The volume fraction of a gas component in a mixture is found by dividing the partial volume of that gas (the volume it would occupy alone at the same temperature and pressure) by the total volume of the mixture. This is equivalent to the mole fraction assuming ideal gas behavior.
Understanding Volume Fraction
Volume fraction represents the proportion of the total volume occupied by a specific gas in a mixture. It's calculated as:
Volume Fraction (A) = VA / V
Where:
- VA is the partial volume of gas A. This is the volume that gas A would occupy if it were alone at the same temperature and pressure as the mixture.
- V is the total volume of the gas mixture.
Calculating Volume Fraction Assuming Ideal Gas Behavior
For ideal gases, a significant simplification occurs. The ideal gas law states:
PV = nRT
Where:
- P is the pressure
- V is the volume
- n is the number of moles
- R is the ideal gas constant
- T is the temperature
Let's consider a gas mixture containing gas A. For gas A alone at the same temperature and pressure as the mixture, we have:
PVA = nART
Where:
- nA is the number of moles of gas A
For the entire mixture, we have:
PV = nRT
Where:
- n is the total number of moles of gas in the mixture.
Now, let's divide the first equation by the second:
(PVA) / (PV) = (nART) / (nRT)
Since P, R, and T are the same in both equations, they cancel out:
VA / V = nA / n
We recognize that VA / V is the volume fraction of gas A, and nA / n is the mole fraction of gas A. Therefore:
Volume Fraction (A) = Mole Fraction (A)
Practical Implications
This relationship is extremely useful because it allows us to determine the volume fraction directly from the mole fraction, which is often easier to measure or calculate, when the gases behave ideally.
Example
Suppose a mixture of gases has a total volume of 10 L, and it's known that the partial volume of nitrogen (N2) is 7.8 L.
The volume fraction of N2 is therefore: 7.8 L / 10 L = 0.78 or 78%.
If the gases in this mixture behave ideally, then the mole fraction of N2 is also 0.78.
Conditions for Ideal Gas Behavior
It's crucial to remember that the equivalence of volume fraction and mole fraction only holds for ideal gases. Gases behave ideally at:
- Low pressures
- High temperatures
Under these conditions, intermolecular forces between gas molecules are negligible, which is a key assumption of the ideal gas law. If the conditions are not ideal, more complex equations of state (e.g., Van der Waals equation) must be used, and the volume fraction will not be equal to the mole fraction.
