Question

If the two gases have the same number of moles then can we say that their partial pressure is also the same.

Answer 1

Hint: We can see from the ideal gas equation that pressure is directly proportional to number of moles. The temperature needs to be constant. Partial pressure can be related through Dalton’s law.

Complete step by step answer:
The ideal gas equation is \[{\text{PV}} = {\text{nRT}}\]
Here P is the pressure, V is the volume, n is the number of moles of gas, R is the universal gas constant and T is the temperature.
If the temperature remains constant then the number of moles will be directly proportional with the pressure of gas. Any two gases having the same number of moles, then they will have the same pressure.
 Talking about partial pressure, the equation for partial pressure was given by Dalton. According to this the partial pressure is equals to the mole fraction multiplied by the total pressure of the system, we can write the equation as \[{{\text{P}}_{\text{A}}} = {\chi _{\text{A}}}{{\text{P}}_{\text{T}}}\]
\[{{\text{P}}_{\text{A}}}\] is the partial pressure of the component A, \[{\chi _{\text{A}}}\] is the mole fraction of component A and \[{{\text{P}}_{\text{T}}}\] is the total pressure of the system.
Now, since the number of moles of both the gases is same then their mole fraction will also be same. Mole fraction is defined as the number of moles of that component divider by the total number of moles present in the solution.
Hence the partial pressure of two gases will be the same, so it is clear that if two gases have the same number then their partial pressure is also the same.

Note:
Along with partial pressure, the kinetic energy of the two gases will also be the same because the average kinetic energy is a function of temperature only.