To calculate the molar mass of a gas, you need to use a rearranged form of the ideal gas law, incorporating the relationship between moles and mass. Here’s how it works:
Understanding the Relationship
The foundation lies in the ideal gas law:
-
PV = nRT
- Where:
- P = Pressure
- V = Volume
- n = Number of moles
- R = Ideal gas constant
- T = Temperature
- Where:
We also know that the number of moles (n) is related to mass (m) and molar mass (M) through the formula:
- M = m / n
Deriving the Molar Mass Formula
The reference indicates that we can rearrange the ideal gas law to solve for 'n':
- n = PV / RT
Then, substituting this expression for 'n' into the molar mass equation:
- M = m / (PV/RT)
Which simplifies to:
- M = mRT / PV
This equation directly gives you the molar mass (M) of a gas.
Applying the Formula:
To use this equation:
- Measure: Obtain the mass (m) of the gas sample.
- Measure: Determine the pressure (P), volume (V), and temperature (T) of the gas.
- Know: The ideal gas constant (R) is a known value (e.g., 0.0821 L·atm/mol·K or 8.314 J/mol·K, depending on the units).
- Calculate: Plug your measurements into the formula M = mRT / PV to find the molar mass (M) of the gas.
Example:
Let's say you have a gas sample with:
- m = 1 gram
- P = 1 atm
- V = 0.821 liters
- T = 300 K
- R = 0.0821 L·atm/mol·K
Then:
- M = (1 g 0.0821 L·atm/mol·K 300 K) / (1 atm * 0.821 L)
- M = 30 g/mol (approximately)
So, the molar mass of this gas is approximately 30 g/mol.
Summary:
- The molar mass of a gas is calculated by the following formula M = m R T / P V where:
- M is the molar mass
- m is the mass of the gas
- R is the ideal gas constant
- T is the temperature
- P is the pressure
- V is the volume
