* 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.