Question

A vessel is filled with a mixture of oxygen and nitrogen. At what ratio of partial pressure will the mass of gases be identical?
A. \[({P_{{O_2}}})\, = \,0.785\,({P_{{N_2}}})\,\]
B. \[({P_{{O_2}}})\, = \,8.75\,({P_{{N_2}}})\]
C. \[({P_{{O_2}}})\, = \,11.4({P_{{N_2}}})\,\,\]
D. \[({P_{{O_2}}})\, = \,0.875\,({P_{{N_2}}})\,\]

Answer 1

Hint: You all have studied about the partial pressure of gases. When there is a mixture of gases, each constituent gas exerts a partial pressure which is the notional pressure of that constituent gas. The sum of all the partial pressure is equal to the total pressure of the gas.

Complete answer:
We know that the partial pressure of the gases. Partial pressure of the gas is the pressure exerted by an individual gas when there is a mixture of gases. The ideal gas behavior allows the gaseous mixture to be specified in a simple way. The ideal gas law holds for each constituent of the mixture separately. Each constituent exerts its own pressure which is termed as partial pressure. The total pressure of an ideal gas is the sum of the partial pressure exerted by each constituent gas.
According to the ideal gas equations-
\[PV = nRT\]
Where,
\[P\],\[V\]and \[T\] is the pressure, volume and temperature of the gases.
\[n\] is the amount of the substances or in other words, the number of moles of the gases.
\[R\]is the ideal gas constant.
Also, \[n = \dfrac{w}{M}\]
Where, \[w\]is the given weight of the substance and \[M\]is its molar mass.
So, in the given question:
\[PV = nRT\]
\[PV = \dfrac{w}{M}RT\]
For oxygen,
\[({P_{{O_2}}})V = \dfrac{w}{{32}}RT\] …..(\[1\])
For nitrogen,
\[({P_{{N_2}}})V = \dfrac{w}{{28}}RT\] …..(\[2\])
Divide (\[1\]) by (\[2\]), we get,
\[\dfrac{{{P_{{O_2}}}}}{{{P_{{N_2}}}}} = \dfrac{{28}}{{32}}\]
\[({P_{{O_2}}})\, = \,0.875\,({P_{{N_2}}})\,\]

The correct answer is option (D).

Note:
Remember that there is no ideal gas that exists in reality. The ideal gas concept helps us in studying real gases. All the real gases tend to approach the ideal gas property when the density is low enough. This is possible when the molecules of the gas are so far apart from one another so that they do not interact with each other.