Molar concentration (M) of the reactant in excess.
Usually 1 for first-order dependence on the excess reagent.
Pseudo Rate Constant (k')
0.000
How to Calculate Pseudo Rate Constant
In chemical kinetics, determining the rate law for reactions involving multiple reactants can be mathematically complex. The Pseudo Rate Constant is a simplification technique used to isolate the behavior of one reactant by swamping the reaction mixture with a large excess of the other reactants.
General Formula:
k' = k × [B]n
Understanding the Variables
k' (k-prime): The observed pseudo rate constant. If the reaction becomes pseudo-first-order, the units are typically s-1.
k: The actual rate constant of the reaction.
[B]: The concentration of the reactant present in large excess (so large that its concentration is effectively constant during the reaction).
n: The order of the reaction with respect to reactant B.
The Logic Behind the Calculation
Consider a standard bimolecular reaction: A + B → Products.
The rate law is typically expressed as:
Rate = k [A] [B]
If we add reactant B in large excess (e.g., [B] > 10 × [A]), the concentration of B changes very little as the reaction proceeds. We can therefore treat [B] as a constant value.
The equation simplifies to:
Rate = k' [A]
Where k' = k[B]. This transforms a second-order reaction into a Pseudo-First-Order reaction, making it much easier to analyze experimentally using integrated rate laws.
Example Calculation
Let's say you are studying a reaction with an actual rate constant k = 0.05 M-1s-1.
You run the experiment with an excess concentration of reactant B at 2.0 M, and the reaction is first-order with respect to B (n=1).
To find the pseudo rate constant:
Identify k: 0.05
Identify [B]: 2.0
Identify n: 1
Calculate: k' = 0.05 × (2.0)1 = 0.1 s-1
Why is this important?
This technique, often called the Ostwald Isolation Method, allows chemists to determine the reaction order of individual reactants one by one. By calculating the pseudo rate constant at various concentrations of the excess reactant, one can determine the specific reaction order (n) and eventually solve for the true rate constant (k).
function calculatePseudoConstant() {
// Get input values using var
var k = document.getElementById('actualRateK').value;
var b_conc = document.getElementById('excessConc').value;
var n_order = document.getElementById('reactionOrder').value;
// Get result display elements
var resultBox = document.getElementById('resultBox');
var resultValue = document.getElementById('resultValue');
var resultText = document.getElementById('resultText');
// Validate inputs
if (k === "" || b_conc === "" || n_order === "") {
alert("Please fill in all fields correctly.");
return;
}
var kNum = parseFloat(k);
var bConcNum = parseFloat(b_conc);
var nOrderNum = parseFloat(n_order);
// Check for valid numbers
if (isNaN(kNum) || isNaN(bConcNum) || isNaN(nOrderNum)) {
alert("Please enter valid numeric values.");
return;
}
// Check for physical validity (concentration cannot be negative)
if (bConcNum < 0) {
alert("Concentration cannot be negative.");
return;
}
// Perform Calculation: k' = k * [B]^n
var kPrime = kNum * Math.pow(bConcNum, nOrderNum);
// Format formatting logic for scientific notation if number is very small or large
var formattedResult;
if (kPrime 10000) {
formattedResult = kPrime.toExponential(4);
} else {
formattedResult = kPrime.toFixed(4);
}
// Display Results
resultBox.style.display = "block";
resultValue.innerHTML = formattedResult;
// Dynamic explanation
resultText.innerHTML = "Given an actual rate constant of " + kNum + " and excess concentration of " + bConcNum + " M (Order " + nOrderNum + "), the observed pseudo rate constant is " + formattedResult + ".";
}