The rate constant, often denoted by 'k', is a proportionality constant that relates the rate of a chemical reaction to the concentration of the reactants. Its value is specific to a particular reaction at a given temperature and is independent of reactant concentrations. The units of the rate constant depend on the order of the reaction.
Zero Order
First Order
Second Order
Third Order
Understanding Rate Constants
The rate of a chemical reaction is typically expressed by a rate law, which shows how the rate depends on the concentration of reactants. For a general reaction aA + bB → products, the rate law is often written as:
Rate = k[A]m[B]n
where [A] and [B] are the concentrations of reactants A and B, respectively, and m and n are the orders of the reaction with respect to A and B. The overall order of the reaction is m + n. The rate constant, 'k', is the proportionality factor in this equation.
Integrated Rate Laws:
While the rate law relates instantaneous rate to concentration, integrated rate laws relate concentration to time. These are useful for determining the rate constant when you have data on how concentration changes over time.
Zero Order: [A]t = -kt + [A]0. Rearranging for k: k = ([A]0 – [A]t) / t. Units of k are M/s.
First Order: ln[A]t = -kt + ln[A]0. Rearranging for k: k = (ln[A]0 – ln[A]t) / t. Units of k are 1/s or s-1.
Second Order: 1/[A]t = kt + 1/[A]0. Rearranging for k: k = (1/[A]t – 1/[A]0) / t. Units of k are 1/(M·s) or M-1s-1.
Third Order: 1/[A]t2 = 2kt + 1/[A]02. Rearranging for k: k = (1/(2[A]t2) – 1/(2[A]02)) / t. Units of k are 1/(M2·s) or M-2s-1.
This calculator uses these integrated rate laws to determine the rate constant based on the provided initial concentration, final concentration, time, and reaction order.
function calculateRateConstant() {
var reactionOrder = parseInt(document.getElementById("reactionOrder").value);
var initialConcentration = parseFloat(document.getElementById("initialConcentration").value);
var finalConcentration = parseFloat(document.getElementById("finalConcentration").value);
var time = parseFloat(document.getElementById("time").value);
var resultDiv = document.getElementById("result");
var k = NaN;
var units = "";
if (isNaN(initialConcentration) || isNaN(finalConcentration) || isNaN(time) || time <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for concentrations and time.";
return;
}
if (reactionOrder === 0) {
// Zero Order: k = ([A]0 – [A]t) / t
k = (initialConcentration – finalConcentration) / time;
units = "M/s";
} else if (reactionOrder === 1) {
// First Order: k = (ln[A]0 – ln[A]t) / t
if (initialConcentration <= 0 || finalConcentration <= 0) {
resultDiv.innerHTML = "For first-order reactions, concentrations must be positive.";
return;
}
k = (Math.log(initialConcentration) – Math.log(finalConcentration)) / time;
units = "s-1";
} else if (reactionOrder === 2) {
// Second Order: k = (1/[A]t – 1/[A]0) / t
if (initialConcentration === 0 || finalConcentration === 0) {
resultDiv.innerHTML = "For second-order reactions, concentrations must be non-zero to avoid division by zero.";
return;
}
k = (1 / finalConcentration – 1 / initialConcentration) / time;
units = "M-1s-1";
} else if (reactionOrder === 3) {
// Third Order: k = (1/(2[A]t^2) – 1/(2[A]0^2)) / t
if (initialConcentration === 0 || finalConcentration === 0) {
resultDiv.innerHTML = "For third-order reactions, concentrations must be non-zero to avoid division by zero.";
return;
}
k = (1 / (2 * Math.pow(finalConcentration, 2)) – 1 / (2 * Math.pow(initialConcentration, 2))) / time;
units = "M-2s-1";
}
if (!isNaN(k)) {
resultDiv.innerHTML = "The calculated rate constant (k) is: " + k.toFixed(6) + " " + units + "";
} else {
resultDiv.innerHTML = "Could not calculate rate constant. Please check your inputs.";
}
}
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