Rate Law Calculator
Calculate Rate Law
Understanding and Calculating Rate Laws
In chemical kinetics, a rate law (or rate equation) is an equation that links the rate of a chemical reaction to the concentration of the reactants. It describes how the speed of a reaction changes as the amounts of the reacting substances change. The general form of a rate law for a reaction involving reactants A and B is:
Rate = k[A]^x[B]^y
Where:
Rate is the reaction rate (typically in units of mol/(L·s)).k is the rate constant, a proportionality constant that is specific to a particular reaction at a particular temperature. Its units depend on the overall order of the reaction.[A] and [B] are the molar concentrations of reactants A and B, respectively (in mol/L).x and y are the reaction orders with respect to reactants A and B. These are exponents that indicate how the rate is affected by changes in the concentration of each reactant. They are often small integers (0, 1, 2) but can be fractions or even negative. The reaction orders are determined experimentally and cannot generally be predicted from the stoichiometry of the balanced chemical equation.
Determining Reaction Orders (x and y)
The most common method for determining the reaction orders x and y is the "method of initial rates". This involves running several experiments where the initial concentrations of the reactants are systematically varied, and the initial rate of the reaction is measured for each experiment. By comparing the changes in rate to the changes in concentration, the orders can be deduced.
Method of Initial Rates Explained:
Compare two experiments where the concentration of one reactant changes while the other stays constant: For example, to find the order with respect to A (x), compare two experiments where [B] is constant but [A] changes. The ratio of the rates will be directly related to the ratio of the concentrations raised to the power of x.Use logarithms to solve for the exponent: Once you have the relationship, you can use logarithms to solve for x or y.Repeat for the other reactant: To find the order with respect to B (y), compare two experiments where [A] is constant but [B] changes.
Calculating the Rate Constant (k)
Once the reaction orders (x and y) are determined, you can calculate the rate constant k using the data from any one of the experiments. Plug the values of the rate, concentrations, and determined orders into the rate law equation and solve for k.
Example Calculation:
Consider the reaction: A + B -> Products
We have the following experimental data:
Experiment 1: [A] = 0.5 mol/L, [B] = 0.5 mol/L, Rate = 0.01 mol/(L·s)Experiment 2: [A] = 1.0 mol/L, [B] = 0.5 mol/L, Rate = 0.04 mol/(L·s)Experiment 3: [A] = 0.5 mol/L, [B] = 1.0 mol/L, Rate = 0.02 mol/(L·s)
Determining the order with respect to A (x):
Compare Experiment 1 and Experiment 2 (where [B] is constant at 0.5 mol/L):
Rate2 / Rate1 = (k[A]2^x[B]2^y) / (k[A]1^x[B]1^y)
0.04 / 0.01 = (1.0^x) / (0.5^x)
4 = (1.0 / 0.5)^x
4 = 2^x
Therefore, x = 2.
Determining the order with respect to B (y):
Compare Experiment 1 and Experiment 3 (where [A] is constant at 0.5 mol/L):
Rate3 / Rate1 = (k[A]3^x[B]3^y) / (k[A]1^x[B]1^y)
0.02 / 0.01 = (1.0^y) / (0.5^y)
2 = (1.0 / 0.5)^y
2 = 2^y
Therefore, y = 1.
Determining the rate constant (k):
Using the data from Experiment 1 and the determined orders (x=2, y=1):
Rate = k[A]^x[B]^y
0.01 mol/(L·s) = k * (0.5 mol/L)^2 * (0.5 mol/L)^1
0.01 = k * (0.25) * (0.5)
0.01 = k * 0.125
k = 0.01 / 0.125 = 0.08
The units of k can be determined from the rate law. For this reaction, the overall order is 2 + 1 = 3. The units of k will be L²/mol²/s.
