A gas mixture composed of helium and argon has a density of 0.670 g/L at a 755 mmHg and 298 K. What is the composition of the mixture by volume?

Verified step by step guidance

1. Start by using the ideal gas law equation: \( PV = nRT \). Rearrange it to solve for the molar mass \( M \) of the gas mixture: \( M = \frac{dRT}{P} \), where \( d \) is the density, \( R \) is the ideal gas constant, \( T \) is the temperature in Kelvin, and \( P \) is the pressure in atm.
2. Convert the given pressure from mmHg to atm using the conversion factor: 1 atm = 760 mmHg.
3. Substitute the given values into the rearranged ideal gas law equation to calculate the molar mass of the gas mixture.
4. Let \( x \) be the mole fraction of helium in the mixture. The molar mass of the mixture can be expressed as: \( M = xM_{\text{He}} + (1-x)M_{\text{Ar}} \), where \( M_{\text{He}} \) and \( M_{\text{Ar}} \) are the molar masses of helium and argon, respectively.
5. Solve the equation for \( x \) to find the mole fraction of helium, and then calculate the mole fraction of argon as \( 1-x \). The volume percent composition is the same as the mole fraction for ideal gases.

Key Concepts

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 understanding the behavior of gases under various conditions and allows for the calculation of gas properties when given specific parameters such as pressure and temperature.

Density of Gases

The density of a gas is defined as its mass per unit volume, typically expressed in g/L. For gas mixtures, the density can be calculated using the molar masses of the individual gases and their respective mole fractions, which is crucial for determining the composition of the mixture in this question.

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 is important for analyzing gas mixtures, as it allows for the determination of the contribution of each gas to the overall pressure, which can be used to find their volume composition.