function calculateDiffusion() {
// Get Input Values
var m1 = parseFloat(document.getElementById('molarMass1').value);
var m2 = parseFloat(document.getElementById('molarMass2').value);
var rate2 = parseFloat(document.getElementById('knownRate').value);
var resultBox = document.getElementById('calc-results');
var resultRatio = document.getElementById('result-ratio');
var resultText = document.getElementById('result-text');
var resultRateA = document.getElementById('result-rate-a');
var rateRow = document.getElementById('specific-rate-row');
// Validation
if (isNaN(m1) || isNaN(m2) || m1 <= 0 || m2 1) {
resultText.innerHTML = "Gas A diffuses " + ratio.toFixed(2) + "x faster than Gas B.";
} else if (ratio < 1) {
var inverse = 1 / ratio;
resultText.innerHTML = "Gas A diffuses " + inverse.toFixed(2) + "x slower than Gas B.";
} else {
resultText.innerHTML = "Both gases diffuse at the same rate.";
}
// Calculate Specific Rate if Rate 2 is provided
if (!isNaN(rate2) && rate2 > 0) {
var rate1 = ratio * rate2;
rateRow.style.display = "flex";
resultRateA.innerHTML = rate1.toFixed(4) + " (units match input)";
} else {
rateRow.style.display = "none";
}
}
How to Calculate the Rate of Diffusion
Calculating the rate of diffusion usually involves comparing the speeds at which two different gases move. This behavior is governed by Graham's Law of Effusion (often applied to diffusion), which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
In simpler terms, lighter gases travel faster than heavier gases. This calculator allows you to determine how much faster one gas diffuses compared to another, or to solve for a specific rate if one is known.
Rate₁ / Rate₂ = √(M₂ / M₁)
Understanding the Variables
Rate₁ ($Rate_A$): The rate of diffusion for the first gas (Gas A).
Rate₂ ($Rate_B$): The rate of diffusion for the second gas (Gas B).
M₁ ($M_A$): The molar mass of the first gas, usually expressed in grams per mole (g/mol).
M₂ ($M_B$): The molar mass of the second gas (g/mol).
Step-by-Step Calculation Example
Let's calculate the relative rate of diffusion between Hydrogen ($H_2$) and Oxygen ($O_2$).
Identify Molar Masses:
Hydrogen ($H_2$): Approximately 2.02 g/mol.
Oxygen ($O_2$): Approximately 32.00 g/mol.
Set up the Formula: We want to know how much faster Hydrogen (Gas A) is compared to Oxygen (Gas B).
Formula: $\frac{Rate_{H2}}{Rate_{O2}} = \sqrt{\frac{M_{O2}}{M_{H2}}}$
Insert Values:
Ratio = $\sqrt{\frac{32.00}{2.02}}$
Ratio = $\sqrt{15.84}$
Calculate:
Ratio ≈ 3.98
Result: Hydrogen gas diffuses approximately 4 times faster than Oxygen gas.
Factors Affecting Diffusion Rate
While molar mass is the primary factor in Graham's Law, other real-world factors influence the actual rate of diffusion:
Temperature: Higher temperatures increase the kinetic energy of particles, leading to faster diffusion.
Concentration Gradient: The greater the difference in concentration between two areas, the faster the diffusion occurs (Fick's Law).
Medium: Diffusion happens much faster in gases than in liquids, and much faster in liquids than in solids.