Question

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

Short answer

\(1.25 \text{ g/L}\)

Step-by-step solution

Identify Given Values and Formula for Molar Volume

Recognize that the molar volume of a gas at STP (Standard Temperature and Pressure) is 22.4 L/mol. Furthermore, the molar mass of nitrogen gas (N₂) is required and can be calculated as the sum of the molar masses of two nitrogen atoms. The atomic mass of nitrogen is approximately 14.01 g/mol, therefore the molar mass of N₂ is 2 * 14.01 g/mol.

Calculate Molar Mass of Nitrogen Gas

To calculate the molar mass of nitrogen gas (N₂), multiply the atomic mass of nitrogen by two: Molar mass of N₂ = 2 * 14.01 g/mol = 28.02 g/mol.

Calculate the Density of Nitrogen Gas

Use the formula for density \(\rho = \frac{m}{V}\), where \(\rho\) is the density, m is the mass, and V is the volume. For one mole of nitrogen gas at STP, the mass is the molar mass of nitrogen and the volume is the molar volume. Thus, the density of nitrogen gas is: \(\rho = \frac{28.02 \text{ g}}{22.4 \text{ L}}\). Perform the division to obtain the density in g/L.

Final Calculation

Completing the calculation: \(\rho = \frac{28.02 \text{ g}}{22.4 \text{ L}} \approx 1.25 \text{ g/L}\), which is the density of nitrogen gas at STP.

Key concepts

STP in Chemistry

Understanding Standard Temperature and Pressure (STP) is fundamental when studying gas laws and performing calculations on gaseous substances. STP is a set of conditions used as a standard reference point for expressing the properties of gases. At STP, the temperature is defined as 0°C (273.15 K) and the pressure is set at 1 atmosphere (101.325 kPa).

At STP, one mole of an ideal gas occupies a volume of 22.4 liters, a figure that becomes instrumental in calculations involving gases. This standard molar volume is derived from the ideal gas law when applied to the specified conditions of STP. Knowing the volume of one mole of gas at STP allows chemists to make comparisons between different gases and perform stoichiometric calculations.

When working with exercises, it's important to know that these standardized conditions help create a predictable baseline for calculations, thus simplifying complex concepts and making chemistry more approachable to students.

Density Calculations

The concept of density is pivotal in a multitude of scientific disciplines, serving as a bridge between the mass of an object and the space it occupies. Density can be concisely defined as mass per unit volume and is represented by the Greek letter rho \(\rho\). In the context of gases, like nitrogen, calculating density at STP facilitates the understanding of their behavior in different scenarios.

The formula for density is \(\rho = \frac{m}{V}\), where m is the substance’s mass in grams and V is the volume in liters. This relationship can be applied to find the density of a gas once the molar mass and molar volume are known. When teaching density calculations, it's crucial to emphasize the practicality of knowing how much space a certain mass of substance will occupy, or inversely, how much mass fits within a certain volume. This concept is especially helpful in determining the quantities required for reactions and helps in visualizing the physical characteristics of substances in different states of matter.

Molar Mass of Nitrogen

Nitrogen, represented by the symbol N, is a diatomic molecule consisting of two nitrogen atoms, therefore its chemical formula is \( \text{N}_2 \). The molar mass of nitrogen gas is thus twice the atomic mass of a single nitrogen atom. Atomic mass, also known as atomic weight, is the average mass of atoms of an element, measured in atomic mass units (amu), and for nitrogen, this value is approximately 14.01 amu.

To find the molar mass of nitrogen gas (N2), we simply add the atomic masses of the two nitrogen atoms: \( 2 \times 14.01 \text{ g/mol} = 28.02 \text{ g/mol} \). This molar mass is essential in stoichiometric calculations, which allow chemists to predict the outcomes of chemical reactions. Understanding how to calculate molar mass is a foundational concept in chemistry, enabling students to link microscopic properties, like the mass of atoms, to macroscopic quantities that are more tangible and observable.