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

To determine the partial pressure of gas X, we first calculate the number of moles of each gas using their masses and molar masses.

1. Calculate moles of gas X:
   Given: mass of X = 0.6 g, molar mass of X = 20 g/mol,
   moles of X = \(\frac{0.6}{20}\) = 0.03 mol.
2. Calculate moles of gas Y:
   Given: mass of Y = 0.45 g, molar mass of Y = 45 g/mol,
   moles of Y = \(\frac{0.45}{45}\) = 0.01 mol.
3. Using Dalton's Law of Partial Pressures:
   Total moles = 0.03 + 0.01 = 0.04 mol.
   Partial pressure of a gas = total pressure * (moles of the gas/total moles).
4. Calculate partial pressure of X:
   Total pressure = 740 mm Hg,
   Partial pressure of X = \(740 \times \frac{0.03}{0.04}\) = 555 mm Hg (nearest integer).
5. Verify the result falls within the expected range (555,555).
   Since 555 is within the given range, the calculation is confirmed.

The partial pressure of gas X is 555 mm Hg.