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A mixture of Helium and Neon gases are collected over water at 28.0 $^{\text{o}}{\text{C}}$ and 745 ${\text{mmHg}}$. If the partial pressure of Helium is 368${\text{mmHg}}$. What is the partial pressure of neon?

Last updated date: 25th Jun 2024
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Hint: Partial pressure is defined as the pressure exerted by anyone of the gas in the mixture of gases if it occupies the same volume. Dalton’s law states that the total pressure over the solution phase in a container will be the sum of partial pressures of components

Complete step by step solution:
The mixture of volatile liquids Helium and Neon are taken in a closed vessel and collected over water, the two components evaporate and eventually equilibrium is attained between the vapour phase and liquid phase. The total vapour pressure is taken as ${{\text{p}}_{{\text{total}}}}$, ${{\text{p}}_{{\text{He}}}}$and ${{\text{p}}_{{\text{Ne}}}}$ be the partial vapour pressures of Helium and Neon
According to Dalton’s law of partial pressures, the total pressure will be the sum of partial vapour pressures of components
${{\text{p}}_{{\text{total}}}}$ $=$ ${{\text{p}}_{\text{1}}}{\text{ + }}{{\text{p}}_{\text{2}}}$
${{\text{p}}_{{\text{total}}}}$ $=$ ${{\text{p}}_{{\text{He}}}}{\text{ + }}{{\text{p}}_{{\text{Ne}}}}$
From the given data the partial pressure of Helium is 368${\text{mmHg}}$ and the total pressure of the mixture is
On substituting and rearranging the equation
${{\text{p}}_{{\text{Ne}}}}$ $=$ ${{\text{p}}_{{\text{total}}}}{\text{ - }}{{\text{p}}_{{\text{He}}}}$
${{\text{p}}_{{\text{Ne}}}}$ $=$ 745-368
${{\text{p}}_{{\text{Ne}}}}$ $=$ 377 ${\text{mmHg}}$

Thus the partial pressure of Neon is 377 ${\text{mmHg}}$.

Additional Information
Partial pressure is the measure of thermodynamic activity of the gas molecules where the gases react based on their partial pressures
The total vapour pressure over the solution is related to mole fraction of one of the component which is given by
${{\text{p}}_{{\text{total}}}}$ $=$ ${{\text{p}}_{\text{1}}}^{\text{o}}{\text{ + }}\left( {{{\text{p}}_{\text{2}}}^{\text{o}}{\text{ - p}}_{\text{1}}^{\text{o}}} \right){{\text{x}}_{\text{2}}}$
There is linear variation of total vapour pressure with the mole fraction of component 2 over the solution

Note: Vapour pressure is defined as the pressure exerted by the vapour in equilibrium with its condensed phases i.e, either solid or liquid. Higher the vapour pressure of liquid at a given temperature lower will be its boiling point than its actual value.