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How to Calculate Reaction Rate from Absorbance and Time
In spectrophotometry and chemical kinetics, determining the rate of a reaction is often achieved by monitoring the change in absorbance of a solution over time. Whether you are studying enzyme kinetics (like the Michaelis-Menten equation) or simple chemical degradation, understanding how to convert spectrophotometer readings into a quantifiable rate is essential.
1. The Basic Concept: Slope of Absorbance
The most direct measurement from a kinetic assay is the rate at which the absorbance changes. This is essentially the slope of the line when Absorbance is plotted against Time.
The formula for the Absorbance Rate is:
RateAbs = (Afinal – Ainitial) / Time Interval
Example: If a solution starts at 0.100 AU (Absorbance Units) and increases to 0.500 AU over 60 seconds:
ΔA = 0.500 – 0.100 = 0.400 AU
Rate = 0.400 / 60 = 0.0067 AU/sec
2. Converting to Molar Rate (The Beer-Lambert Law)
While the change in absorbance tells you something is happening, scientists usually need to know the rate in terms of concentration (Molarity per second). To do this, we apply the Beer-Lambert Law:
A = ε · l · c
- A: Absorbance (unitless)
- ε (Epsilon): Molar Extinction Coefficient (M-1cm-1)
- l: Path length of the cuvette (usually 1 cm)
- c: Concentration (Molar)
To find the Reaction Rate (v) in concentration per unit time, we rearrange the formula to solve for the change in concentration (Δc):
Reaction Rate (M/s) = ΔA / (ε · l · Δt)
3. Step-by-Step Calculation
- Measure Absorbance: Record the absorbance at the start ($t=0$) and at the end of your specific time interval.
- Calculate ΔA: Subtract the initial absorbance from the final absorbance. Note: If the product is being formed, ΔA is positive. If the substrate is being consumed, ΔA is negative.
- Determine Time: Calculate the total duration in consistent units (seconds or minutes).
- Apply Extinction Coefficient: If you know the specific $\epsilon$ for your substance at the wavelength used, divide the Absorbance Rate by $\epsilon$ (and path length) to get the Molar Rate.
Common Applications
Enzyme Kinetics: When assaying enzymes (e.g., NADH oxidation), the rate is often calculated in $\mu mol/min$. To convert from Molar (mol/L) to simpler units, remember that $1 M = 1,000,000 \mu M$.
Chemical Order Determination: By calculating initial rates at different starting concentrations, researchers can determine if a reaction is zero-order, first-order, or second-order.
Troubleshooting Data
Ensure your absorbance readings fall within the linear range of the spectrophotometer (typically 0.1 to 1.0 AU). Readings above 2.0 AU are often inaccurate due to detector saturation. Additionally, ensure there are no bubbles in the cuvette, as these scatter light and cause artificial spikes in absorbance rates.
function calculateRate() {
// 1. Get input values
var a1 = document.getElementById('initialAbs').value;
var a2 = document.getElementById('finalAbs').value;
var timeVal = document.getElementById('timeValue').value;
var timeUnit = document.getElementById('timeUnit').value;
var epsilon = document.getElementById('epsilon').value;
var pathLength = document.getElementById('pathLength').value;
// 2. Validate inputs
if (a1 === "" || a2 === "" || timeVal === "") {
alert("Please fill in Initial Absorbance, Final Absorbance, and Time.");
return;
}
var abs1 = parseFloat(a1);
var abs2 = parseFloat(a2);
var t = parseFloat(timeVal);
var eps = parseFloat(epsilon); // May be NaN if empty
var l = parseFloat(pathLength); // May be NaN if empty
if (t === 0) {
alert("Time interval cannot be zero.");
return;
}
// 3. Calculate basic Absorbance Rate (Slope)
var deltaA = abs2 – abs1;
var absRate = deltaA / t;
// 4. Display Basic Results
document.getElementById('resDeltaA').innerHTML = deltaA.toFixed(4) + " AU";
document.getElementById('resAbsRate').innerHTML = absRate.toExponential(4) + " AU/" + timeUnit;
// 5. Calculate Molar Rate if Epsilon is provided
var molarDiv = document.getElementById('molarResults');
if (!isNaN(eps) && eps !== 0 && !isNaN(l) && l !== 0) {
// Delta C = Delta A / (epsilon * l)
var deltaC = deltaA / (eps * l);
// Rate = Delta C / t
var reactionRate = deltaC / t;
// Format Concentration units
document.getElementById('resDeltaC').innerHTML = deltaC.toExponential(4) + " M";
document.getElementById('resMolarRate').innerHTML = reactionRate.toExponential(4) + " M/" + timeUnit;
molarDiv.style.display = "block";
} else {
molarDiv.style.display = "none";
}
// Show result section
document.getElementById('resultSection').style.display = "block";
}