How to Calculate Rate of Reaction from Absorbance and Time
In chemical kinetics, spectrophotometry is one of the most accurate methods to determine the rate of a reaction. By measuring the absorbance of a solution at specific time intervals, chemists can track how quickly reactants are consumed or products are formed. This calculator helps you determine the average rate of reaction based on absorbance data.
The Basic Formula: Absorbance Rate
The simplest way to express the rate is in terms of the change in Absorbance Units (AU) per unit of time. This is often the first step in analyzing kinetic data from a spectrophotometer.
Rate (Abs) = | Afinal – Ainitial | / Time Elapsed
Where:
Afinal is the absorbance reading at time t.
Ainitial is the absorbance reading at the start (t=0).
Time Elapsed is the duration between the two measurements.
Converting to Molar Rate (Concentration)
To calculate the true chemical rate in terms of concentration (Molarity per second, M/s), we apply the Beer-Lambert Law. This law states that absorbance is directly proportional to concentration.
A = ε ċ l ċ c
By rearranging this formula, we can find the change in concentration (ΔC) and subsequently the molar rate:
Rate (M/s) = ΔA / (ε ċ l ċ Δt)
Where:
ε (Epsilon) is the Molar Absorptivity Coefficient (Lċmol-1ċcm-1).
l is the path length of the cuvette (usually 1 cm).
ΔA is the change in absorbance.
Δt is the change in time.
Example Calculation
Imagine you are studying the oxidation of a dye. The solution starts with an absorbance of 0.850. After 60 seconds, the absorbance drops to 0.620. You are using a standard 1 cm cuvette, and the molar absorptivity of the dye is 15,000 M-1cm-1.
Absorbance changes because the concentration of the light-absorbing species changes as the reaction proceeds. If the product is colored and the reactant is clear, absorbance increases. If the reactant is colored and the product is clear (bleaching), absorbance decreases. The rate calculation uses the absolute difference, so the rate is always expressed as a positive value.
function calculateReactionRate() {
// Get Input Values
var aInitial = document.getElementById('initialAbs').value;
var aFinal = document.getElementById('finalAbs').value;
var timeVal = document.getElementById('timeVal').value;
var timeUnitMultiplier = document.getElementById('timeUnit').value;
var epsilon = document.getElementById('molarAbs').value;
var pathLen = document.getElementById('pathLength').value;
// Validation
if (aInitial === "" || aFinal === "" || timeVal === "") {
alert("Please fill in Initial Absorbance, Final Absorbance, and Time.");
return;
}
var a1 = parseFloat(aInitial);
var a2 = parseFloat(aFinal);
var tInput = parseFloat(timeVal);
var multiplier = parseFloat(timeUnitMultiplier);
// Handle path length default
var l = (pathLen === "" || parseFloat(pathLen) <= 0) ? 1 : parseFloat(pathLen);
if (tInput 0);
if (hasEpsilon) {
var e = parseFloat(epsilon);
// Delta C = Delta A / (epsilon * l)
var deltaC = deltaA / (e * l);
// Rate M/s = Delta C / Time (seconds)
// Usually reported in M/s regardless of input time unit, but let's match input unit logic for consistency or standard scientific notation
var rateMolarPerSec = deltaC / timeSeconds;
var rateMolarPerInputUnit = deltaC / tInput;
document.getElementById('concRow').style.display = 'flex';
document.getElementById('molarRateRow').style.display = 'flex';
// Format scientific notation for small numbers
document.getElementById('deltaCResult').innerText = deltaC.toExponential(4) + " M";
document.getElementById('molarRateResult').innerText = rateMolarPerInputUnit.toExponential(4) + " M/" + unitLabel;
document.getElementById('mainResult').innerText = "Rate: " + rateMolarPerInputUnit.toExponential(3) + " M/" + unitLabel;
} else {
document.getElementById('concRow').style.display = 'none';
document.getElementById('molarRateRow').style.display = 'none';
document.getElementById('mainResult').innerText = "Rate: " + rateAbsDisplay;
}
}