Question

The total pressure of a mixture of non-reacting gases $X (0.6 \,g )$ and $Y (0.45 \, g )$ in a vessel is $740 mm$ of $Hg$ The partial pressure of the gas $X$ is ____$mm$ of $Hg$(Nearest Integer)(Given : molar mass $X =20$ and $Y =45 \, g \, mol ^{-1}$ )

Hint:

The mole fraction of a gas in a mixture is given by the ratio of its moles to the total moles of all gases in the mixture. Use Dalton’s Law to find the partial pressures.

Answer 1

Correct Answer: 555

The correct answer is 555
$P_x={\chi }_X{P}_T$
$=\frac{\frac{0.6}{20}}{\frac{0.6}{20}+\frac{0.45}{45}}\times 740$
$P_X=555mmHg$

Answer 2

We can use Dalton's law of partial pressures to find the partial pressure of gas X:

\[ P_X = \chi_X P_T \]

Where:

• \(\chi_X\) is the mole fraction of gas X, and
• \(P_T\) is the total pressure.

First, calculate the moles of gases X and Y:

\[ \text{Moles of X} = \frac{0.6}{20} = 0.03 \, \text{mol}, \quad \text{Moles of Y} = \frac{0.45}{45} = 0.01 \, \text{mol} \]

Total moles:

\[ n_T = 0.03 + 0.01 = 0.04 \, \text{mol} \]

Now, calculate the mole fraction of gas X:

\[ \chi_X = \frac{0.03}{0.04} = 0.75 \]

Finally, calculate the partial pressure of X:

\[ P_X = 0.75 \times 740 = 555 \, \text{mm Hg} \]

The partial pressure of gas X is calculated by multiplying the mole fraction of gas X by the total pressure. This gives us the contribution of gas X to the overall pressure in the system.