Calculating Rate Constant from Half Life

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Rate Constant Calculator from Half-Life

The rate constant (k) is a crucial parameter in chemical kinetics that describes the speed of a chemical reaction. It quantizes how fast reactants are consumed or products are formed. For first-order reactions, the half-life (t1/2) is the time required for the concentration of a reactant to decrease to half of its initial value. The relationship between the rate constant and the half-life for a first-order reaction is fundamental and can be expressed by the equation:

k = ln(2) / t1/2

Where:

  • k is the rate constant (typically in units of time-1, e.g., s-1, min-1, hr-1)
  • ln(2) is the natural logarithm of 2, approximately 0.693
  • t1/2 is the half-life of the reaction (in the same time units as the desired rate constant)

This calculator allows you to easily determine the rate constant of a first-order reaction if you know its half-life. Simply enter the half-life value and select the corresponding time unit.

Rate Constant Calculator

Seconds (s) Minutes (min) Hours (hr) Days (day)
function calculateRateConstant() { var halfLifeInput = document.getElementById("halfLife"); var timeUnit = document.getElementById("timeUnit").value; var resultDiv = document.getElementById("result"); var halfLife = parseFloat(halfLifeInput.value); if (isNaN(halfLife) || halfLife <= 0) { resultDiv.innerHTML = "Please enter a valid positive number for Half-Life."; return; } // Natural logarithm of 2 var ln2 = 0.69314718056; var rateConstant = ln2 / halfLife; var displayUnit = ""; switch (timeUnit) { case "s": displayUnit = "s-1"; break; case "min": displayUnit = "min-1"; break; case "hr": displayUnit = "hr-1"; break; case "day": displayUnit = "day-1"; break; } resultDiv.innerHTML = "The calculated Rate Constant (k) is: " + rateConstant.toFixed(5) + " " + displayUnit + ""; }

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