Thus, the rate law for this reaction is Rate = 0.08 L²/mol²/s * [A]²[B].
function calculateRateLaw() {
var initialConcentrationA = parseFloat(document.getElementById("initialConcentrationA").value);
var initialConcentrationB = parseFloat(document.getElementById("initialConcentrationB").value);
var initialRate = parseFloat(document.getElementById("initialRate").value);
var changeConcentrationAExperiment2 = parseFloat(document.getElementById("changeConcentrationAExperiment2").value);
var changeConcentrationBExperiment2 = parseFloat(document.getElementById("changeConcentrationBExperiment2").value);
var changeRateExperiment2 = parseFloat(document.getElementById("changeRateExperiment2").value);
var changeConcentrationAExperiment3 = parseFloat(document.getElementById("changeConcentrationAExperiment3").value);
var changeConcentrationBExperiment3 = parseFloat(document.getElementById("changeConcentrationBExperiment3").value);
var changeRateExperiment3 = parseFloat(document.getElementById("changeRateExperiment3").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(initialConcentrationA) || isNaN(initialConcentrationB) || isNaN(initialRate) ||
isNaN(changeConcentrationAExperiment2) || isNaN(changeConcentrationBExperiment2) || isNaN(changeRateExperiment2) ||
isNaN(changeConcentrationAExperiment3) || isNaN(changeConcentrationBExperiment3) || isNaN(changeRateExperiment3)) {
resultDiv.innerHTML = "Please enter valid numbers for all inputs.";
return;
}
// — Determine order with respect to A (x) —
var orderA = "Undetermined";
var ratioRate2_1 = changeRateExperiment2 / initialRate;
var ratioConcentrationA2_1 = changeConcentrationAExperiment2 / initialConcentrationA;
var ratioConcentrationB2_1 = changeConcentrationBExperiment2 / initialConcentrationB;
if (ratioConcentrationB2_1 === 1 && ratioConcentrationA2_1 > 0 && ratioRate2_1 > 0) {
// B is constant, A changes
if (ratioConcentrationA2_1 === 1) { // If A also didn't change (unlikely for this scenario but for completeness)
orderA = (ratioRate2_1 === 1) ? 0 : "Invalid Data (Rate changed but concentration didn't)";
} else if (Math.abs(Math.log(ratioRate2_1) / Math.log(ratioConcentrationA2_1) – 2) < 0.01) { // Check if order is approximately 2
orderA = 2;
} else if (Math.abs(Math.log(ratioRate2_1) / Math.log(ratioConcentrationA2_1) – 1) < 0.01) { // Check if order is approximately 1
orderA = 1;
} else if (Math.abs(Math.log(ratioRate2_1) / Math.log(ratioConcentrationA2_1) – 0) 0 && ratioRate3_1 > 0) {
if (ratioConcentrationA3_1 === 1) {
orderA = (ratioRate3_1 === 1) ? 0 : "Invalid Data (Rate changed but concentration didn't)";
} else if (Math.abs(Math.log(ratioRate3_1) / Math.log(ratioConcentrationA3_1) – 2) < 0.01) {
orderA = 2;
} else if (Math.abs(Math.log(ratioRate3_1) / Math.log(ratioConcentrationA3_1) – 1) < 0.01) {
orderA = 1;
} else if (Math.abs(Math.log(ratioRate3_1) / Math.log(ratioConcentrationA3_1) – 0) 0 && ratioRate3_1_forB > 0) {
// A is constant, B changes
if (ratioConcentrationB3_1_forB === 1) {
orderB = (ratioRate3_1_forB === 1) ? 0 : "Invalid Data (Rate changed but concentration didn't)";
