(a) Calculate the mass of nitrogen present in a volume of 3000 cm^3 if the gas is at 22.0^∘ C a

step 1 Problem number 17. For question number A. To calculate the mass M, if it's employed by M equal N

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

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

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

Key Concepts

Gas Density

Density of a gas is defined as its mass per unit volume and is a critical parameter in many applications. It can be derived either directly from the mass and volume calculations or indirectly by manipulating the ideal gas law. Understanding gas density is important for comparing the behavior of different gases under similar conditions and determining real-world applicability in processes and laboratory settings.

Unit Conversions

Accurate calculations in gas law problems require converting units appropriately. For example, temperatures must be converted from Celsius to Kelvin when used in the ideal gas law, and volumes and pressures must be expressed in compatible units as specified by the gas constant R. Proper unit conversion ensures that all quantities are in the correct scale and facilitates accurate computation of properties like mass and density.

Mole Concept and Molar Mass

The mole concept is essential in chemistry for converting between the number of particles and the mass of a substance. Molar mass, defined as the mass of one mole of a substance, is used alongside the number of moles (derived from the ideal gas law) to calculate the total mass of a gas. This is especially useful for gases like nitrogen, where using its molar mass provides a direct way to convert from moles to grams or kilograms.

Ideal Gas Law

The ideal gas law (PV = nRT) links the pressure, volume, number of moles, and temperature of a gas. It is foundational for determining quantities like mass and density of a gas when other variables are known. This equation assumes that a gas behaves ideally, meaning interactions between its molecules are negligible and the volume of the molecules themselves is much smaller than the volume occupied by the gas.

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