Reaction Rate Constant (k) Calculator
This calculator helps determine the rate constant (k) for a chemical reaction based on experimental data. The method used here assumes a simple rate law, often of the form Rate = k[A]^m[B]^n, where [A] and [B] are reactant concentrations, and m and n are the reaction orders. For many elementary reactions or simplified analyses, we might be interested in the rate constant derived from concentration-time data for a single reactant, assuming a known or easily determined reaction order.
This calculator specifically addresses scenarios where you have initial rate and initial concentration data, or concentration-time data for a pseudo-order reaction where the rate law can be simplified. A common scenario is determining 'k' using the integrated rate law or by calculating the initial rate from concentration-time profiles.
Method 1: Using Initial Rate and Initial Concentration
This method is suitable when you have conducted experiments where you can measure the initial rate of reaction at different initial reactant concentrations. The general form is Rate = k[A]^m. If the reaction order 'm' is known:
Method 2: Using Concentration-Time Data (First-Order Reaction)
For a first-order reaction ([A] decreases over time), the integrated rate law is ln([A]t) = -kt + ln([A]0). Rearranging, k = (ln([A]0) – ln([A]t)) / t. This method uses two points from a single experiment.
Method 3: Using Concentration-Time Data (Second-Order Reaction)
For a second-order reaction where Rate = k[A]^2, the integrated rate law is 1/[A]t = kt + 1/[A]0. Rearranging, k = (1/[A]t – 1/[A]0) / t. This method also uses two points from a single experiment.
function calculateRateConstant1() { var initialRate = parseFloat(document.getElementById("initialRate1").value); var initialConcentration = parseFloat(document.getElementById("initialConcentration1").value); var reactionOrder = parseFloat(document.getElementById("reactionOrder1").value); var resultDiv = document.getElementById("result1"); resultDiv.innerHTML = ""; // Clear previous result if (isNaN(initialRate) || isNaN(initialConcentration) || isNaN(reactionOrder)) { resultDiv.innerHTML = "Please enter valid numbers for all fields."; return; } if (initialConcentration <= 0) { resultDiv.innerHTML = "Initial concentration must be greater than zero."; return; } if (initialRate k = Rate / [A]^m var k = initialRate / Math.pow(initialConcentration, reactionOrder); // Determine units of k based on reaction order // Rate units are typically M/s or mol L^-1 s^-1 // If m=1 (first order): k units are s^-1 // If m=2 (second order): k units are M^-1 s^-1 or L mol^-1 s^-1 // If m=0 (zero order): k units are M s^-1 var rateUnits = "M/s"; // Assuming M/s for rate as a common example var kUnits = ""; if (reactionOrder === 0) { kUnits = rateUnits.replace("M/s", "M s⁻¹"); } else if (reactionOrder === 1) { kUnits = rateUnits.replace("M/s", "s⁻¹"); } else { // For a general order m, the unit of [A]^m is M^m. // So k units are (M/s) / M^m = M^(1-m) s^-1 kUnits = "M^(" + (1 – reactionOrder) + ") s⁻¹"; } resultDiv.innerHTML = "Calculated Rate Constant (k): " + k.toExponential(3) + " " + kUnits; } function calculateRateConstant2() { var initialConcentration = parseFloat(document.getElementById("initialConcentration2").value); var finalConcentration = parseFloat(document.getElementById("finalConcentration2").value); var time = parseFloat(document.getElementById("time2").value); var resultDiv = document.getElementById("result2"); resultDiv.innerHTML = ""; // Clear previous result if (isNaN(initialConcentration) || isNaN(finalConcentration) || isNaN(time)) { resultDiv.innerHTML = "Please enter valid numbers for all fields."; return; } if (initialConcentration <= 0) { resultDiv.innerHTML = "Initial concentration must be greater than zero."; return; } if (finalConcentration <= 0) { resultDiv.innerHTML = "Final concentration must be greater than zero."; return; } if (time = initialConcentration) { resultDiv.innerHTML = "For a reactant, concentration should decrease over time."; return; } // k = (ln([A]0) – ln([A]t)) / t var k = (Math.log(initialConcentration) – Math.log(finalConcentration)) / time; // For first-order reactions, k has units of s⁻¹ (if time is in seconds) resultDiv.innerHTML = "Calculated Rate Constant (k) for First-Order: " + k.toExponential(3) + " s⁻¹"; } function calculateRateConstant3() { var initialConcentration = parseFloat(document.getElementById("initialConcentration3").value); var finalConcentration = parseFloat(document.getElementById("finalConcentration3").value); var time = parseFloat(document.getElementById("time3").value); var resultDiv = document.getElementById("result3"); resultDiv.innerHTML = ""; // Clear previous result if (isNaN(initialConcentration) || isNaN(finalConcentration) || isNaN(time)) { resultDiv.innerHTML = "Please enter valid numbers for all fields."; return; } if (initialConcentration <= 0) { resultDiv.innerHTML = "Initial concentration must be greater than zero."; return; } if (finalConcentration <= 0) { resultDiv.innerHTML = "Final concentration must be greater than zero."; return; } if (time = initialConcentration) { resultDiv.innerHTML = "For a reactant, concentration should decrease over time."; return; } // k = (1/[A]t – 1/[A]0) / t var k = (1 / finalConcentration – 1 / initialConcentration) / time; // For second-order reactions, k has units of M⁻¹ s⁻¹ (if concentration in M and time in s) resultDiv.innerHTML = "Calculated Rate Constant (k) for Second-Order: " + k.toExponential(3) + " M⁻¹ s⁻¹"; }