II (a) Calculate the mass of nitrogen present in a volume of 3000 cm^3 if the temperature of th

step 1 So first we have the density of the gas is to be equal to the pressure multiplied by the molar m

II (a) Calculate the mass of nitrogen present in a volume of...

II (a) Calculate the mass of nitrogen present in a volume of $3000 \mathrm{~cm}^{3}$ if the temperature of the gas is $22.0^{\circ} \mathrm{C}$ and the absolute pressure is $2.00 \times 10^{-13} \mathrm{~atm},$ a partial vacuum easily obtained in laboratories. The molar mass of nitrogen $\left(\mathrm{N}_{2}\right)$ is $28.0 \mathrm{~g} / \mathrm{mol}$. (b) What is the density (in $\mathrm{kg} / \mathrm{m}^{3}$ ) of the $\mathrm{N}_{2} ?$

Key Concepts

Density Calculation

Density is defined as the mass per unit volume of a substance. Once the mass of a gas is determined using the ideal gas law and molar mass, calculating density involves dividing this mass by the volume, after ensuring both are in compatible units. This concept is important in characterizing the substance's compactness or sparsity in a given space.

Ideal Gas Law

The ideal gas law is a fundamental equation in chemistry and physics described by PV = nRT, where P represents pressure, V is volume, n is the number of moles, R is the gas constant, and T is the absolute temperature. It is used to relate the macroscopic properties of gases and allows the calculation of one variable when the others are known.

Unit Conversions

Unit conversions are crucial in problems involving gases to ensure all measurements are compatible. This includes converting volumes (e.g., from cubic centimeters to liters or cubic meters), temperatures (e.g., from degrees Celsius to Kelvin), and pressures, to match the units required by the gas constant and the equations used for calculations.

Molar Mass

Molar mass is the mass of one mole of a substance and is used to transition from the amount of substance in moles to an actual mass in grams or kilograms. It plays a key role in converting the result from the ideal gas law into a tangible mass by linking the molecular scale to the macroscopic scale.

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