Calculating the Density of a Gas with a Molar Mass of 46.0 g/mol at STP

At standard temperature and pressure (STP), which is defined as 0°C (273.15 K) and 1 atmosphere (atm) pressure, one mole of an ideal gas occupies a specific volume. This volume, known as the molar volume, is 22.4 liters (L) per mole. To calculate the density of any gas under these conditions, you can use the ideal gas law and the relationship between molar mass and density.

Understanding the Ideal Gas Law and Density

The ideal gas law states that PV nRT, where:

P is the pressure of the gas V is the volume of the gas n is the number of moles of the gas R is the ideal gas constant T is the temperature of the gas

Given the condition of STP, the density of a gas can be calculated using the formula:

density (d) molar mass (M) / molar volume (V)

Calculations and Conversions

Given a molar mass of 46.0 g/mol, the molar volume at STP is 22.4 L/mol. Plugging these values into the formula:

d 46.0 g/mol / 22.4 L/mol

Performing the division yields:

d ≈ 2.05 g/L

Unit Cancellation and Dimensional Analysis

Another method to calculate the density involves using unit cancellation and dimensional analysis:

1 mole of gas 46.0 g / 22.4 L 2.05 g/L To convert g/L to g/mL, multiply by 1 L/1000 mL: 2.05 g/L × 1 L/1000 mL 0.00205 g/mL

This shows that the density of the gas at STP is approximately 2.05 g/L.

Note that STP is defined as 0°C (273.15 K) and 1 atm pressure for an ideal gas, and the molar volume of a gas at these conditions is 22.4 L/mol. The molar mass and molar volume can therefore be used to calculate the density of any gas:

density 46.0 g/mol ÷ 22.4 L 2.05 g/L

Conclusion

By understanding the properties of ideal gases at STP, the relationship between molar mass, volume, and density becomes clear. This method not only helps in calculating the density but also in solving various chemistry problems involving ideal gases.

Mastering unit cancellation and dimensional analysis is crucial for accurately solving chemistry problems. Practice these skills to ensure you can tackle any related questions confidently.