Results
Enter experimental data to see the results.
Understanding Rate Laws
Chemical kinetics is the study of reaction rates and mechanisms. A rate law is an equation that relates the rate of a chemical reaction to the concentrations of its reactants. For a general reaction:
aA + bB → products
The rate law is typically expressed as:
Rate = k[A]^m[B]^n
Where:
Rate is the speed at which the reaction occurs.k is the rate constant, which is specific to the reaction and temperature.[A] and [B] are the molar concentrations of reactants A and B.m and n are the reaction orders with respect to reactants A and B, respectively. These exponents are determined experimentally and are not necessarily equal to the stoichiometric coefficients (a and b).
How to Determine Reaction Orders and Rate Constant
The method of initial rates is a common technique for determining the orders of a reaction and the rate constant. It involves comparing the initial rates of reaction under different sets of initial reactant concentrations.
Consider two experiments with different initial concentrations:
Experiment 1: Rate1 = k[A1]^m[B1]^n
Experiment 2: Rate2 = k[A2]^m[B2]^n
To find the order m (with respect to A), we choose an experiment where [A] changes but [B] remains constant (or vice versa for finding n). If we keep [B] constant, we can divide the rate law expressions:
Rate2 / Rate1 = ([A2]^m * [B2]^n) / ([A1]^m * [B1]^n)
If [B1] = [B2], then [B1]^n = [B2]^n and they cancel out:
Rate2 / Rate1 = [A2]^m / [A1]^m = ([A2] / [A1])^m
Taking the logarithm of both sides allows us to solve for m:
log(Rate2 / Rate1) = m * log([A2] / [A1])
m = log(Rate2 / Rate1) / log([A2] / [A1])
Similarly, to find the order n (with respect to B), we look for experiments where [B] changes and [A] remains constant.
n = log(Rate2 / Rate1) / log([B2] / [B1]) (assuming [A] is constant in experiments 1 and 2)
Once m and n are determined, you can substitute these values along with the concentrations and rate from any experiment into the rate law equation to solve for the rate constant k.
function calculateRateLaw() {
var concA1 = parseFloat(document.getElementById("concentrationA").value);
var concB1 = parseFloat(document.getElementById("concentrationB").value);
var rate1 = parseFloat(document.getElementById("initialRate").value);
var concA2 = parseFloat(document.getElementById("concentrationA2").value);
var concB2 = parseFloat(document.getElementById("concentrationB2").value);
var rate2 = parseFloat(document.getElementById("initialRate2").value);
var resultsDiv = document.getElementById("results");
resultsDiv.innerHTML = ""; // Clear previous results
if (isNaN(concA1) || isNaN(concB1) || isNaN(rate1) || isNaN(concA2) || isNaN(concB2) || isNaN(rate2)) {
resultsDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
var orderA = "N/A";
var orderB = "N/A";
var rateConstant = "N/A";
// Determine order of A
if (concA1 !== concA2 && concB1 === concB2 && concA1 !== 0 && concA2 !== 0 && rate1 !== 0 && rate2 !== 0) {
var ratioRates = rate2 / rate1;
var ratioConcA = concA2 / concA1;
if (ratioConcA > 0 && ratioRates > 0) { // Avoid log(0) or log of negative numbers
orderA = Math.round(Math.log(ratioRates) / Math.log(ratioConcA) * 10) / 10; // Round to one decimal place for clarity
}
} else if (concA1 === concA2 && concB1 !== concB2 && concB1 !== 0 && concB2 !== 0 && rate1 !== 0 && rate2 !== 0) {
// If A concentrations are the same, we can't directly calculate orderA this way.
// However, if the rate changed, it implies an order for B. If rate is the same, order for B might be 0.
// For simplicity in this example, we'll only calculate if A changes and B is constant.
} else if (concA1 !== concA2 && concB1 !== concB2) {
// If both concentrations change, we need more data or a more complex approach.
// For this calculator, we assume one reactant's concentration is held constant between two experiments to find the other's order.
}
// Determine order of B
if (concB1 !== concB2 && concA1 === concA2 && concB1 !== 0 && concB2 !== 0 && rate1 !== 0 && rate2 !== 0) {
var ratioRates = rate2 / rate1;
var ratioConcB = concB2 / concB1;
if (ratioConcB > 0 && ratioRates > 0) { // Avoid log(0) or log of negative numbers
orderB = Math.round(Math.log(ratioRates) / Math.log(ratioConcB) * 10) / 10; // Round to one decimal place
}
} else if (concB1 === concB2 && concA1 !== concA2 && concA1 !== 0 && concA2 !== 0 && rate1 !== 0 && rate2 !== 0) {
// If B concentrations are the same, we can't directly calculate orderB this way.
// However, if the rate changed, it implies an order for A. If rate is the same, order for A might be 0.
// For simplicity in this example, we'll only calculate if B changes and A is constant.
} else if (concA1 !== concA2 && concB1 !== concB2) {
// If both concentrations change, we need more data or a more complex approach.
}
// Calculate Rate Constant (k) if orders are determined and valid
if (orderA !== "N/A" && orderB !== "N/A") {
// Use Experiment 1 data to calculate k
if (concA1 !== 0 || orderA === 0) { // Handle [A]=0 case if orderA is 0
if (concB1 !== 0 || orderB === 0) { // Handle [B]=0 case if orderB is 0
rateConstant = rate1 / (Math.pow(concA1, orderA) * Math.pow(concB1, orderB));
rateConstant = Math.round(rateConstant * 1000) / 1000; // Round k to 3 decimal places
}
}
} else if (orderA === "N/A" && orderB !== "N/A") { // Only orderB determined
// Attempt to calculate k using orderB and assuming orderA is 0 if concA didn't change
if (concA1 === concA2 && concA1 !== 0) { // Assume orderA is 0
rateConstant = rate1 / Math.pow(concB1, orderB);
rateConstant = Math.round(rateConstant * 1000) / 1000;
orderA = 0;
} else if (concA1 === concA2 && concA1 === 0) {
// If [A] is 0 and constant, and orderA is 0, this calculation is valid.
if (concB1 !== 0 || orderB === 0) {
rateConstant = rate1 / Math.pow(concB1, orderB);
rateConstant = Math.round(rateConstant * 1000) / 1000;
orderA = 0;
}
}
} else if (orderB === "N/A" && orderA !== "N/A") { // Only orderA determined
// Attempt to calculate k using orderA and assuming orderB is 0 if concB didn't change
if (concB1 === concB2 && concB1 !== 0) { // Assume orderB is 0
rateConstant = rate1 / Math.pow(concA1, orderA);
rateConstant = Math.round(rateConstant * 1000) / 1000;
orderB = 0;
} else if (concB1 === concB2 && concB1 === 0) {
// If [B] is 0 and constant, and orderB is 0, this calculation is valid.
if (concA1 !== 0 || orderA === 0) {
rateConstant = rate1 / Math.pow(concA1, orderA);
rateConstant = Math.round(rateConstant * 1000) / 1000;
orderB = 0;
}
}
}
// Display results
var outputHTML = "
Order with respect to Reactant A (m): " + orderA + "";
outputHTML += "
Order with respect to Reactant B (n): " + orderB + "";
outputHTML += "
Rate Constant (k): " + rateConstant + " mol/L·s (units depend on overall order)";
outputHTML += "
Note: To accurately determine the order of a reactant, its concentration should change while the other reactant's concentration is held constant between experiments. If both concentrations change, or if initial concentrations are zero, additional experimental data or analysis methods may be required.";
resultsDiv.innerHTML = outputHTML;
}
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