:root {
–primary-color: #2c3e50;
–secondary-color: #3498db;
–accent-color: #e74c3c;
–light-bg: #f8f9fa;
–border-radius: 8px;
}
body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
margin: 0;
padding: 20px;
}
.calculator-container {
max-width: 800px;
margin: 0 auto;
background: #fff;
padding: 30px;
border-radius: var(–border-radius);
box-shadow: 0 4px 15px rgba(0,0,0,0.1);
}
.calc-header {
text-align: center;
margin-bottom: 30px;
border-bottom: 2px solid var(–light-bg);
padding-bottom: 20px;
}
.calc-header h2 {
color: var(–primary-color);
margin: 0;
}
.input-grid {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 20px;
}
@media (max-width: 600px) {
.input-grid {
grid-template-columns: 1fr;
}
}
.form-group {
margin-bottom: 15px;
}
.form-group label {
display: block;
margin-bottom: 5px;
font-weight: 600;
color: var(–primary-color);
}
.form-group input {
width: 100%;
padding: 10px;
border: 1px solid #ddd;
border-radius: 4px;
font-size: 16px;
box-sizing: border-box;
}
.form-group input:focus {
border-color: var(–secondary-color);
outline: none;
}
.form-group .unit-hint {
font-size: 0.85em;
color: #666;
margin-top: 4px;
}
.calc-btn {
width: 100%;
padding: 12px;
background-color: var(–secondary-color);
color: white;
border: none;
border-radius: 4px;
font-size: 18px;
font-weight: bold;
cursor: pointer;
transition: background 0.2s;
margin-top: 10px;
}
.calc-btn:hover {
background-color: #2980b9;
}
.result-section {
margin-top: 30px;
padding: 20px;
background-color: var(–light-bg);
border-radius: var(–border-radius);
border-left: 5px solid var(–secondary-color);
display: none;
}
.result-title {
font-size: 1.1em;
font-weight: bold;
color: var(–primary-color);
margin-bottom: 10px;
}
.result-value {
font-size: 2em;
color: var(–secondary-color);
font-weight: bold;
}
.error-msg {
color: var(–accent-color);
font-weight: bold;
margin-top: 10px;
display: none;
}
.article-content {
max-width: 800px;
margin: 40px auto;
padding: 20px;
background: #fff;
}
.article-content h2 {
color: var(–primary-color);
border-bottom: 2px solid var(–secondary-color);
padding-bottom: 10px;
margin-top: 30px;
}
.article-content h3 {
color: var(–primary-color);
margin-top: 25px;
}
.article-content ul {
background: var(–light-bg);
padding: 20px 40px;
border-radius: 8px;
}
.article-content li {
margin-bottom: 10px;
}
.formula-box {
background: #f1f8ff;
padding: 15px;
border-radius: 5px;
font-family: 'Courier New', monospace;
text-align: center;
margin: 20px 0;
font-weight: bold;
border: 1px dashed var(–secondary-color);
}
function calculateDiffusion() {
var D = document.getElementById("diffCoef").value;
var A = document.getElementById("surfArea").value;
var C1 = document.getElementById("conc1").value;
var C2 = document.getElementById("conc2").value;
var d = document.getElementById("thickness").value;
var errorDiv = document.getElementById("errorMsg");
var resultDiv = document.getElementById("resultSection");
// Reset display
errorDiv.style.display = "none";
resultDiv.style.display = "none";
// Validation
if (D === "" || A === "" || C1 === "" || C2 === "" || d === "") {
errorDiv.innerText = "Please fill in all fields.";
errorDiv.style.display = "block";
return;
}
var numD = parseFloat(D);
var numA = parseFloat(A);
var numC1 = parseFloat(C1);
var numC2 = parseFloat(C2);
var numDThickness = parseFloat(d);
if (isNaN(numD) || isNaN(numA) || isNaN(numC1) || isNaN(numC2) || isNaN(numDThickness)) {
errorDiv.innerText = "Please enter valid numbers.";
errorDiv.style.display = "block";
return;
}
if (numDThickness === 0) {
errorDiv.innerText = "Membrane thickness cannot be zero.";
errorDiv.style.display = "block";
return;
}
if (numD < 0 || numA < 0 || numDThickness < 0) {
errorDiv.innerText = "Coefficient, Area, and Thickness must be positive numbers.";
errorDiv.style.display = "block";
return;
}
// Calculation: Fick's Law J = (D * A * (C1 – C2)) / d
// We use Math.abs for concentration difference to ensure magnitude of rate is positive
var deltaC = Math.abs(numC1 – numC2);
var rate = (numD * numA * deltaC) / numDThickness;
// Display results
document.getElementById("diffusionResult").innerText = rate.toExponential(4); // Scientific notation for precision
document.getElementById("gradientResult").innerText = deltaC.toFixed(4);
// Efficiency metric (Rate per unit area)
var efficiency = rate / numA;
document.getElementById("efficiencyResult").innerText = efficiency.toExponential(4) + " / area unit";
resultDiv.style.display = "block";
}
How to Calculate Rate of Diffusion Across a Membrane
Diffusion is a fundamental process in biology, physics, and chemistry, describing the net movement of molecules from an area of higher concentration to an area of lower concentration. When this process occurs across a permeable membrane—such as a cell membrane or a synthetic filter—the rate of this movement can be quantified using Fick's First Law of Diffusion.