} else if (Math.abs(Math.log(ratioRate3_1_forB) / Math.log(ratioConcentrationB3_1_forB) – 1) < 0.01) { // Check if order is approximately 1
orderB = 1;
} else if (Math.abs(Math.log(ratioRate3_1_forB) / Math.log(ratioConcentrationB3_1_forB) – 2) < 0.01) { // Check if order is approximately 2
orderB = 2;
} else if (Math.abs(Math.log(ratioRate3_1_forB) / Math.log(ratioConcentrationB3_1_forB) – 0) 0 && ratioRate2_1_forB > 0) {
if (ratioConcentrationB2_1_forB === 1) {
orderB = (ratioRate2_1_forB === 1) ? 0 : "Invalid Data (Rate changed but concentration didn't)";
} else if (Math.abs(Math.log(ratioRate2_1_forB) / Math.log(ratioConcentrationB2_1_forB) – 1) < 0.01) {
orderB = 1;
} else if (Math.abs(Math.log(ratioRate2_1_forB) / Math.log(ratioConcentrationB2_1_forB) – 2) < 0.01) {
orderB = 2;
} else if (Math.abs(Math.log(ratioRate2_1_forB) / Math.log(ratioConcentrationB2_1_forB) – 0) < 0.01) {
orderB = 0;
}
else {
orderB = Math.log(ratioRate2_1_forB) / Math.log(ratioConcentrationB2_1_forB);
}
}
}
var rateConstant = "Undetermined";
var unitsK = "Unknown units";
var overallOrder = "N/A";
if (orderA !== "Undetermined" && orderB !== "Undetermined") {
overallOrder = (orderA + orderB).toFixed(2); // Sum orders for overall order
// Calculate rate constant using data from Experiment 1
var denominatorK = Math.pow(initialConcentrationA, orderA) * Math.pow(initialConcentrationB, orderB);
if (denominatorK !== 0) {
rateConstant = initialRate / denominatorK;
// Determine units of k
// Rate units: mol/(L*s)
// Concentration units: mol/L
// Rate = k * [A]^x * [B]^y
// Units: mol/(L*s) = Units(k) * (mol/L)^(x+y)
// Units(k) = mol/(L*s) / (mol/L)^(x+y)
// Units(k) = mol * L^(x+y) / (L * s * mol^(x+y))
// Units(k) = L^((x+y)-1) * mol^(1-(x+y)) * s^-1
var exponent = overallOrder – 1;
if (exponent === 0) {
unitsK = "s⁻¹";
} else if (exponent === 1) {
unitsK = "L·mol⁻¹·s⁻¹";
} else if (exponent === 2) {
unitsK = "L²·mol⁻²·s⁻¹";
} else if (exponent === -1) {
unitsK = "L⁻¹·mol·s⁻¹";
} else {
unitsK = `L^${exponent}·mol^${-exponent}·s⁻¹`;
}
}
}
var htmlOutput = "
Results: ";
htmlOutput += "Order with respect to Reactant A (x): ";
if (typeof orderA === 'number') {
htmlOutput += orderA.toFixed(2);
} else {
htmlOutput += orderA;
}
htmlOutput += "";
htmlOutput += "Order with respect to Reactant B (y): ";
if (typeof orderB === 'number') {
htmlOutput += orderB.toFixed(2);
} else {
htmlOutput += orderB;
}
htmlOutput += "";
htmlOutput += "Overall Reaction Order: " + overallOrder + "";
htmlOutput += "Rate Constant (k): ";
if (typeof rateConstant === 'number') {
htmlOutput += rateConstant.toFixed(4) + " " + unitsK;
} else {
htmlOutput += rateConstant;
}
htmlOutput += "";
if (typeof orderA === 'number' && typeof orderB === 'number') {
htmlOutput += "Rate Law: Rate = ";
if (typeof rateConstant === 'number') {
htmlOutput += rateConstant.toFixed(4) + " " + unitsK + " [A]
" + orderA.toFixed(0) + " [B]
" + orderB.toFixed(0) + " ";
} else {
htmlOutput += "k [A]
" + orderA.toFixed(0) + " [B]
" + orderB.toFixed(0) + " ";
}
htmlOutput += "";
}
resultDiv.innerHTML = htmlOutput;
}