Calculate the relative rate of effusion between two gases based on their molar masses.
If you leave the known rate blank, we will calculate the ratio (Rate 1 / Rate 2).
Calculated Results
How to Calculate the Effusion Rate of Gas
Effusion is the process where gas particles pass through a tiny opening into a vacuum or an area of lower pressure. The speed at which this occurs depends heavily on the mass of the gas particles. To calculate this, scientists use Graham's Law of Effusion.
The Formula for Graham's Law
The law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. The mathematical representation is:
Rate₁ / Rate₂ = √(Molar Mass₂ / Molar Mass₁)
Where:
Rate₁: The speed/rate of effusion for Gas 1.
Rate₂: The speed/rate of effusion for Gas 2.
Molar Mass₁: The molecular weight of Gas 1 in grams per mole (g/mol).
Molar Mass₂: The molecular weight of Gas 2 in grams per mole (g/mol).
Step-by-Step Calculation Example
Let's compare the effusion rates of Helium (He) and Nitrogen (N₂).
Find Molar Masses: Helium is approximately 4.00 g/mol. Nitrogen (N₂) is approximately 28.01 g/mol.
Identify Values: M₁ = 4.00, M₂ = 28.01.
Apply Formula: Ratio = √(28.01 / 4.00).
Solve: Ratio = √7.0025 ≈ 2.65.
Result: Helium effuses approximately 2.65 times faster than Nitrogen under the same conditions.
Why do lighter gases effuse faster?
According to the kinetic molecular theory, at a constant temperature, all gas particles have the same average kinetic energy (KE = ½mv²). Because the kinetic energy is the same, particles with a smaller mass (m) must have a higher velocity (v) to maintain that energy balance. Higher velocity directly translates to a faster rate of effusion through an aperture.
Practical Applications
Isotope Separation: Graham's Law was famously used to separate Uranium-235 from Uranium-238 by converting them into gas (uranium hexafluoride) and allowing them to effuse.
Gas Leak Detection: Understanding effusion helps in predicting how quickly different gases might escape through microscopic cracks in containers.
Balloon Inflation: This explains why a helium balloon deflates faster than one filled with air; helium atoms are much smaller and lighter than the nitrogen and oxygen molecules in air.
function calculateEffusion() {
var m1 = parseFloat(document.getElementById('molarMass1').value);
var m2 = parseFloat(document.getElementById('molarMass2').value);
var r2 = parseFloat(document.getElementById('knownRate').value);
var resultDiv = document.getElementById('effusionResult');
var ratioText = document.getElementById('ratioText');
var specificRateResult = document.getElementById('specificRateResult');
// Validation
if (isNaN(m1) || isNaN(m2) || m1 <= 0 || m2 <= 0) {
alert('Please enter valid positive numbers for both molar masses.');
return;
}
// Calculation: Rate1/Rate2 = sqrt(M2/M1)
var ratio = Math.sqrt(m2 / m1);
resultDiv.style.display = 'block';
ratioText.innerHTML = 'The ratio of Rate₁ to Rate₂ is: ' + ratio.toFixed(4) + '';
if (!isNaN(r2) && r2 > 0) {
var r1 = ratio * r2;
specificRateResult.innerHTML = 'Based on the known rate of Gas 2 (' + r2 + '), the Rate of Gas 1 is: ' + r1.toFixed(4) + '';
} else {
specificRateResult.innerHTML = 'Note: Gas 1 effuses ' + ratio.toFixed(2) + ' times faster/slower than Gas 2.';
}
}