The mean molar mass (also known as average molar mass) is the weighted average of the molar masses of a mixture of substances. It's particularly important when dealing with gas mixtures. The formula to calculate mean molar mass is:
M = (n1M1 + n2M2 + n3M3 + ... ) / (n1 + n2 + n3 + ...)
Where:
- M is the mean molar mass of the mixture.
- n1, n2, n3, ... are the number of moles of each component in the mixture.
- M1, M2, M3, ... are the molar masses of each individual component.
Alternatively, if you know the mole fractions:
If mole fractions (xi) of each component are given instead of the number of moles (ni), the formula simplifies to:
M = x1M1 + x2M2 + x3M3 + ...
Where:
- x1, x2, x3, ... are the mole fractions of each component in the mixture.
- M1, M2, M3, ... are the molar masses of each individual component.
Example:
Consider a mixture of 2 moles of Nitrogen (N2) and 3 moles of Oxygen (O2).
- Molar mass of N2 (M1) = 28 g/mol
- Molar mass of O2 (M2) = 32 g/mol
- n1 = 2 moles
- n2 = 3 moles
Using the first formula:
M = (2 28 + 3 32) / (2 + 3)
M = (56 + 96) / 5
M = 152 / 5
M = 30.4 g/mol
Therefore, the mean molar mass of the mixture is 30.4 g/mol.
