An 8.40-g sample of argon and an unknown mass of H2 are mixed in a flask at room temperature. The partial pressure of the argon is 44.0 kPa, and that of the hydrogen is 57.33 kPa. What is the mass of the hydrogen?

Verified step by step guidance

1. Identify the known values: mass of argon (8.40 g), partial pressure of argon (44.0 kPa), and partial pressure of hydrogen (57.33 kPa).
2. Use the ideal gas law in the form of \( PV = nRT \) to find the number of moles of argon. Assume the volume and temperature are constant for both gases.
3. Calculate the number of moles of argon using its molar mass (39.95 g/mol) and the given mass.
4. Use the ratio of partial pressures to find the number of moles of hydrogen, since \( \frac{P_{\text{H}_2}}{P_{\text{Ar}}} = \frac{n_{\text{H}_2}}{n_{\text{Ar}}} \).
5. Calculate the mass of hydrogen using the number of moles of hydrogen and its molar mass (2.02 g/mol).

Key Concepts

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of each individual gas. This principle allows us to analyze the behavior of gases in a mixture, as each gas contributes to the total pressure independently of the others.

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 is essential for calculating the properties of gases under various conditions and can be used to find the number of moles of hydrogen in this scenario, given its partial pressure.

Molar Mass and Mass Calculations

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. To find the mass of hydrogen in the mixture, we can first determine the number of moles using the Ideal Gas Law and then convert this to mass using the molar mass of hydrogen (approximately 2.02 g/mol).