A mixture of H2(g) and N2(g) has a density of 0.216 g ·L^-1 at 300 K and 500 torr. What is the m

step 1 So here density, density equal 0 .216 gram per liter. So that means 216 gram of gas is present i

A mixture of H2(g) and N2(g) has a density of 0.216 g ·L^-1...

A mixture of $\mathrm{H}_{2}(\mathrm{g})$ and $\mathrm{N}_{2}(\mathrm{g})$ has a density of $0.216 \mathrm{g} \cdot \mathrm{L}^{-1}$ at $300 \mathrm{K}$ and 500 torr. What is the mole fraction composition of the mixture?

Key Concepts

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, provides a fundamental relation between pressure, volume, temperature, and number of moles of a gas. It is essential for connecting macroscopic measurements such as density with molecular quantities like molar mass. This law underpins many calculations in gas behavior under defined conditions.

Mole Fraction

The mole fraction is a way to express the composition of a mixture by quantifying the proportion of each component relative to the total number of moles. It is dimensionless and is used in various applications, including the calculation of partial pressures and the average molar mass of a gas mixture.

Density of a Gas

The density of a gas, defined as its mass per unit volume, can be linked to its molecular composition when combined with the ideal gas law. It serves as a measurable property that, along with pressure and temperature, can be used to infer the average molar mass of a gas mixture.

Average Molar Mass

The average molar mass of a gas mixture is calculated as the weighted sum of the molar masses of individual gases, where the weights are their mole fractions. This concept is crucial when the overall density of the gas mixture is known, as it connects macroscopic physical properties to molecular-level information.

Dalton's Law of Partial Pressures

Dalton's law states that in a mixture of non-reacting gases, the total pressure is equal to the sum of the partial pressures of the individual gases. Each partial pressure is proportional to the mole fraction of the respective gas, which is a key idea when determining the composition of a gas mixture from its physical properties.

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