Calculate the relative rate of diffusion between two gases based on their molar masses.
function calculateDiffusion() {
var m1 = parseFloat(document.getElementById('molarMass1').value);
var m2 = parseFloat(document.getElementById('molarMass2').value);
var resultDiv = document.getElementById('diffusion-result');
var resultText = document.getElementById('result-text');
if (isNaN(m1) || isNaN(m2) || m1 <= 0 || m2 <= 0) {
resultDiv.style.display = 'block';
resultDiv.style.borderLeftColor = '#e74c3c';
resultText.innerHTML = 'Please enter valid positive molar masses for both gases.';
return;
}
// Graham's Law: Rate1 / Rate2 = sqrt(M2 / M1)
var relativeRate = Math.sqrt(m2 / m1);
var gasAFaster = relativeRate > 1;
resultDiv.style.display = 'block';
resultDiv.style.borderLeftColor = '#3498db';
var output = 'Ratio (Rate A / Rate B):' + relativeRate.toFixed(4) + '';
if (relativeRate === 1) {
output += 'Both gases diffuse at the exact same rate because they have the same molar mass.';
} else if (gasAFaster) {
output += 'Conclusion: Gas A diffuses ' + relativeRate.toFixed(2) + ' times faster than Gas B.';
} else {
var inverseRate = 1 / relativeRate;
output += 'Conclusion: Gas A diffuses ' + relativeRate.toFixed(2) + ' times as fast as Gas B (Gas B is ' + inverseRate.toFixed(2) + ' times faster than Gas A).';
}
resultText.innerHTML = output;
}
Understanding the Diffusion Rate of a Gas
Diffusion is the physical process where molecules spread from an area of high concentration to an area of lower concentration. In chemistry and physics, calculating the speed at which this happens is critical for understanding industrial processes, respiratory functions, and atmospheric science.
Graham's Law of Effusion
The most common way to calculate the relative diffusion rate of two gases is through Graham's Law. Formulated by Thomas Graham in 1848, the law states that the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass.
Rate₁ / Rate₂ = √(Molar Mass₂ / Molar Mass₁)
Key Factors Influencing Diffusion Rate
Molecular Weight: Lighter molecules move faster. A gas with a lower molar mass will always diffuse faster than a heavier gas at the same temperature.
Temperature: As temperature increases, kinetic energy increases, leading to higher diffusion rates.
Concentration Gradient: A steeper difference in concentration between two areas increases the speed of diffusion.
Pressure: While Graham's Law focuses on mass, external pressure can influence the frequency of molecular collisions.
Practical Example Calculation
Let's compare the diffusion rates of Hydrogen (H₂) and Oxygen (O₂):
Molar Mass of Hydrogen (M₁): ~2.016 g/mol
Molar Mass of Oxygen (M₂): ~32.00 g/mol
Apply the formula: Rate(H₂) / Rate(O₂) = √(32.00 / 2.016)
Calculation: √(15.87) ≈ 3.98
Result: Hydrogen molecules diffuse approximately 4 times faster than Oxygen molecules under identical conditions.
How to Use This Calculator
To use the Graham's Law calculator above, follow these steps:
Find the molar mass of your first gas (Gas A) using a periodic table.
Find the molar mass of your second gas (Gas B).
Enter both values into the input fields.
Click "Calculate Relative Rate" to see the ratio and a comparison of which gas moves faster.
This tool is particularly useful for chemistry students and laboratory technicians who need to determine how quickly different gases will mix or escape a container.