A 1.42-g sample of helium and an unknown mass of O2 are mixed in a flask at room temperature. The partial pressure of the helium is 42.5 torr, and that of the oxygen is 158 torr. What is the mass of the oxygen?

Verified step by step guidance

1. Calculate the number of moles of helium using the ideal gas law: \( PV = nRT \). Rearrange to find \( n = \frac{PV}{RT} \). Use the given partial pressure of helium, the volume of the flask, and the temperature to find the moles of helium.
2. Use the molar mass of helium (4.00 g/mol) to convert the mass of helium to moles: \( n = \frac{1.42 \text{ g}}{4.00 \text{ g/mol}} \).
3. Apply Dalton's Law of Partial Pressures, which states that the total pressure is the sum of the partial pressures: \( P_{\text{total}} = P_{\text{He}} + P_{\text{O}_2} \).
4. Calculate the number of moles of oxygen using the ideal gas law: \( n = \frac{P_{\text{O}_2}V}{RT} \). Use the partial pressure of oxygen, the volume of the flask, and the temperature.
5. Convert the moles of oxygen to mass using the molar mass of oxygen (32.00 g/mol): \( \text{mass} = n \times 32.00 \text{ g/mol} \).

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. This principle allows us to relate the pressures of the gases in the mixture to their respective amounts, which is crucial for solving problems involving gas mixtures.

Ideal Gas Law

The Ideal Gas Law, represented as PV = nRT, relates the pressure (P), volume (V), temperature (T), and number of moles (n) of a gas. This law is essential for calculating the number of moles of a gas when its pressure and volume are known, which can then be used to find the mass of the gas using its molar mass.

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 a gas from the number of moles, one can use the formula mass = moles × molar mass. Understanding how to convert between moles and mass is vital for determining the mass of oxygen in the given problem.