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How to Calculate the Relative Molecular Mass of a Gas?

Published in Gas Molecular Mass 3 mins read

To calculate the relative molecular mass (Mr) of a gas, you can use the ideal gas equation and a simple experiment.

Understanding the Ideal Gas Equation

The ideal gas equation is:

PV = nRT

Where:

  • P is the pressure of the gas (in Pascals or atmospheres).
  • V is the volume of the gas (in cubic meters or liters).
  • n is the number of moles of the gas.
  • R is the ideal gas constant (8.314 J/mol·K or 0.0821 L·atm/mol·K, depending on the units used for pressure and volume).
  • T is the temperature of the gas (in Kelvin).

Step-by-Step Calculation

Here's how to calculate the relative molecular mass of a gas:

  1. Collect Data:

    • Record the mass of the gas used in the experiment, for example, in a syringe.
    • Measure the volume (V) of the gas. For instance, the volume of the gas in the syringe.
    • Record the temperature (T) of the gas in Kelvin (room temperature is often adequate).
    • Record the pressure (P) of the gas in Pascals or atmospheres (room pressure).

  2. Calculate the Number of Moles (n):

    • Rearrange the ideal gas equation to solve for 'n': n = PV / RT
    • Substitute your recorded values of P, V, R, and T into the equation.
    • Calculate the number of moles (n) of the gas.

  3. Calculate the Molar Mass (Mr):

    • Molar mass is the mass of the gas in grams divided by the number of moles, given by the formula:
      Mr = mass (g) / n
    • The mass of gas in the syringe (recorded in step 1) is divided by the number of moles (calculated in step 2).
    • The result is the molar mass of the gas, which is equal to the relative molecular mass (Mr) in g/mol.

Summary in a Table

Step Action Equation
1. Data Collection Record mass, volume, temperature, and pressure of the gas.
2. Moles Calculation Calculate the number of moles (n) using the ideal gas equation. n = PV / RT
3. Molar Mass Calculation Calculate molar mass using the mass of gas and the number of moles calculated above. Mr = mass (g) / n

Practical Example

Let's say you have the following measurements for an unknown gas:

  • Mass of gas: 0.100 g
  • Volume of gas: 100 mL (0.1 L)
  • Temperature: 25 °C (298 K)
  • Pressure: 1 atm

  1. Calculate moles (n):

    n = (1 atm 0.1 L) / (0.0821 L·atm/mol·K 298 K)
    n ≈ 0.0041 mol

  2. Calculate molar mass (Mr):

    Mr = 0.100 g / 0.0041 mol
    Mr ≈ 24.4 g/mol

Therefore, the relative molecular mass (Mr) of the gas is approximately 24.4.

Key Considerations

  • Ensure accurate measurements of pressure, volume, and temperature.
  • Use consistent units for all calculations.
  • The accuracy of the result depends on the precision of your measurements.
  • The gas must be behaving ideally for this method to be accurate, this generally means low pressure and high temperature.

By following these steps, you can calculate the relative molecular mass of a gas using the ideal gas equation and experimental data.

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