A mixture of 8.0 g CH₄ and 8.0 g Xe is placed in a container and the total pressure is found to be 0.44 atm. Determine the partial pressure of CH₄.

Verified step by step guidance

1. Calculate the number of moles of CH4 using its molar mass (16.04 g/mol).
2. Calculate the number of moles of Xe using its molar mass (131.29 g/mol).
3. Determine the total number of moles in the mixture by adding the moles of CH4 and Xe.
4. Use the ideal gas law to find the mole fraction of CH4: \( \text{Mole fraction of CH4} = \frac{\text{moles of CH4}}{\text{total moles}} \).
5. Calculate the partial pressure of CH4 using its mole fraction and the total pressure: \( P_{\text{CH4}} = \text{Mole fraction of CH4} \times \text{Total pressure} \).

Key Concepts

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of gases, the total pressure exerted is equal to the sum of the partial pressures of each individual gas. Each gas in the mixture behaves independently, contributing to the total pressure based on its mole fraction and the total number of moles present.

Mole Fraction

The mole fraction is a way of expressing the concentration of a component in a mixture. It is calculated by dividing the number of moles of the component by the total number of moles of all components in the mixture. This value is crucial for determining the partial pressure of each gas using Dalton's Law.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law helps in understanding the behavior of gases under various conditions and is essential for calculating the partial pressures when the total pressure and the amounts of gases are known.