Reaction Rate Constant Calculator
This calculator helps you determine the rate constant (k) for a chemical reaction, given the initial concentrations of reactants and the initial rate of the reaction. The rate constant is a proportionality constant that relates the rate of a chemical reaction to the concentrations of the reactants.
Understanding the Reaction Rate Constant (k)
For a general reaction: aA + bB → Products
The rate law is expressed as: Rate = k[A]m[B]n
Where:
- Rate is the speed at which reactants are consumed or products are formed.
- k is the rate constant, which is specific to a particular reaction at a certain temperature.
- [A] and [B] are the molar concentrations of reactants A and B, respectively.
- m and n are the orders of the reaction with respect to reactants A and B. These are determined experimentally and are not necessarily equal to the stoichiometric coefficients (a and b).
This calculator uses the experimentally determined orders of the reactants (m and n) to calculate the rate constant (k) from the initial rate and initial concentrations.
The formula used is derived from the rate law:
k = Rate / ([A]m[B]n)
How to Use the Calculator:
- Enter the experimentally determined order for Reactant A (e.g., 1, 2, 0.5).
- Enter the experimentally determined order for Reactant B.
- Input the measured initial rate of the reaction.
- Input the initial molar concentration of Reactant A.
- Input the initial molar concentration of Reactant B.
- Click "Calculate Rate Constant (k)".
Example:
Consider the reaction: 2NO(g) + O₂(g) → 2NO₂(g)
The experimentally determined rate law is: Rate = k[NO]²[O₂]
This means the order with respect to NO is 2, and the order with respect to O₂ is 1.
If the initial rate was measured to be 0.01 M/s when the initial concentration of NO was 0.1 M and the initial concentration of O₂ was 0.2 M:
- Order of Reactant A (NO): 2
- Order of Reactant B (O₂): 1
- Initial Rate: 0.01 M/s
- Initial Concentration of NO: 0.1 M
- Initial Concentration of O₂: 0.2 M
Using the calculator with these values, you would find the rate constant (k).
function calculateRateConstant() {
var orderA = parseFloat(document.getElementById("orderA").value);
var orderB = parseFloat(document.getElementById("orderB").value);
var initialRate = parseFloat(document.getElementById("initialRate").value);
var initialConcentrationA = parseFloat(document.getElementById("initialConcentrationA").value);
var initialConcentrationB = parseFloat(document.getElementById("initialConcentrationB").value);
var resultDiv = document.getElementById("result");
if (isNaN(orderA) || isNaN(orderB) || isNaN(initialRate) || isNaN(initialConcentrationA) || isNaN(initialConcentrationB)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (initialConcentrationA <= 0 || initialConcentrationB <= 0) {
resultDiv.innerHTML = "Initial concentrations must be greater than zero.";
return;
}
var concentrationTerm = Math.pow(initialConcentrationA, orderA) * Math.pow(initialConcentrationB, orderB);
if (concentrationTerm === 0) {
resultDiv.innerHTML = "Error: The denominator (concentration term) is zero. Cannot calculate.";
return;
}
var rateConstant = initialRate / concentrationTerm;
// Determine the units of k based on the overall order of the reaction
var overallOrder = orderA + orderB;
var unit;
if (overallOrder === 0) {
unit = "s⁻¹"; // First order
} else if (overallOrder === 1) {
unit = "M⁻¹s⁻¹"; // Second order
} else if (overallOrder === 2) {
unit = "M⁻²s⁻¹"; // Third order
} else if (overallOrder === 3) {
unit = "M⁻³s⁻¹"; // Fourth order
} else if (overallOrder === 0.5) {
unit = "M⁻⁰.⁵s⁻¹"; // Fractional order
}
else if (overallOrder === 1.5) {
unit = "M⁻¹·⁵s⁻¹"; // Fractional order
}
else if (overallOrder === 2.5) {
unit = "M⁻²·⁵s⁻¹"; // Fractional order
}
else {
unit = "M⁻" + overallOrder + "s⁻¹"; // General case for other orders
}
resultDiv.innerHTML = "The calculated rate constant (k) is:
" + rateConstant.toFixed(6) + " " + unit + "";
}
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