The density of air at 760.0 torr and 25.0^∘ C is 1.186 g / L. (a) Calculate the average molar m

step 1 The molar mass of the gas can be calculated by taking the mass of the gas multiplied by R and th

The density of air at 760.0 torr and 25.0^∘ C is 1.186 g /...

The density of air at $760.0$ torr and $25.0^{\circ} \mathrm{C}$ is $1.186 \mathrm{~g} / \mathrm{L}$. (a) Calculate the average molar mass of air. (b) From this value, and assuming that air contains only molecular nitrogen and molecular oxygen gases, calculate the mass percent of $\mathrm{N}_{2}$ and of $\mathrm{O}_{2}$ in air.

The density of air at $760.0$ torr and $25.0^{\circ} \mathrm{C}$ is $1.186 \mathrm{~g} / \mathrm{L}$.
(a) Calculate the average molar mass of air.
(b) From this value, and assuming that air contains only molecular nitrogen and molecular oxygen gases, calculate the mass percent of $\mathrm{N}_{2}$ and of $\mathrm{O}_{2}$ in air.

Key Concepts

Calculating Composition of Gas Mixtures

Determining the composition of a gas mixture by mass percent involves correlating the average molar mass of the mixture with the molar masses of the individual gases. By setting up a system of equations that relates the mole fractions to the overall average molar mass, one can solve for the mass percentages of the components. This method is widely used in analytical chemistry to assess and control the quality of gas mixtures.

Average Molar Mass of a Mixture

For a gas mixture, the average molar mass is calculated as a weighted average based on the individual molar masses and their mole fractions in the mixture. This concept is important for understanding the overall properties of the mixture and can be derived from the density and the Ideal Gas Law, making it possible to characterize the composition of the gas.

Density and Molar Mass Relationship

In the context of the Ideal Gas Law, the density of a gas can be linked to its molar mass using the equation ? = (PM)/(RT), where ? is the density, P is the pressure, M is the molar mass, R is the gas constant, and T is the absolute temperature. This relationship allows for the determination of the average molar mass of a gas or gas mixture when the density is known.

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, is a fundamental equation in physical chemistry that relates the pressure, volume, amount, and temperature of an ideal gas. It serves as the basis for understanding the behavior of gases under various conditions and is crucial for deriving relationships involving gas density, molar mass, and other properties.

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