Reaction Rate from Absorbance Calculator
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Reaction Rate from Absorbance Calculator
This calculator determines the reaction rate (change in concentration over time) based on spectrophotometric absorbance data using the Beer-Lambert Law. It is designed for students, chemists, and researchers analyzing kinetic data.
Calculate Rate
Change in Absorbance ($\Delta A$):
0.000
Change in Concentration ($\Delta c$):
0.000 M
Reaction Rate ($v$):
0.000 M/s
How to Calculate Reaction Rate from Absorbance
Calculating the reaction rate from absorbance data requires converting raw spectrophotometer readings into concentration values using the Beer-Lambert Law. This method is non-destructive and allows for real-time monitoring of reaction kinetics.
1. The Beer-Lambert Law
The core relationship used in this calculation is:
$A = \varepsilon \cdot l \cdot c$
A : Absorbance (no units)$\varepsilon$ (Epsilon) : Molar Extinction Coefficient (or Molar Absorptivity) ($M^{-1} cm^{-1}$)l : Path length of the cuvette (usually 1 cm)c : Concentration ($M$ or $mol/L$)
2. Formula for Reaction Rate
The average reaction rate is defined as the change in concentration over the change in time. Since absorbance is directly proportional to concentration, we calculate the rate as follows:
Step 1: Calculate $\Delta A$
Step 2: Calculate $\Delta c$ (Change in Concentration)
Step 3: Calculate Rate
Where $\Delta t$ is the time interval in seconds. The final unit for the reaction rate is typically Molarity per second ($M/s$ or $mol \cdot L^{-1} \cdot s^{-1}$).
Example Calculation
Imagine monitoring the decomposition of a dye.
Initial Absorbance: 0.800
Final Absorbance: 0.400
Time Elapsed: 100 seconds
Molar Extinction Coefficient: 5000 $M^{-1}cm^{-1}$
Path Length: 1 cm
1. $\Delta A$: $|0.400 – 0.800| = 0.400$
2. $\Delta c$: $0.400 / (5000 \times 1) = 0.00008 M$
3. Rate: $0.00008 M / 100 s = 8.0 \times 10^{-7} M/s$
function calculateReactionRate() {
// Get input values
var absInitial = document.getElementById('abs-initial').value;
var absFinal = document.getElementById('abs-final').value;
var timeElapsed = document.getElementById('time-elapsed').value;
var molarCoeff = document.getElementById('molar-coeff').value;
var pathLength = document.getElementById('path-length').value;
var errorDiv = document.getElementById('error-message');
var resultArea = document.getElementById('result-area');
// Reset error state
errorDiv.style.display = 'none';
resultArea.style.display = 'none';
// Validation
if (absInitial === "" || absFinal === "" || timeElapsed === "" || molarCoeff === "" || pathLength === "") {
errorDiv.innerText = "Please fill in all fields.";
errorDiv.style.display = 'block';
return;
}
// Parse numbers
var a1 = parseFloat(absInitial);
var a2 = parseFloat(absFinal);
var t = parseFloat(timeElapsed);
var epsilon = parseFloat(molarCoeff);
var l = parseFloat(pathLength);
// Logical validation
if (t <= 0) {
errorDiv.innerText = "Time elapsed must be greater than zero.";
errorDiv.style.display = 'block';
return;
}
if (epsilon <= 0) {
errorDiv.innerText = "Molar Extinction Coefficient must be greater than zero.";
errorDiv.style.display = 'block';
return;
}
if (l <= 0) {
errorDiv.innerText = "Path length must be greater than zero.";
errorDiv.style.display = 'block';
return;
}
// Calculation Logic
// 1. Calculate change in absorbance (Absolute value for magnitude of rate)
var deltaA = Math.abs(a2 – a1);
// 2. Calculate change in concentration using Beer's Law: c = A / (epsilon * l)
var deltaC = deltaA / (epsilon * l);
// 3. Calculate Rate = deltaC / deltaT
var rate = deltaC / t;
// Formatting results for display (Scientific notation for very small rates)
var displayRate = rate < 0.0001 ? rate.toExponential(4) : rate.toFixed(6);
var displayDeltaC = deltaC < 0.0001 ? deltaC.toExponential(4) : deltaC.toFixed(6);
var displayDeltaA = deltaA.toFixed(4);
// Update DOM
document.getElementById('res-delta-a').innerText = displayDeltaA;
document.getElementById('res-delta-c').innerText = displayDeltaC + " M";
document.getElementById('res-rate').innerText = displayRate + " M/s";
// Show results
resultArea.style.display = 'block';
}