Question

A closed vessel contains an equal number of nitrogen and oxygen molecules at pressure of P mm. If nitrogen is removed from the system, then the pressure will be:

Answer 1

Hint: We need to remember that the solution depends on pressure which is denoted by P and volume also plays a very important role, volume is represented by V . We have to know that the deductions and derived based on the observations are states as laws of physics, by nature which depend on the repeated experiments and or observations.

Complete step by step answer:
We need to know that the temperature has a vital role in the solution.Ideal gas equation is used for knowing about the solution of the above question.
$PV = nRT$
The above equation is known as the ideal gas equation. Ideal gas equation is true for all gases that are present in the universe.
Where,
P= pressure
V=Volume
n=amount of substance
R= gas constant
T=temperature
According to the ideal gas equation pressure into volume is equal to ideal gas constant into temperature into amount of substance.
As we now know that , since ${N_2}$ is removed, total pressure will be equal to partial pressure which will be exerted by ${O_2}$ gas and vice versa. Hence, pressure after ${N_2}$ of any gas would be equal to P/2 mm of Hg.
\[p_1 = n_2p_2\]​​ (As molecules of $N_2$​= molecules $O_2$​)
(∴ Moles $N_2$​=moles $O_2$​)
As $N_2​$ molecules removed= moles become half
\[1p_1 = \dfrac{1}{{2p}}\]
\[2p = 21p_1\]
Pressure has been reduced to half hence the answer is $\dfrac{P}{2}$ .
Hence a closed vessel that contains equal number of oxygen and nitrogen molecules at a Pressure of P mm. If nitrogen is removed from the system, then pressure will be $\dfrac{P}{2}$ .

Note:
We also remember that there are a lot of laws proposed regarding pressure, in which Boyle’s law states the pressure of the ideal gas is inversely proportional to its volume of the system at constant temperature.
We also know that the following points,
1.The particles here have no volume.
2.All collisions between particles are usually elastic collisions and they don’t lose kinetic energy
3.The particles don’t attract each other or repel.
4.They always have random movement in all directions.