First-Order Reaction Rate Constant Calculator
This calculator helps you determine the rate constant (k) of a first-order chemical reaction. A first-order reaction is one whose rate depends on the concentration of only one reactant. The integrated rate law for a first-order reaction is commonly expressed in two forms:
Natural Log Form: ln([A]t) = -kt + ln([A]0)
Exponential Form: [A]t = [A]0 * e^(-kt)
Where:
- [A]t is the concentration of reactant A at time t
- [A]0 is the initial concentration of reactant A at time t=0
- k is the rate constant (what we want to calculate)
- t is the time elapsed
Rearranging the natural log form to solve for k gives us:
k = (ln([A]0) – ln([A]t)) / t
Or, more simply:
k = ln([A]0 / [A]t) / t
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function calculateRateConstant() {
var initialConcentration = parseFloat(document.getElementById("initialConcentration").value);
var finalConcentration = parseFloat(document.getElementById("finalConcentration").value);
var timeElapsed = parseFloat(document.getElementById("timeElapsed").value);
var errorMessage = "";
if (isNaN(initialConcentration) || initialConcentration <= 0) {
errorMessage += "Please enter a valid positive initial concentration.\n";
}
if (isNaN(finalConcentration) || finalConcentration <= 0) {
errorMessage += "Please enter a valid positive concentration at time t.\n";
}
if (isNaN(timeElapsed) || timeElapsed = initialConcentration) {
errorMessage += "The concentration at time t must be less than the initial concentration for a reactant.\n";
}
if (errorMessage !== "") {
document.getElementById("rateConstantValue").innerText = "Error";
document.getElementById("units").innerText = errorMessage.trim();
return;
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var numerator = Math.log(initialConcentration / finalConcentration);
var rateConstant = numerator / timeElapsed;
document.getElementById("rateConstantValue").innerText = rateConstant.toFixed(4);
document.getElementById("units").innerText = "Units: 1/" + "time unit" + " (e.g., s⁻¹, min⁻¹)"; // Placeholder for unit based on time input
}