Unit: mL/s, mol/min, etc. (Leave blank for ratio only)
Please enter valid molar masses greater than zero.
Relative Rate Ratio ($r_1 / r_2$):–
Calculated Rate of Gas 2:–
Comparison:–
How to Calculate Rate of Effusion for a Gas
Effusion is the process by which gas molecules pass through a tiny hole into a vacuum or a region of lower pressure. Understanding how to calculate the rate of effusion is fundamental in physical chemistry, particularly when dealing with gas separation processes or determining the molar mass of an unknown gas.
This calculator utilizes Graham's Law of Effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Graham's Law Formula
The mathematical representation used to compare the rates of two different gases is:
Rate₁ / Rate₂ = √(M₂ / M₁)
Where:
Rate₁ = Rate of effusion for Gas 1
Rate₂ = Rate of effusion for Gas 2
M₁ = Molar mass of Gas 1
M₂ = Molar mass of Gas 2
Key Concepts of Effusion
The logic behind the calculation is rooted in kinetic molecular theory. At a constant temperature, gas molecules have the same average kinetic energy ($KE = 1/2 mv^2$). Therefore, lighter molecules (smaller mass $m$) must move at higher velocities ($v$) to maintain the same energy as heavier molecules. Consequently, lighter gases effuse faster.
Example Calculation
Let's calculate the effusion rate comparison between Hydrogen ($H_2$) and Oxygen ($O_2$).
Result: Hydrogen gas effuses approximately 3.98 times faster than Oxygen gas.
Applications
Scientists and engineers use effusion rate calculations for uranium enrichment (separating isotopes), detecting gas leaks (lighter gases leak faster), and identifying unknown gases by comparing their effusion rates against known standards.
function calculateEffusion() {
// 1. Get Input Elements
var m1Input = document.getElementById("gas1MolarMass");
var m2Input = document.getElementById("gas2MolarMass");
var r1Input = document.getElementById("gas1Rate");
// 2. Get Values
var m1 = parseFloat(m1Input.value);
var m2 = parseFloat(m2Input.value);
var r1 = parseFloat(r1Input.value); // May be NaN if empty
// 3. Error Handling
var errorDiv = document.getElementById("errorDisplay");
var resultDiv = document.getElementById("effusionResult");
if (isNaN(m1) || isNaN(m2) || m1 <= 0 || m2 0) {
// If Rate1/Rate2 = ratio, then Rate2 = Rate1 / ratio
var r2 = r1 / ratio;
document.getElementById("rate2Result").innerHTML = r2.toFixed(4) + " (units match Gas 1)";
rate2Row.style.display = "flex";
} else {
rate2Row.style.display = "none";
}
// 7. Comparison Text
var comparisonText = "";
if (m1 < m2) {
comparisonText = "Gas 1 is lighter and effuses " + ratio.toFixed(2) + "x faster than Gas 2.";
} else if (m1 > m2) {
// To make it readable, we invert the ratio for the text "Gas 2 is X times faster"
var inverseRatio = Math.sqrt(m1 / m2);
comparisonText = "Gas 1 is heavier and effuses slower. (Gas 2 is " + inverseRatio.toFixed(2) + "x faster).";
} else {
comparisonText = "Both gases have the same molar mass and effuse at the same rate.";
}
document.getElementById("comparisonText").innerHTML = comparisonText;
// 8. Show Results
resultDiv.style.display = "block";
}