Diffusion Rate Calculator

Diffusion Rate Calculator

Units: m²/s (e.g., m²/s)
Units: mol/m⁴ (e.g., mol/m⁴)
Units: m² (e.g., m²)

Results:

Understanding Diffusion Rate

Diffusion is the net movement of anything generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in chemical potential of a diffusion species, which is usually a consequence of uniform differences in concentration. In physics, it is the net movement of particles from a region of higher concentration to a region of lower concentration due to random thermal motion.

Fick's First Law of Diffusion describes the rate of diffusion. It states that the diffusion flux (J) of a substance is proportional to the negative of the concentration gradient. Mathematically, this is expressed as:

J = -D * (dC/dx)

Where:

  • J is the diffusion flux (amount of substance crossing a unit area per unit time, e.g., mol/(m²·s)).
  • D is the diffusion coefficient, a measure of how quickly a substance diffuses through another (units: m²/s).
  • dC/dx is the concentration gradient, the rate of change of concentration with distance (units: mol/m⁴).

The Diffusion Rate, which is the total amount of substance diffusing per unit time across a specific area, can be calculated by multiplying the diffusion flux by the cross-sectional area (A) through which diffusion is occurring:

Diffusion Rate = J * A = -D * (dC/dx) * A

The negative sign indicates movement from high to low concentration. For calculating the magnitude of the rate, we often consider the absolute values. This calculator focuses on the magnitude of the diffusion rate.

Example Calculation:

Imagine a scenario where a substance has a diffusion coefficient (D) of 1.5 x 10⁻⁹ m²/s. The concentration gradient across a barrier is 500 mol/m⁴. If diffusion occurs through a cross-sectional area (A) of 0.01 m², what is the diffusion rate?

Using the formula: Diffusion Rate = D * (dC/dx) * A Diffusion Rate = (1.5 x 10⁻⁹ m²/s) * (500 mol/m⁴) * (0.01 m²) Diffusion Rate = 7.5 x 10⁻¹² mol/s

This means that approximately 7.5 x 10⁻¹² moles of the substance will diffuse across the specified area every second.

function calculateDiffusionRate() { var D = parseFloat(document.getElementById("diffusionCoefficient").value); var dCdx = parseFloat(document.getElementById("concentrationGradient").value); var A = parseFloat(document.getElementById("crossSectionalArea").value); var resultDiv = document.getElementById("result"); if (isNaN(D) || isNaN(dCdx) || isNaN(A)) { resultDiv.innerHTML = "Please enter valid numbers for all fields."; return; } // We calculate the magnitude of the diffusion rate, so we use absolute values. var diffusionRate = Math.abs(D * dCdx * A); if (isNaN(diffusionRate)) { resultDiv.innerHTML = "Calculation resulted in an invalid number. Please check your inputs."; } else { resultDiv.innerHTML = "Diffusion Rate: " + diffusionRate.toExponential(4) + " mol/s"; } } .diffusion-calculator-container { font-family: sans-serif; border: 1px solid #ddd; padding: 20px; border-radius: 8px; max-width: 700px; margin: 20px auto; background-color: #f9f9f9; } .diffusion-calculator-container h2, .diffusion-calculator-container h3 { text-align: center; color: #333; } .calculator-inputs { margin-top: 20px; display: grid; grid-template-columns: 1fr; gap: 15px; } .input-group { display: flex; flex-direction: column; } .input-group label { margin-bottom: 5px; font-weight: bold; color: #555; } .input-group input[type="number"] { padding: 10px; border: 1px solid #ccc; border-radius: 4px; font-size: 1rem; } .input-group small { font-size: 0.8em; color: #777; margin-top: 4px; } .diffusion-calculator-container button { background-color: #4CAF50; color: white; padding: 12px 20px; border: none; border-radius: 4px; cursor: pointer; font-size: 1.1rem; margin-top: 10px; transition: background-color 0.3s ease; } .diffusion-calculator-container button:hover { background-color: #45a049; } .calculator-results { margin-top: 30px; padding: 15px; background-color: #eef; border: 1px solid #ccd; border-radius: 4px; text-align: center; } #result { font-size: 1.2rem; font-weight: bold; color: #333; } .calculator-explanation { margin-top: 30px; padding-top: 20px; border-top: 1px dashed #ccc; font-size: 0.95rem; line-height: 1.6; color: #444; } .calculator-explanation h4 { margin-top: 15px; color: #333; } .calculator-explanation ul { margin-top: 5px; padding-left: 20px; } .calculator-explanation li { margin-bottom: 5px; } .calculator-explanation strong { color: #000; }

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