Calculate the Ratio of Effusion Rates

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

  1. Identify the two gases you are comparing.
  2. Look up their molar masses in g/mol (usually found on a periodic table).
  3. Enter the molar mass of Gas 1 in the first field.
  4. Enter the molar mass of Gas 2 in the second field.
  5. Click "Calculate Ratio" to see how many times faster (or slower) Gas 1 moves compared to Gas 2.
function calculateEffusionRatio() { var m1 = parseFloat(document.getElementById('molarMass1').value); var m2 = parseFloat(document.getElementById('molarMass2').value); var resultDiv = document.getElementById('effusionResult'); var ratioDisplay = document.getElementById('ratioDisplay'); var explanationDisplay = document.getElementById('explanationDisplay'); if (isNaN(m1) || isNaN(m2) || m1 <= 0 || m2 <= 0) { alert("Please enter valid positive numbers for both molar masses."); return; } // Graham's Law Formula: Rate1/Rate2 = sqrt(M2/M1) var ratio = Math.sqrt(m2 / m1); var formattedRatio = ratio.toFixed(4); resultDiv.style.display = 'block'; resultDiv.style.backgroundColor = '#e8f4fd'; resultDiv.style.border = '1px solid #3498db'; ratioDisplay.innerHTML = "Effusion Ratio (R1/R2) = " + formattedRatio; if (ratio > 1) { explanationDisplay.innerHTML = "Gas 1 effuses " + formattedRatio + " times faster than Gas 2 because it is lighter."; } else if (ratio < 1) { var inverseRatio = (1 / ratio).toFixed(4); explanationDisplay.innerHTML = "Gas 1 effuses " + formattedRatio + " times as fast as Gas 2 (Gas 2 is " + inverseRatio + " times faster) because Gas 1 is heavier."; } else { explanationDisplay.innerHTML = "Both gases have the same molar mass and will effuse at the same rate."; } }

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