How to Calculate the Ratio of Effusion Rates

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Graham's Law Effusion Rate Calculator

Formula: Rate1 / Rate2 = √(Molar Mass2 / Molar Mass1)

Understanding Graham's Law of Effusion

Effusion is the process where gas particles pass through a tiny opening into a vacuum or a region of lower pressure. Graham's Law, named after the Scottish chemist Thomas Graham, provides a quantitative relationship between the effusion rate of a gas and its molar mass.

The Physics Behind the Calculation

The core principle of Graham's Law is that at a constant temperature, the kinetic energy of different gases is the same. Because kinetic energy depends on both mass and velocity (KE = ½mv²), lighter molecules must move faster than heavier molecules to maintain the same energy level. Consequently, lighter gases effuse much more rapidly than heavier ones.

How to Calculate the Ratio of Effusion Rates

To find the ratio between two gases, you follow these steps:

  1. Identify the molar masses (M) of both gases (usually found on the periodic table).
  2. Divide the molar mass of the second gas (M2) by the molar mass of the first gas (M1).
  3. Take the square root of that result.

Practical Example

Consider Hydrogen (H2) with a molar mass of 2.02 g/mol and Oxygen (O2) with a molar mass of 32.00 g/mol.

  • M1 = 2.02
  • M2 = 32.00
  • Ratio = √(32.00 / 2.02)
  • Ratio = √15.84 ≈ 3.98

This means Hydrogen gas effuses nearly 4 times faster than Oxygen gas under identical conditions.

function calculateEffusionRatio() { var m1 = parseFloat(document.getElementById('molarMass1').value); var m2 = parseFloat(document.getElementById('molarMass2').value); var resultDiv = document.getElementById('effusionResult'); if (isNaN(m1) || isNaN(m2) || m1 <= 0 || m2 <= 0) { resultDiv.style.display = 'block'; resultDiv.style.backgroundColor = '#f8d7da'; resultDiv.style.color = '#721c24'; resultDiv.innerHTML = 'Error: Please enter valid positive molar masses for both gases.'; return; } // Graham's Law: Rate1 / Rate2 = sqrt(M2 / M1) var ratio = Math.sqrt(m2 / m1); var inverseRatio = 1 / ratio; resultDiv.style.display = 'block'; resultDiv.style.backgroundColor = '#d4edda'; resultDiv.style.color = '#155724'; var html = '

Calculation Results

'; html += 'The ratio of effusion rates (Rate1 : Rate2) is ' + ratio.toFixed(4) + ''; if (ratio > 1) { html += 'Gas 1 effuses ' + ratio.toFixed(2) + ' times faster than Gas 2.'; } else if (ratio < 1) { html += 'Gas 1 effuses ' + inverseRatio.toFixed(2) + ' times slower than Gas 2.'; } else { html += 'Both gases effuse at the same rate.'; } resultDiv.innerHTML = html; }

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