How to Calculate the Rate Law of a Reaction

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Rate Law & Reaction Order Calculator

Calculate reaction orders (m, n) and the rate constant (k) using the method of initial rates.

Enter data from three experimental trials:

Trial [A] (Molarity) [B] (Molarity) Initial Rate (M/s)
1
2
3

Calculation Results:

How to Calculate the Rate Law of a Reaction

The rate law is an expression that relates the rate of a chemical reaction to the concentration of its reactants. For a reaction involving two reactants, A and B, the general rate law is written as:

Rate = k [A]m [B]n
  • k: The rate constant, specific to the reaction and temperature.
  • m & n: The reaction orders with respect to reactant A and B. These are usually small integers (0, 1, 2).
  • Overall Order: The sum of the individual orders (m + n).

Step-by-Step Determination

To find the exponents m and n, chemists use the Method of Initial Rates. This involves comparing trials where only one reactant concentration changes while the other stays constant.

  1. Find order 'm': Look for two trials where [B] is constant. Divide the rate of Trial 2 by Trial 1, and the concentration of [A] in Trial 2 by [A] in Trial 1.
    Formula: (Rate 2 / Rate 1) = ([A]2 / [A]1)m
  2. Find order 'n': Look for two trials where [A] is constant. Divide the rate of Trial 3 by Trial 1, and the concentration of [B] in Trial 3 by [B] in Trial 1.
    Formula: (Rate 3 / Rate 1) = ([B]3 / [B]1)n
  3. Solve for k: Once m and n are known, plug the values from any single trial into the rate law equation and solve for k.

Example Calculation

Suppose Trial 1 has [A]=0.1M, Rate=0.01. Trial 2 has [A]=0.2M, Rate=0.04. Since the concentration doubled (2x) and the rate quadrupled (4x), we solve 2m = 4. Therefore, m = 2 (Second Order).

function calculateRateLaw() { var errorBox = document.getElementById("error-box"); var resultBox = document.getElementById("rate-result-box"); var display = document.getElementById("results-display"); errorBox.style.display = "none"; resultBox.style.display = "none"; // Get Inputs var a1 = parseFloat(document.getElementById("concA1").value); var b1 = parseFloat(document.getElementById("concB1").value); var r1 = parseFloat(document.getElementById("rate1").value); var a2 = parseFloat(document.getElementById("concA2").value); var b2 = parseFloat(document.getElementById("concB2").value); var r2 = parseFloat(document.getElementById("rate2").value); var a3 = parseFloat(document.getElementById("concA3").value); var b3 = parseFloat(document.getElementById("concB3").value); var r3 = parseFloat(document.getElementById("rate3").value); // Validation if (isNaN(a1) || isNaN(b1) || isNaN(r1) || isNaN(a2) || isNaN(b2) || isNaN(r2) || isNaN(a3) || isNaN(b3) || isNaN(r3)) { errorBox.innerHTML = "Error: Please enter valid numeric values for all fields."; errorBox.style.display = "block"; return; } if (a1 <= 0 || a2 <= 0 || a3 <= 0 || b1 <= 0 || b2 <= 0 || b3 <= 0 || r1 <= 0 || r2 <= 0 || r3 <= 0) { errorBox.innerHTML = "Error: Concentrations and rates must be greater than zero for logarithmic calculation."; errorBox.style.display = "block"; return; } try { // Find Order m (using Trial 1 and 2 where B is constant) // Rate2/Rate1 = (A2/A1)^m var m = Math.log(r2 / r1) / Math.log(a2 / a1); // Find Order n (using Trial 1 and 3 where A is constant) // Rate3/Rate1 = (B3/B1)^n var n = Math.log(r3 / r1) / Math.log(b3 / b1); // Rounding to nearest 0.5 or integer as usually found in chemistry var m_round = Math.round(m * 2) / 2; var n_round = Math.round(n * 2) / 2; // Find Rate Constant k using Trial 1 // k = Rate / ([A]^m * [B]^n) var k = r1 / (Math.pow(a1, m_round) * Math.pow(b1, n_round)); var overallOrder = m_round + n_round; // Build result output var html = "Order with respect to A (m): " + m.toFixed(2) + " (approx. " + m_round + ")"; html += "Order with respect to B (n): " + n.toFixed(2) + " (approx. " + n_round + ")"; html += "Overall Reaction Order: " + overallOrder + ""; html += "Rate Constant (k): " + k.toExponential(4) + ""; html += "
"; html += "The Rate Law is:"; html += "Rate = " + k.toExponential(2) + " [A]" + m_round + "[B]" + n_round + ""; html += "
"; display.innerHTML = html; resultBox.style.display = "block"; } catch (e) { errorBox.innerHTML = "Mathematical Error: Ensure that concentration changes significantly between trials to determine order."; errorBox.style.display = "block"; } }

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