The molecular weight of a gas can be calculated by determining its density at Standard Temperature and Pressure (STP) and then using a conversion factor.
Steps to Calculate Molecular Weight:
Here's a breakdown of the process, incorporating the information provided in the reference:
-
Measure Gas Weight and Volume: Determine the weight of a known volume of the gas.
-
Convert to STP: Adjust the measured volume to its equivalent volume at STP (Standard Temperature and Pressure) using Boyle's and Charles' laws.
- Boyle's Law relates pressure and volume: P₁V₁ = P₂V₂ (at constant temperature).
- Charles's Law relates volume and temperature: V₁/T₁ = V₂/T₂ (at constant pressure).
- Combining these allows you to adjust the volume from your measurement conditions to STP (0°C or 273.15K and 1 atm).
-
Calculate Density: Divide the measured weight of the gas by its STP volume. This provides the density of the gas in mass per unit volume.
-
Determine Molecular Weight: Multiply the density of the gas by 22.4 mol⁻¹. This conversion factor arises from the molar volume of an ideal gas at STP (22.4 liters per mole). This yields the molecular weight of the gas.
- Example: Let's say you've found the density of the gas at STP to be 1.25 g/L.
- Molecular Weight = 1.25 g/L * 22.4 L/mol = 28 g/mol
- The result indicates a molecular weight of approximately 28 g/mol, as can be found in gases like Nitrogen (N₂).
Why This Works:
- At STP, one mole of any ideal gas occupies approximately 22.4 liters. This is the molar volume of an ideal gas.
- Density (mass per unit volume) relates the mass of a substance to its volume.
- By multiplying the density by the molar volume, we are effectively converting the mass of gas in a given volume to mass per mole, which is the definition of molecular weight.
Summary Table:
| Step | Description | Formula(s) |
|---|---|---|
| 1. Measure Weight and Volume | Determine mass and volume of the gas sample. | |
| 2. Convert to STP | Adjust measured volume to STP using Boyle's and Charles' laws. | P₁V₁/T₁ = P₂V₂/T₂ |
| 3. Calculate Density | Divide mass of the gas by its STP volume. | Density = Mass / Volume |
| 4. Determine Molecular Weight | Multiply density by the molar volume of an ideal gas at STP (22.4 L/mol) | Molecular Weight = Density * 22.4 L/mol |
This method provides a clear, direct way to determine the molecular weight of a gas using its density and the universal gas constant as the core.
