How to Calculate Dissolution Rate

Dissolution Rate Calculator (Noyes-Whitney Equation)

Formula: dc/dt = (D × A / h) × (Cs – Cb)

Instantaneous Dissolution Rate (dc/dt):
0.00 mg/s

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Understanding Dissolution Rate and the Noyes-Whitney Equation

In pharmaceutics and chemistry, the dissolution rate is the speed at which a solid substance dissolves in a solvent to form a solution. This process is critical for drug absorption in the human body, as a drug must be in solution form before it can cross biological membranes.

The Physics of Dissolution

The calculation of dissolution rate is most commonly performed using the Noyes-Whitney Equation. This formula describes how a solute moves from the solid phase into the bulk liquid through a thin, stagnant layer of liquid surrounding the solid particle, known as the "diffusion layer."

Key Components of the Calculation

• Diffusion Coefficient (D): This represents how fast molecules move through the solvent. Higher temperatures typically increase this value.
• Surface Area (A): The total area of the solid exposed to the liquid. This is why crushing a tablet (increasing surface area) speeds up dissolution.
• Saturation Solubility (Cs): The maximum amount of the substance that can dissolve in the solvent at a specific temperature.
• Bulk Concentration (Cb): The amount of substance already dissolved in the surrounding liquid.
• Diffusion Layer Thickness (h): The thickness of the stagnant liquid film. Agitation (stirring) reduces this thickness, thereby increasing the dissolution rate.

Example Calculation

Imagine a drug particle with a surface area of 2 cm² and a diffusion coefficient of 0.00001 cm²/s. If the stagnant layer thickness is 0.002 cm, the saturation solubility is 10 mg/cm³, and the current concentration in the beaker is 1 mg/cm³:

Rate = (0.00001 × 2 / 0.002) × (10 – 1)
Rate = (0.01) × (9)
Rate = 0.09 mg/s

Factors That Increase Dissolution Rate

1. Increasing Agitation: Reduces 'h' (thickness), speeding up the process.
2. Decreasing Particle Size: Increases 'A' (surface area).
3. Increasing Temperature: Usually increases 'D' and 'Cs'.
4. Changing Solvent: Can significantly alter 'Cs' (solubility).

function calculateDissolutionRate() { var D = parseFloat(document.getElementById("diffusionCoeff").value); var A = parseFloat(document.getElementById("surfaceArea").value); var Cs = parseFloat(document.getElementById("saturationSol").value); var Cb = parseFloat(document.getElementById("bulkConc").value); var h = parseFloat(document.getElementById("layerThickness").value); var resultDiv = document.getElementById("dissolutionResult"); var rateSpan = document.getElementById("finalRate"); if (isNaN(D) || isNaN(A) || isNaN(Cs) || isNaN(Cb) || isNaN(h) || h <= 0) { alert("Please enter valid positive numbers. Diffusion layer thickness must be greater than zero."); return; } // Noyes-Whitney: dc/dt = (D * A / h) * (Cs – Cb) var rate = (D * A / h) * (Cs – Cb); // Logic to handle scientific notation for very small rates var formattedRate; if (rate 0) { formattedRate = rate.toExponential(4); } else { formattedRate = rate.toFixed(4); } rateSpan.innerText = formattedRate; resultDiv.style.display = "block"; // Smooth scroll to result resultDiv.scrollIntoView({ behavior: 'smooth', block: 'nearest' }); }