What is the average molecular weight of a diving-gas mixture that contains 2.0% by volume O2 and 98.0% by volume He?

Verified step by step guidance

1. Step 1: Understand that the average molecular weight of a gas mixture can be calculated using the mole fraction and molecular weight of each component in the mixture.
2. Step 2: Convert the percentage by volume of each gas to a mole fraction. Since the gas mixture is at the same temperature and pressure, the volume percentage is equivalent to the mole fraction. Therefore, the mole fraction of O2 is 0.02 and the mole fraction of He is 0.98.
3. Step 3: Identify the molecular weights of the gases involved. The molecular weight of O2 (oxygen) is approximately 32 g/mol, and the molecular weight of He (helium) is approximately 4 g/mol.
4. Step 4: Calculate the contribution of each gas to the average molecular weight by multiplying the mole fraction of each gas by its molecular weight. For O2, multiply 0.02 by 32 g/mol. For He, multiply 0.98 by 4 g/mol.
5. Step 5: Add the contributions from each gas to find the average molecular weight of the mixture. This is done by summing the results from Step 4.

Key Concepts

Molecular Weight

Molecular weight, or molar mass, is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic weights of all atoms in a molecule. Understanding molecular weight is essential for determining the average molecular weight of a gas mixture, as it influences properties like density and behavior under various conditions.

Gas Mixture Composition

A gas mixture consists of two or more gases that can be described by their individual volume percentages or mole fractions. In this case, the mixture contains 2.0% O2 and 98.0% He by volume. The average molecular weight of the mixture can be calculated by weighing the molecular weights of the individual gases according to their proportions in the mixture.

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 gas. This principle is important for understanding how the individual components of a gas mixture contribute to its overall properties, including average molecular weight, which is influenced by the proportions of each gas present.