Graham's Law: Effusion Rate Ratio Calculator
Understanding Graham's Law of Effusion
Graham's Law of Effusion states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Effusion occurs when gas particles pass through a tiny opening into a vacuum or an area of lower pressure.
The Formula
Rate1 / Rate2 = √(M2 / M1)
Where:
- Rate1: Effusion rate of the first gas.
- Rate2: Effusion rate of the second gas.
- M1: Molar mass of gas 1.
- M2: Molar mass of gas 2.
Why Molar Mass Affects Effusion
At a constant temperature, all gas molecules have the same average kinetic energy. Since kinetic energy is defined by the formula KE = ½mv², lighter molecules (those with lower molar mass) must travel at higher velocities to maintain the same kinetic energy as heavier molecules. Consequently, lighter gases effuse through small openings faster than heavier ones.
Practical Examples
Example 1: Hydrogen vs. Oxygen
Hydrogen gas (H2) has a molar mass of ~2.02 g/mol. Oxygen gas (O2) has a molar mass of ~32.00 g/mol.
Ratio = √(32.00 / 2.02) = √15.84 ≈ 3.98.
Result: Hydrogen effuses nearly 4 times faster than Oxygen.
Example 2: Helium vs. Nitrogen
Helium (He) is 4.00 g/mol. Nitrogen (N2) is 28.01 g/mol.
Ratio = √(28.01 / 4.00) = √7.00 ≈ 2.65.
Result: Helium atoms move 2.65 times faster than Nitrogen molecules.
How to Use This Calculator
- Identify the two gases you are comparing.
- Look up their molar masses in g/mol (usually found on a periodic table).
- Enter the molar mass of Gas 1 in the first field.
- Enter the molar mass of Gas 2 in the second field.
- Click "Calculate Ratio" to see how many times faster (or slower) Gas 1 moves compared to Gas 2.