Calculating the rate of diffusion in liquids is a fundamental task in chemistry, biology, and chemical engineering. Unlike solids, particles in liquids have more freedom to move, yet they are more restricted than in gases due to higher density and intermolecular forces. The primary mathematical model used to calculate this rate is Fick's First Law of Diffusion.
This calculator determines the net movement of substance (mass or moles) from a region of higher concentration to a region of lower concentration over a specific time period.
The Formula: Fick's First Law
For steady-state diffusion, the rate of diffusion is directly proportional to the surface area and the concentration gradient, and inversely proportional to the diffusion distance. The formula used is:
Rate = (D × A × (C₁ – C₂)) / L
Where:
Rate = The amount of substance diffusing per unit time (mol/s or kg/s).
D = Diffusion Coefficient (m²/s). This represents how fast a substance diffuses through a specific medium.
A = Surface Area (m²) through which diffusion occurs.
C₁ – C₂ = Concentration Difference (mol/m³ or kg/m³).
L = Diffusion Distance or membrane thickness (m).
Understanding the Variables
1. Diffusion Coefficient (D)
The diffusion coefficient is specific to the solute-solvent pair and is heavily dependent on temperature and viscosity. For example, glucose diffuses slower in cold water than in hot water.
Typical value for small molecules in water: ~10⁻⁹ m²/s
Typical value for proteins in water: ~10⁻¹¹ m²/s
2. Concentration Gradient (ΔC/L)
The "driving force" of diffusion is the difference in concentration. The steeper the gradient (higher difference over a shorter distance), the faster the rate of diffusion.
Example Calculation
Let's calculate the diffusion rate of Glucose in water across a membrane.
Temperature: Higher temperatures increase the kinetic energy of particles, increasing the Diffusion Coefficient (D).
Viscosity: More viscous liquids (like honey) offer more resistance to particle movement, lowering D.
Particle Size: According to the Stokes-Einstein equation, larger particles diffuse more slowly than smaller ones.
Why Use Molar vs. Mass Units?
This calculator works with both. If you input your concentration in mol/m³, your result will be in mol/s. If you input concentration in kg/m³, your result will be in kg/s. Consistency is key.
function calculateDiffusion() {
// 1. Get input elements
var diffCoefInput = document.getElementById('diffCoef');
var surfAreaInput = document.getElementById('surfArea');
var conc1Input = document.getElementById('conc1');
var conc2Input = document.getElementById('conc2');
var distanceInput = document.getElementById('distance');
var resultArea = document.getElementById('result-area');
var finalRateDisplay = document.getElementById('final-rate');
var fluxResultDisplay = document.getElementById('flux-result');
var errorMsg = document.getElementById('error-message');
// 2. Parse values
var D = parseFloat(diffCoefInput.value);
var A = parseFloat(surfAreaInput.value);
var C1 = parseFloat(conc1Input.value);
var C2 = parseFloat(conc2Input.value);
var L = parseFloat(distanceInput.value);
// 3. Reset display
resultArea.style.display = 'none';
errorMsg.style.display = 'none';
// 4. Validation Logic
if (isNaN(D) || isNaN(A) || isNaN(C1) || isNaN(C2) || isNaN(L)) {
errorMsg.innerText = "Please enter valid numbers for all fields.";
errorMsg.style.display = 'block';
return;
}
if (L <= 0) {
errorMsg.innerText = "Distance (L) must be greater than zero.";
errorMsg.style.display = 'block';
return;
}
if (D < 0 || A < 0) {
errorMsg.innerText = "Diffusion Coefficient and Area cannot be negative.";
errorMsg.style.display = 'block';
return;
}
// 5. Calculation Logic (Fick's First Law)
// Rate = (D * A * (C1 – C2)) / L
// We use Math.abs for concentration difference to ensure positive flow rate magnitude
var concentrationDiff = Math.abs(C1 – C2);
var rate = (D * A * concentrationDiff) / L;
// Calculate Flux (J) = Rate / A
var flux = rate / A;
// 6. Formatting Output
// Use scientific notation if the number is very small or very large
var formattedRate = (rate 1000) ? rate.toExponential(4) : rate.toFixed(6);
var formattedFlux = (flux 1000) ? flux.toExponential(4) : flux.toFixed(6);
// 7. Display Result
finalRateDisplay.innerHTML = formattedRate + " (units/s)";
fluxResultDisplay.innerHTML = "Flux (Rate/Area): " + formattedFlux + " (units/m²/s)";
resultArea.style.display = 'block';
}