How to Calculate Rate Law for a Reaction
The rate law is a crucial mathematical equation in chemical kinetics that links the rate of a reaction to the concentration of its reactants. Understanding how to calculate the rate law allows chemists to deduce the reaction mechanism and predict how the reaction speed changes under different conditions. This guide covers the method of initial rates, reaction orders, and the rate constant.
Use data from two experiments where the concentration of one reactant changes while others remain constant (Method of Initial Rates).
Understanding the Rate Law Formula
The general form of a rate law for a reaction involving reactant A is:
Rate = k [A]n
- Rate: The speed of the reaction, usually measured in Molarity per second (M/s).
- k: The rate constant. This value is specific to the reaction and temperature.
- [A]: The molar concentration of reactant A.
- n: The reaction order with respect to A. This must be determined experimentally.
The Method of Initial Rates
To calculate the rate law, we typically use the Method of Initial Rates. This involves running the reaction multiple times with different initial concentrations and measuring the initial rate for each run.
By comparing two experiments where the concentration of one reactant changes, we can solve for the order n using the following logarithmic relationship derived from the ratio of the rate laws:
n = log(Rate₂ / Rate₁) / log([A]₂ / [A]₁)
Interpreting Reaction Orders
The reaction order tells us how sensitive the rate is to changes in concentration:
- Zero Order (n=0): Changing concentration has no effect on the rate. Rate = k.
- First Order (n=1): Rate is directly proportional to concentration. Doubling concentration doubles the rate.
- Second Order (n=2): Rate is proportional to the square of the concentration. Doubling concentration quadruples the rate.
Calculating the Rate Constant (k)
Once the reaction order (n) is known, the rate constant (k) can be calculated by rearranging the rate law equation using the data from any single experiment:
k = Rate / [A]n
The units of k change depending on the overall order of the reaction. For a first-order reaction, the unit is s⁻¹. For a second-order reaction, it is M⁻¹s⁻¹.
function calculateRateLaw() { // Get input values using var var c1 = parseFloat(document.getElementById('conc1').value); var r1 = parseFloat(document.getElementById('rate1').value); var c2 = parseFloat(document.getElementById('conc2').value); var r2 = parseFloat(document.getElementById('rate2').value); var resultBox = document.getElementById('result'); // Validation: Check for valid numbers and non-zero concentrations if (isNaN(c1) || isNaN(r1) || isNaN(c2) || isNaN(r2)) { alert("Please enter valid numerical values for all fields."); return; } if (c1 <= 0 || c2 <= 0 || r1 <= 0 || r2 <= 0) { alert("Concentrations and rates must be positive numbers."); return; } if (c1 === c2) { alert("Concentration [A]1 and [A]2 must be different to determine the order."); return; } // Logic: Calculate Reaction Order (n) // Formula: n = log(rate2/rate1) / log(c2/c1) var rateRatio = r2 / r1; var concRatio = c2 / c1; var order = Math.log(rateRatio) / Math.log(concRatio); // Logic: Calculate Rate Constant (k) // Formula: k = rate1 / (c1 ^ n) var k = r1 / Math.pow(c1, order); // Formatting results // Determine if order is close to an integer (0, 1, 2) var displayOrder = order.toFixed(2); var roundedOrder = Math.round(order); // If it's very close to an integer (within 0.05), display the integer if (Math.abs(order – roundedOrder) < 0.05) { displayOrder = roundedOrder; } // Determine units for k based on rounded order var kUnits = ""; if (Math.abs(order – 0) < 0.1) kUnits = "M/s"; // Zero order else if (Math.abs(order – 1) < 0.1) kUnits = "s⁻¹"; // First order else if (Math.abs(order – 2) < 0.1) kUnits = "M⁻¹s⁻¹"; // Second order else kUnits = "(M)^(1-n) s⁻¹"; // Generic // Display Logic document.getElementById('orderResult').innerHTML = displayOrder; document.getElementById('kResult').innerHTML = k.toExponential(3) + " " + kUnits; // Construct the final Rate Law string var lawString = "Rate = " + k.toExponential(2) + " [A]" + displayOrder + ""; document.getElementById('lawDisplay').innerHTML = lawString; // Show result box resultBox.style.display = "block"; }