Question

What is the density of each gas at STP? a) \(\mathrm{H}_{2}\) b) \(\mathrm{O}_{2}\) c) \(\mathrm{N}_{2}\)

Short answer

The densities at STP are: \(\mathrm{H}_2\) - 0.0893 g/L, \(\mathrm{O}_2\) - 1.429 g/L, \(\mathrm{N}_2\) - 1.250 g/L.

Step-by-step solution

Understand STP Conditions

STP (Standard Temperature and Pressure) is defined as a temperature of 0 degrees Celsius (273.15 K) and a pressure of 1 atm. At STP, 1 mole of any ideal gas occupies 22.4 liters.

Find Molar Mass of Each Gas

To calculate the density, we first need the molar mass of each gas. - For hydrogen (\(\mathrm{H}_2\)), the molar mass is 2 g/mol.- For oxygen (\(\mathrm{O}_2\)), the molar mass is 32 g/mol.- For nitrogen (\(\mathrm{N}_2\)), the molar mass is 28 g/mol.

Use Density Formula

Density of a gas at STP can be calculated using the formula: \[ \text{Density} = \frac{\text{Molar Mass}}{\text{Volume at STP}} \]Replace the molar mass with appropriate values for each gas.

Calculate Density of \(\mathrm{H}_2\)

Density of \(\mathrm{H}_2\):\[ \text{Density} = \frac{2 \text{ g/mol}}{22.4 \text{ L/mol}} \approx 0.0893 \text{ g/L} \]

Calculate Density of \(\mathrm{O}_2\)

Density of \(\mathrm{O}_2\):\[ \text{Density} = \frac{32 \text{ g/mol}}{22.4 \text{ L/mol}} \approx 1.429 \text{ g/L} \]

Calculate Density of \(\mathrm{N}_2\)

Density of \(\mathrm{N}_2\):\[ \text{Density} = \frac{28 \text{ g/mol}}{22.4 \text{ L/mol}} \approx 1.250 \text{ g/L} \]

Key concepts

Molar Mass Calculation

Calculating the molar mass of a gas is a crucial step in determining its density at standard temperature and pressure (STP). Each gas has a unique molar mass, which is the mass of one mole of its molecules.

To find the molar mass, you need to know the atomic masses of the elements that make up the gas, as listed on the periodic table. For diatomic gases like hydrogen (\( \mathrm{H}_2 \)), oxygen (\( \mathrm{O}_2 \)), and nitrogen (\( \mathrm{N}_2 \)), this means multiplying the atomic mass by two because they each consist of two atoms bound together.

• For \( \mathrm{H}_2 \): the atomic mass of hydrogen is roughly 1 g/mol, so the molar mass is \( 2 \times 1 \text{ g/mol} = 2 \text{ g/mol} \).
• For \( \mathrm{O}_2 \): the atomic mass of oxygen is approximately 16 g/mol, leading to a molar mass of \( 2 \times 16 \text{ g/mol} = 32 \text{ g/mol} \).
• For \( \mathrm{N}_2 \): with nitrogen's atomic mass around 14 g/mol, the molar mass comes to \( 2 \times 14 \text{ g/mol} = 28 \text{ g/mol} \).

Once you have the molar masses, you can proceed to calculate the gas density using these values.

Ideal Gas Law

The ideal gas law is an essential principle in chemistry that relates the pressure, volume, temperature, and amount of gas. It is usually expressed in the formula:\[ PV = nRT \]where:

• \( P \): The pressure of the gas
• \( V \): Volume of the gas
• \( n \): Number of moles
• \( R \): Ideal gas constant (\( 0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1} \))
• \( T \): Temperature in Kelvin

The formula describes how these properties interact in an ideal gas condition, and it is fundamental for understanding gas behavior. At STP, these variables are set at easily measurable conditions, allowing us to predict certain behaviors using the formula.

Though not directly used for calculating density in this exercise, knowing the ideal gas law helps understand why 1 mole of a gas occupies 22.4 liters at STP. It provides the basis for many computations in gas chemistry and allows extrapolation to different conditions beyond STP.

Standard Temperature and Pressure (STP)

Understanding the conditions of standard temperature and pressure (STP) is vital when calculating gas densities. STP serves as a baseline for measurements and calculations involving gases.

At STP, the temperature is set at 0 degrees Celsius (273.15 Kelvin), and the pressure is precisely 1 atmosphere.

• The significance of these conditions is that they standardize measurements across different gases, allowing for consistent comparison.
• One mole of any ideal gas at STP occupies 22.4 liters, a figure frequently used in calculations involving gases.

These standard conditions make it simpler to calculate properties like density without needing to recalibrate for temperature or pressure variations. By knowing this, students can easily convert other gaseous properties or predict behavior under different conditions. This foundational concept ensures that calculations involving gases remain universally accurate and comprehensible.