Question

Use the molar volume of a gas at STP to calculate the density (in \(\mathrm{g} / \mathrm{L}\) ) of nitrogen gas at \(\mathrm{STP}\).

Short answer

The density of nitrogen gas at STP is approximately 1.25 g/L.

Step-by-step solution

Identify the molar volume of a gas at STP

At standard temperature and pressure (STP), which is 0°C and 1 atmosphere, one mole of any gas occupies 22.4 liters.

Find the molar mass of nitrogen gas

Nitrogen gas (N2) consists of two nitrogen atoms. The atomic mass of nitrogen is approximately 14.01 g/mol, therefore the molar mass of N2 is 14.01 g/mol * 2 = 28.02 g/mol.

Calculate the density of nitrogen gas at STP

Density is mass per unit volume. Using the molar mass and the molar volume at STP, density can be calculated as follows: Density = Molar mass / Molar volume. Thus, the density of nitrogen gas at STP is 28.02 g/mol / 22.4 L/mol.

Key concepts

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is a common reference point used in chemistry to provide a standard set of conditions for comparing the properties of gases. At STP, the temperature is set at 0°C (273.15 K), and the pressure at 1 atmosphere (atm). This is significant because gases have variable volume, and comparing them at a common temperature and pressure allows for consistent calculations. For instance, at STP, one mole of any ideal gas occupies 22.4 liters, a value that is crucial when calculating gas densities, as seen in the nitrogen gas density exercise.
Understanding STP is essential for students as it serves as a baseline for many experiments and calculations involving gases. When given any gas-related problem, it's always important to check whether the conditions are at STP, because this directly affects the calculations of other properties, such as volume and density.

Molar Mass

Molar mass is a fundamental concept in chemistry, representing the mass of one mole of a substance (typically in grams per mole, g/mol). It is the sum of the atomic masses of all atoms in a molecule. For nitrogen gas (2), which consists of two nitrogen atoms, the molar mass is calculated by doubling the atomic mass of nitrogen, because there are two nitrogen atoms in the molecule. In our case, the atomic mass of nitrogen is about 14.01 g/mol, so the molar mass of 2 is 28.02 g/mol. Molar mass serves as a bridge between the microscopic world of atoms and molecules and the macroscopic world we measure in the lab. It allows us to convert between the number of moles of a substance and its mass, which is key in stoichiometric calculations and when determining the density of gases, as with our nitrogen example.

Density of Nitrogen Gas

Density is a characteristic property of matter, defined as mass per unit volume. The density of nitrogen gas specifically at STP can be calculated using its molar mass and the known molar volume of a gas at these conditions. As indicated in the solution, nitrogen's molar mass (28.02 g/mol) and the standard molar volume (22.4 L/mol) gives us the density of nitrogen at STP by dividing the molar mass by the molar volume.
Understanding density is imperative for predicting how substances will interact in different scenarios, such as whether a gas will rise or sink in air. In practical applications, density calculations of gases are used in industries ranging from aerodynamics to the medical field, where the density of breathable gases needs to be controlled and monitored.

Gas Laws

The behavior of gases is described by a series of fundamental principles known as the gas laws. These include Boyle's Law, Charles's Law, Gay-Lussac's Law, Avogadro's Law, and the combined gas law. These laws interrelate the properties of gases, such as pressure (P), volume (V), temperature (T), and the number of moles (n).
For example, Avogadro's Law states that at constant temperature and pressure, the volume of a gas is directly proportional to the amount of moles of gas present. The Ideal Gas Law, which is derived from a combination of the previous laws, is often written as PV = nRT, where R is the universal gas constant. These laws are foundational when working with gases, as they allow us to predict and calculate one property if others are known, as we did while establishing the molar volume of a gas at STP in the given nitrogen gas density problem.