body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
max-width: 1200px;
margin: 0 auto;
padding: 20px;
}
.calculator-wrapper {
background: #f8f9fa;
border: 1px solid #e9ecef;
border-radius: 8px;
padding: 30px;
margin-bottom: 40px;
box-shadow: 0 4px 6px rgba(0,0,0,0.05);
}
.calc-header {
text-align: center;
margin-bottom: 25px;
color: #2c3e50;
}
.input-group {
margin-bottom: 20px;
}
.input-group label {
display: block;
margin-bottom: 8px;
font-weight: 600;
color: #495057;
}
.input-group input {
width: 100%;
padding: 12px;
border: 1px solid #ced4da;
border-radius: 4px;
font-size: 16px;
box-sizing: border-box;
}
.input-group .help-text {
font-size: 0.85em;
color: #6c757d;
margin-top: 5px;
}
button.calc-btn {
width: 100%;
padding: 15px;
background-color: #27ae60;
color: white;
border: none;
border-radius: 4px;
font-size: 18px;
font-weight: bold;
cursor: pointer;
transition: background-color 0.2s;
}
button.calc-btn:hover {
background-color: #219150;
}
#results-area {
margin-top: 30px;
display: none;
background: white;
padding: 20px;
border-radius: 6px;
border-left: 5px solid #27ae60;
}
.result-row {
display: flex;
justify-content: space-between;
margin-bottom: 15px;
padding-bottom: 10px;
border-bottom: 1px solid #eee;
}
.result-row:last-child {
border-bottom: none;
}
.result-label {
font-weight: 600;
color: #555;
}
.result-value {
font-weight: bold;
color: #2c3e50;
font-size: 1.1em;
}
.article-content {
background: #fff;
padding: 20px;
}
h2 {
color: #2c3e50;
border-bottom: 2px solid #ecf0f1;
padding-bottom: 10px;
margin-top: 30px;
}
p {
margin-bottom: 15px;
}
.formula-box {
background: #e8f6f3;
padding: 15px;
border-radius: 5px;
font-family: "Courier New", Courier, monospace;
margin: 15px 0;
}
.error-msg {
color: #e74c3c;
font-weight: bold;
text-align: center;
display: none;
margin-bottom: 15px;
}
function calculateDiffusion() {
// Get input values
var side = parseFloat(document.getElementById("cubeSide").value);
var depth = parseFloat(document.getElementById("diffusionDepth").value);
var time = parseFloat(document.getElementById("timeElapsed").value);
var errorDisplay = document.getElementById("error-display");
var resultsArea = document.getElementById("results-area");
// Reset display
errorDisplay.style.display = "none";
errorDisplay.innerHTML = "";
resultsArea.style.display = "none";
// Validation
if (isNaN(side) || side <= 0) {
errorDisplay.innerHTML = "Please enter a valid positive number for the Cube Side Length.";
errorDisplay.style.display = "block";
return;
}
if (isNaN(depth) || depth < 0) {
errorDisplay.innerHTML = "Please enter a valid number for the Diffusion Depth.";
errorDisplay.style.display = "block";
return;
}
if (isNaN(time) || time <= 0) {
errorDisplay.innerHTML = "Please enter a valid positive number for Time Elapsed.";
errorDisplay.style.display = "block";
return;
}
// Logic for full saturation
// If depth * 2 is greater than or equal to side, the whole cube is pink/diffused.
// We calculate the inner "dry" cube side length.
var innerSide = side – (2 * depth);
// Handle full diffusion overlap
if (innerSide < 0) {
innerSide = 0;
}
// Calculate Volumes
var totalVolume = Math.pow(side, 3);
var innerVolume = Math.pow(innerSide, 3);
var diffusedVolume = totalVolume – innerVolume;
// Calculate Percent
var percentDiffusion = (diffusedVolume / totalVolume) * 100;
// Calculate Rate (Speed)
var diffusionRate = depth / time;
// Calculate Surface Area and Ratio
var surfaceArea = 6 * Math.pow(side, 2);
var saToVolRatio = surfaceArea / totalVolume;
// Display Results
document.getElementById("res-rate").innerHTML = diffusionRate.toFixed(4) + " mm/min";
document.getElementById("res-total-vol").innerHTML = totalVolume.toFixed(2);
document.getElementById("res-diff-vol").innerHTML = diffusedVolume.toFixed(2);
document.getElementById("res-percent").innerHTML = percentDiffusion.toFixed(2) + "%";
document.getElementById("res-sa").innerHTML = surfaceArea.toFixed(2);
document.getElementById("res-ratio").innerHTML = saToVolRatio.toFixed(3) + " : 1";
resultsArea.style.display = "block";
}
How to Calculate Rate of Diffusion in Agar
Understanding how substances move into and out of cells is a fundamental concept in biology. The agar cube experiment is a classic laboratory demonstration used to model cell size limitations and diffusion efficiency. This guide covers how to calculate the rate of diffusion, percent diffusion, and the surface area to volume ratio using experimental data.
The Agar Cube Experiment Explained
In this experiment, agar cubes containing a pH indicator (often phenolphthalein) are used to represent cells. These cubes are submerged in an acidic or basic solution (like sodium hydroxide or vinegar). As the solution diffuses into the agar, the indicator changes color, allowing you to visually measure how far the substance has traveled into the "cell."
Step 1: Calculating Surface Area and Volume
Before analyzing diffusion, you must understand the geometry of your cube. This helps determine the Surface Area to Volume Ratio (SA:V), which is critical for understanding why cells are microscopic.
Surface Area (SA) = Side Length × Side Length × 6
Total Volume (V) = Side Length³
SA:V Ratio = Surface Area ÷ Total Volume
A higher SA:V ratio indicates that a cell is more efficient at moving materials across its membrane relative to its internal volume.
Step 2: Calculating Rate of Diffusion
The rate of diffusion tells you the speed at which particles are moving through the agar medium. This is a linear measurement.
Rate of Diffusion = Depth of Diffusion (mm) ÷ Time (min)
For example, if the solution penetrated 2mm into the cube over the course of 10 minutes, the rate is 0.2 mm/min. Generally, the rate of diffusion is constant regardless of the cube size, provided the concentration gradient and temperature remain stable.
Step 3: Calculating Percent Diffusion
Percent diffusion measures how much of the total volume of the cube has been reached by the solution. This requires calculating the volume of the inner, un-diffused section and subtracting it from the total volume.
1. Total Volume = Side³
2. Inner (Un-diffused) Side = Side – (2 × Depth)
3. Inner Volume = (Inner Side)³
4. Diffused Volume = Total Volume – Inner Volume
5. % Diffusion = (Diffused Volume ÷ Total Volume) × 100
Note: We subtract (2 × Depth) from the side length because diffusion occurs from all sides simultaneously (left and right, top and bottom, front and back).
Why Does This Matter?
In biology, this calculation demonstrates that while the rate (speed) of diffusion might be similar across different cell sizes, the efficiency (percent diffusion) drops drastically as the cell gets larger. Large cells have a lower SA:V ratio, making it difficult to transport enough nutrients to the center of the cell, which is why cells divide rather than growing indefinitely.
Example Calculation
Imagine a 20mm agar cube soaked for 10 minutes, resulting in a 2mm pink border.
- Total Volume: 20³ = 8,000 mm³
- Inner Side: 20 – (2×2) = 16mm
- Inner Volume: 16³ = 4,096 mm³
- Diffused Volume: 8,000 – 4,096 = 3,904 mm³
- Percent Diffusion: (3,904 / 8,000) × 100 = 48.8%