Question

Two non - reactive gases A and B are present in a container with partial pressures 200 and 180 mm of Hg. When a third non - reactive gas C is added, the total pressure becomes 1 atm. Then mole fraction of C will be:
(A) 0.225
(B) 0.75
(C) 0.5
(D) None of these

Answer 1

Hint: Use Dalton’s law of partial pressures, which states that the total pressure of a mixture of gases is the sum of partial pressures of its components.
- From the ideal gas law, we can deduce that partial pressure of any gas in a mixture is the total pressure multiplied by mole fraction of that gas. This can be used to find the mole fraction.
- 1 atm = 760 mm Hg.
Equation used:
- Dalton’s law of partial pressures - ${{P}_{total}}={{P}_{A}}+{{P}_{B}}+{{P}_{C}}$
- Ideal gas law - ${{P}_{C}}={{P}_{total}}\times {{X}_{C}}$

Complete answer:
- We have been given the partial pressure of A (${{P}_{A}}$ ) and the partial pressure of B (${{P}_{B}}$ ) as 200 and 180 mm of Hg respectively.
- We have also been given the total pressure (${{P}_{total}}$ ) as 1 atm.
- We know that 1 atm = 760 mm Hg.
- The Dalton’s law of partial pressures states that the total pressure of a mixture of gases is the sum of partial pressures of its components.
- The Dalton’s law can hence be used to calculate the partial pressure of C (${{P}_{C}}$ )
- We have the Dalton’s law, ${{P}_{total}}={{P}_{A}}+{{P}_{B}}+{{P}_{C}}$

- We can rearrange the terms to get partial pressure of C as -
${{P}_{C}}={{P}_{total}}-{{P}_{A}}-{{P}_{B}}$
- Substituting the values of ${{P}_{total}}$, ${{P}_{A}}$ and${{P}_{B}}$, we get the value of ${{P}_{C}}$ as –
${{P}_{C}}=760-200-180=380mmHg$

- We can now use the value of ${{P}_{C}}$ to find the mole fraction of C by using the ideal gas law.
- From the ideal gas law, we can deduce that partial pressure of any gas in a mixture is the total pressure multiplied by mole fraction of that gas. This can be used to find the mole fraction.
- For C, the ideal gas law will be - ${{P}_{C}}={{P}_{total}}\times {{X}_{C}}$, where ${{X}_{C}}$ is the mole fraction of C.

- Rearranging, the terms, we get - ${{X}_{C}}={{P}_{C}}/{{P}_{total}}$

- We can now substitute the values of ${{P}_{C}}$ and ${{P}_{total}}$ to get the value of ${{X}_{C}}$ as -

${{X}_{C}}=380/760=0.5$

- Hence the correct answer is option (C) 0.5

Note: The fact that the term non-reactive is mentioned in the question is very important. If any sort of reaction occurs, these equations cannot be used directly as there will be a new product formed.