(a) What is the number of molecules per cubic meter in air at 20^∘ C and at a pressure of 1.0 at

step 1 So we're given temperature is 20 degrees Celsius, which is 293 degrees Kelvin, and we're at one

(a) What is the number of molecules per cubic meter in air...

(a) What is the number of molecules per cubic meter in air at $20^{\circ} \mathrm{C}$ and at a pressure of 1.0 $\mathrm{atm}\left(=1.01 \times 10^{5} \mathrm{Pa}\right)$ ? (b) What is the mass of 1.0 $\mathrm{m}^{3}$ of this air? Assume that 75$\%$ of the molecules are nitrogen $\left(\mathrm{N}_{2}\right)$ and 25$\%$ are oxygen $\left(\mathrm{O}_{2}\right)$ .

(a) What is the number of molecules per cubic meter in air at $20^{\circ} \mathrm{C}$ and at a pressure of 1.0 $\mathrm{atm}\left(=1.01 \times 10^{5} \mathrm{Pa}\right)$ ? (b) What is
the mass of 1.0 $\mathrm{m}^{3}$ of this air? Assume that 75$\%$ of the molecules
are nitrogen $\left(\mathrm{N}_{2}\right)$ and 25$\%$ are oxygen $\left(\mathrm{O}_{2}\right)$ .

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Key Concepts

Avogadro's Number

Avogadro's Number, approximately 6.02 x 10^23, is the number of elementary entities (atoms or molecules) in one mole of a substance. It is essential for converting the amount of gas in moles to the actual number of molecules, linking macroscopic measurements with microscopic counts.

Molar Mass and Weighted Average Calculations

The molar mass is the mass of one mole of a substance, typically expressed in grams per mole. When dealing with mixtures of gases, calculating a weighted average molar mass based on the mole or volume fractions of the constituents is crucial for determining the overall mass of the mixture.

Unit Conversions

Unit conversions are an important aspect of solving gas law problems, as they ensure consistency between the units used for pressure, volume, temperature, and energy. For example, converting temperature from Celsius to Kelvin and pressure from atmospheres to Pascals is necessary to correctly apply the ideal gas equation.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) is a fundamental relation in thermodynamics that connects the pressure, volume, temperature, and amount (in moles) of a gas. It provides a framework to compute any one of these quantities if the others are known, and is critical for determining the number of moles of a gas sample under given conditions.

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