Gas fraction, also known as fractional concentration, is calculated by dividing the amount of a specific gas by the total amount of all gases in a mixture.
Here's a detailed breakdown:
Understanding Gas Fraction
The gas fraction represents the proportion of a particular gas in a mixture of gases. It essentially tells you how much of the total gas is made up of a specific gas. The reference video describes this as "the amount of gas A plus the amount of gas B, plus the amount of gas C" and so on, to obtain the total amount of gas in the mixture.
Calculation Steps
- Identify the gases: Determine all the individual gases present in the mixture. For example, the mixture might consist of gases A, B, and C.
- Determine the amount of each gas: Find the quantity of each individual gas. This could be in moles, number of molecules, or partial pressures, as long as all measurements are in the same units.
- Calculate the total amount of gas: Sum the quantities of all individual gases to find the total amount of gas in the mixture. According to the reference, this involves adding "the amount of gas A plus the amount of gas B, plus the amount of gas C. For our mixture here."
- Calculate the fraction of a specific gas: Divide the quantity of the specific gas by the total quantity of gas in the mixture.
Formula
The general formula for calculating the gas fraction of a specific gas "X" is:
Gas Fraction of X = (Amount of Gas X) / (Total Amount of All Gases)Example
Let's say you have a mixture containing:
- 2 moles of Gas A
- 3 moles of Gas B
- 5 moles of Gas C
- Total Amount of Gas: 2 + 3 + 5 = 10 moles
- Gas Fraction of A: 2 moles / 10 moles = 0.2 or 20%
- Gas Fraction of B: 3 moles / 10 moles = 0.3 or 30%
- Gas Fraction of C: 5 moles / 10 moles = 0.5 or 50%
Practical Insights
- Units must be consistent: When calculating gas fraction, ensure that all quantities (like moles, number of molecules, or partial pressures) are in the same units.
- Gas fractions are always less than or equal to 1: Since you are dividing a part by the whole, the resulting fraction will always be between 0 and 1 (or 0% and 100%).
- Total Gas Fractions Sum to 1: The sum of the gas fractions of all the individual gases in the mixture should add up to 1 (or 100%).
Summary Table
| Gas | Amount (moles) | Gas Fraction |
|---|---|---|
| Gas A | 2 | 0.2 |
| Gas B | 3 | 0.3 |
| Gas C | 5 | 0.5 |
| Total | 10 | 1.0 |
