How to Calculate Rate Equation

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Part 1: Calculate Reaction Order

Use data from two experiments where the concentration of one reactant changes while others remain constant.

Molarity (M or mol/L)
M/s
Molarity (M or mol/L)
M/s
Reaction Order (n):
0

Part 2: Calculate Rate Constant (k)

Calculate k using the general rate law: Rate = k[A]x[B]y

M/s
Molarity (M)
If only one reactant, leave as 1 and order 0
Rate Constant (k):
0

Units depend on total order.

function calculateOrder() { 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); if (isNaN(c1) || isNaN(r1) || isNaN(c2) || isNaN(r2) || c1 <= 0 || c2 <= 0) { alert("Please enter valid positive numbers for concentrations and rates."); return; } // Formula: (Rate2/Rate1) = (Conc2/Conc1)^n // log(Rate2/Rate1) = n * log(Conc2/Conc1) // n = log(Rate2/Rate1) / log(Conc2/Conc1) var rateRatio = r2 / r1; var concRatio = c2 / c1; var n = Math.log(rateRatio) / Math.log(concRatio); // Round to 2 decimal places for display, but usually it's an integer var nRounded = Math.round(n * 100) / 100; var nInteger = Math.round(n); // Check if it's close to an integer var displayVal = (Math.abs(n – nInteger) < 0.05) ? nInteger : nRounded; document.getElementById('orderValue').innerHTML = displayVal; document.getElementById('orderExplanation').innerHTML = "Since the concentration changed by factor " + concRatio.toFixed(2) + " and rate changed by factor " + rateRatio.toFixed(2) + ", the order is approx " + displayVal + "."; document.getElementById('orderResult').style.display = "block"; } function calculateK() { var rate = parseFloat(document.getElementById('k_rate').value); var concA = parseFloat(document.getElementById('k_concA').value); var orderA = parseFloat(document.getElementById('k_orderA').value); var concB = parseFloat(document.getElementById('k_concB').value); var orderB = parseFloat(document.getElementById('k_orderB').value); if (isNaN(rate) || isNaN(concA) || isNaN(orderA) || isNaN(concB) || isNaN(orderB)) { alert("Please enter valid numbers for all fields."); return; } if (concA === 0 || concB === 0) { alert("Concentrations cannot be zero."); return; } // Rate = k [A]^x [B]^y // k = Rate / ([A]^x * [B]^y) var denominator = Math.pow(concA, orderA) * Math.pow(concB, orderB); if (denominator === 0) { alert("Calculation error: Denominator is zero."); return; } var k = rate / denominator; // Determine units var totalOrder = orderA + orderB; var unitText = ""; if (totalOrder == 0) unitText = "Units: M·s⁻¹"; else if (totalOrder == 1) unitText = "Units: s⁻¹"; else if (totalOrder == 2) unitText = "Units: M⁻¹·s⁻¹"; else if (totalOrder == 3) unitText = "Units: M⁻²·s⁻¹"; else unitText = "Units: M^(" + (1-totalOrder) + ")·s⁻¹"; // Format k for scientific notation if very small or large var displayK = k; if (k 10000) { displayK = k.toExponential(4); } else { displayK = k.toFixed(4); } document.getElementById('kValue').innerHTML = displayK; document.getElementById('kUnits').innerHTML = unitText; document.getElementById('kResult').style.display = "block"; }

How to Calculate Rate Equation and Reaction Orders

In chemical kinetics, the Rate Equation (or Rate Law) is a mathematical expression that links the rate of a reaction to the concentrations of the reactants. Determining the rate equation is crucial for understanding the reaction mechanism and predicting how fast a reaction will proceed under different conditions.

The General Formula

For a generic reaction \( A + B \rightarrow C \), the rate law takes the form:

Rate = k [A]x [B]y

  • k: The rate constant (specific to the reaction and temperature).
  • [A], [B]: Molar concentrations of reactants.
  • x, y: Reaction orders with respect to A and B.

Note: The orders \(x\) and \(y\) are not necessarily the stoichiometric coefficients from the balanced equation. They must be determined experimentally.

Method of Initial Rates

The most common way to calculate the reaction order is the Method of Initial Rates. This involves running multiple experiments where the initial concentration of one reactant varies while the others are held constant.

Step-by-Step Calculation

To find the order \(x\) with respect to reactant A:

  1. Select two experiments where [B] is constant but [A] changes.
  2. Set up the ratio of the rates:
    \(\frac{Rate_2}{Rate_1} = \frac{k[A]_2^x [B]^y}{k[A]_1^x [B]^y}\)
  3. Simplify (since \(k\) and \([B]\) cancel out):
    \(\frac{Rate_2}{Rate_1} = \left( \frac{[A]_2}{[A]_1} \right)^x\)
  4. Solve for \(x\) using logarithms:
    \(x = \frac{\log(Rate_2 / Rate_1)}{\log([A]_2 / [A]_1)}\)

Calculating the Rate Constant (k)

Once you have determined the reaction orders (the exponents), you can calculate the rate constant \(k\) using data from any single experiment.

Rearrange the rate law:

k = \(\frac{Rate}{[A]^x [B]^y}\)

Units of k

The units of the rate constant depend on the overall order of the reaction (sum of exponents \(x + y\)):

  • Zero Order (0): M/s (or M·s⁻¹)
  • First Order (1): 1/s (or s⁻¹)
  • Second Order (2): 1/(M·s) (or M⁻¹·s⁻¹)

Example Problem

Experiment 1: [A] = 0.1 M, Rate = 0.002 M/s
Experiment 2: [A] = 0.2 M, Rate = 0.008 M/s

Since the concentration doubled (0.1 to 0.2) and the rate quadrupled (0.002 to 0.008), the reaction is Second Order (\(2^2 = 4\)).

Using our calculator above simplifies this logarithmic process instantly.

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