Fick's Law Formula
The rate of diffusion ($J$) is determined by several key factors: the permeability of the membrane to the specific substance, the surface area available for transport, the concentration difference, and the thickness of the membrane. The mathematical representation is:
J = (D × A × ΔC) / d
Where:
- J (Rate of Diffusion): The amount of substance moving across the membrane per unit of time (e.g., mol/s).
- D (Diffusion Coefficient): A constant representing how easily a specific substance moves through a specific medium. This depends on temperature, the size of the molecule, and the viscosity of the fluid.
- A (Surface Area): The total area of the membrane available for diffusion. A larger area allows more molecules to pass through simultaneously.
- ΔC (Concentration Gradient): The difference in concentration between the two sides of the membrane ($C_1 – C_2$). The steeper the gradient, the faster the diffusion.
- d (Thickness): The distance the molecules must travel. A thicker membrane slows down the rate of diffusion.
Example Calculation
Let's look at a practical example involving oxygen diffusion across a theoretical respiratory membrane.
Parameters:
- Diffusion Coefficient ($D$): $2.0 \times 10^{-5} \, \text{cm}^2/\text{s}$
- Surface Area ($A$): $50 \, \text{cm}^2$
- Concentration High ($C_1$): $0.005 \, \text{mol/cm}^3$
- Concentration Low ($C_2$): $0.001 \, \text{mol/cm}^3$
- Membrane Thickness ($d$): $0.0002 \, \text{cm}$
Step 1: Calculate the Concentration Gradient ($ΔC$)
$ΔC = 0.005 – 0.001 = 0.004 \, \text{mol/cm}^3$
Step 2: Apply Fick's Law
Numerator = $D \times A \times ΔC$
Numerator = $(2.0 \times 10^{-5}) \times 50 \times 0.004$
Numerator = $4.0 \times 10^{-6}$
Step 3: Divide by Thickness
$J = 4.0 \times 10^{-6} / 0.0002$
$J = 0.02 \, \text{mol/s}$
Factors Affecting Diffusion Rate
Understanding these variables helps in various fields, from drug delivery systems to environmental engineering.
- Membrane Thickness: This is inversely proportional to the rate. This is why respiratory surfaces in lungs (alveoli) are extremely thin—to maximize gas exchange.
- Surface Area: Directly proportional. Microvilli in the human intestine increase surface area drastically to aid nutrient absorption.
- Concentration Gradient: The driving force of simple diffusion. Without a difference in concentration, net diffusion is zero.
- Temperature: While not a direct input in the simplified formula above, temperature affects the Diffusion Coefficient ($D$). Higher temperatures increase molecular kinetic energy, increasing $D$ and thus the rate of diffusion.
Unit Consistency
When using the calculator above, it is critical to ensure your units are consistent. If your Area is in $m^2$, your Diffusion Coefficient should be in $m^2/s$, your Concentration in $mol/m^3$, and your Thickness in $m$. Mixing units (e.g., cm for thickness but meters for area) will result in incorrect calculations unless manually converted beforehand.