How to Calculate the Value of Rate Constant

by

Rate Constant (k) Calculator

Calculation Result:

function calculateRateConstant() { var rate = parseFloat(document.getElementById('reactionRate').value); var cA = parseFloat(document.getElementById('concA').value); var nA = parseFloat(document.getElementById('orderA').value); var cBInput = document.getElementById('concB').value; var mBInput = document.getElementById('orderB').value; var cB = cBInput === "" ? 1 : parseFloat(cBInput); var mB = mBInput === "" ? 0 : parseFloat(mBInput); if (isNaN(rate) || isNaN(cA) || isNaN(nA)) { alert("Please enter valid numbers for Rate, Concentration A, and Order A."); return; } // Formula: k = Rate / ([A]^n * [B]^m) var denominator = Math.pow(cA, nA) * Math.pow(cB, mB); if (denominator === 0) { alert("Concentration values cannot result in zero."); return; } var k = rate / denominator; var totalOrder = nA + mB; // Determine units var units = ""; if (totalOrder === 0) { units = "M/s"; } else if (totalOrder === 1) { units = "s⁻¹"; } else if (totalOrder === 2) { units = "M⁻¹s⁻¹"; } else if (totalOrder === 3) { units = "M⁻²s⁻¹"; } else { units = "M^(" + (1 – totalOrder).toFixed(0) + ")s⁻¹"; } document.getElementById('kValue').innerHTML = "Rate Constant (k) = " + k.toExponential(4); document.getElementById('kUnits').innerHTML = "Units: " + units; document.getElementById('totalOrder').innerHTML = "Overall Reaction Order: " + totalOrder; document.getElementById('resultDisplay').style.display = "block"; }

How to Calculate the Value of Rate Constant (k)

In chemical kinetics, the rate constant (k) is a proportionality constant that links the rate of a chemical reaction to the molar concentrations of the reactants. Understanding how to calculate its value is fundamental for predicting how fast a reaction will proceed under specific conditions.

The Rate Law Formula

The calculation is based on the general Rate Law for a reaction like aA + bB → Products:

Rate = k [A]n [B]m

To solve for k, we rearrange the formula:

k = Rate / ([A]n [B]m)

Step-by-Step Calculation Guide

  1. Determine the Reaction Order: The exponents (n and m) are usually determined experimentally through methods like the Method of Initial Rates. They are not necessarily the same as the stoichiometric coefficients.
  2. Measure Concentration and Rate: Perform an experiment to find the initial rate of the reaction at specific molar concentrations of reactants.
  3. Substitute and Solve: Plug the measured rate and concentrations into the rearranged rate law equation.
  4. Determine the Units: The units for k vary depending on the overall reaction order (n + m).

Common Units for k

Overall Order Units (Standard)
Zero Order M/s (or mol L⁻¹ s⁻¹)
First Order s⁻¹ (per second)
Second Order M⁻¹s⁻¹ (or L mol⁻¹ s⁻¹)
Third Order M⁻²s⁻¹ (or L² mol⁻² s⁻¹)

Example Calculation

Scenario: A reaction is first order in respect to Reactant A. The concentration of A is 0.20 M, and the measured rate is 0.0050 M/s.

Formula: k = Rate / [A]1

Calculation: k = 0.0050 / 0.20 = 0.025

Result: k = 0.025 s⁻¹

Factors Affecting the Rate Constant

It is important to remember that the rate constant is only constant at a specific temperature. If the temperature changes, k changes according to the Arrhenius Equation. Additionally, the presence of a catalyst will increase the value of k by lowering the activation energy of the reaction.

Leave a Comment