Answer
Verified
89.4k+ views
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.
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.
Recently Updated Pages
Name the scale on which the destructive energy of an class 11 physics JEE_Main
Write an article on the need and importance of sports class 10 english JEE_Main
Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main
Choose the one which best expresses the meaning of class 9 english JEE_Main
What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main
A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main
Other Pages
Assertion The trajectory of a projectile is quadratic class 11 physics JEE_Main
Derive an expression for maximum speed of a car on class 11 physics JEE_Main
A block of mass 5 kg is on a rough horizontal surface class 11 physics JEE_Main
A pendulum clock keeps the correct time at 20 degrees class 11 physics JEE_Main
Ethylidene dichloride is obtained by the reaction of class 12 chemistry JEE_Main
The average and RMS value of voltage for square waves class 12 physics JEE_Main