Calculate Rate Constant from Graph

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Calculating the Rate Constant (k) from a Reaction Graph

In chemical kinetics, understanding the rate at which a reaction proceeds is crucial. The rate constant, denoted by 'k', is a proportionality constant that relates the rate of a reaction to the concentration of the reactants. For many reactions, especially those studied using graphical methods, the rate constant can be determined by analyzing a plot of concentration versus time or its integrated form.

First-Order Reactions: For a first-order reaction, the integrated rate law can be expressed as:
ln[A]t = -kt + ln[A]0
where:

  • [A]t is the concentration of reactant A at time t
  • [A]0 is the initial concentration of reactant A
  • k is the rate constant
  • t is time
A plot of ln[A]t (y-axis) versus time 't' (x-axis) for a first-order reaction yields a straight line. The slope of this line is equal to -k. Therefore, to find the rate constant k, you simply take the negative of the slope.

Second-Order Reactions: For a second-order reaction (where the rate depends on the square of the concentration of one reactant, or the product of two reactant concentrations), the integrated rate law can be expressed as:
1/[A]t = kt + 1/[A]0
where:

  • [A]t is the concentration of reactant A at time t
  • [A]0 is the initial concentration of reactant A
  • k is the rate constant
  • t is time
A plot of 1/[A]t (y-axis) versus time 't' (x-axis) for a second-order reaction also yields a straight line. In this case, the slope of the line is equal to the rate constant k.

This calculator helps you determine the rate constant (k) by providing two points from your concentration-time graph, effectively calculating the slope of the linearized plot.

Rate Constant Calculator

First Order Second Order
function calculateRateConstant() { var time1 = parseFloat(document.getElementById("time1").value); var concentration1 = parseFloat(document.getElementById("concentration1").value); var time2 = parseFloat(document.getElementById("time2").value); var concentration2 = parseFloat(document.getElementById("concentration2").value); var reactionOrder = parseInt(document.getElementById("reactionOrder").value); var resultDiv = document.getElementById("result"); if (isNaN(time1) || isNaN(concentration1) || isNaN(time2) || isNaN(concentration2)) { resultDiv.innerHTML = "Please enter valid numerical values for all fields."; return; } if (time1 === time2) { resultDiv.innerHTML = "Time 1 and Time 2 cannot be the same."; return; } if (concentration1 <= 0 || concentration2 <= 0) { resultDiv.innerHTML = "Concentrations must be positive."; return; } var deltaT = time2 – time1; var y1, y2; if (reactionOrder === 1) { // For first-order, plot ln[A] vs t. Slope = -k. if (concentration1 <= 0 || concentration2 <= 0) { resultDiv.innerHTML = "Logarithm of concentration is undefined for non-positive values. Please enter positive concentrations."; return; } y1 = Math.log(concentration1); y2 = Math.log(concentration2); } else if (reactionOrder === 2) { // For second-order, plot 1/[A] vs t. Slope = k. if (concentration1 === 0 || concentration2 === 0) { resultDiv.innerHTML = "Inverse of concentration is undefined for zero values. Please enter non-zero concentrations."; return; } y1 = 1 / concentration1; y2 = 1 / concentration2; } else { resultDiv.innerHTML = "Invalid reaction order selected."; return; } var slope = (y2 – y1) / deltaT; var rateConstant; var units; if (reactionOrder === 1) { rateConstant = -slope; units = "s⁻¹"; } else { // reactionOrder === 2 rateConstant = slope; units = "M⁻¹s⁻¹"; } // Displaying the result with appropriate units resultDiv.innerHTML = "Calculated Rate Constant (k): " + rateConstant.toFixed(6) + " " + units + ""; } .calculator-container { font-family: sans-serif; max-width: 800px; margin: 20px auto; padding: 20px; border: 1px solid #ddd; border-radius: 8px; display: flex; flex-wrap: wrap; gap: 20px; background-color: #f9f9f9; } .article-content { flex: 1; min-width: 300px; line-height: 1.6; } .article-content h2 { color: #333; margin-bottom: 15px; } .article-content p { color: #555; margin-bottom: 10px; } .article-content ul { margin-left: 20px; margin-bottom: 10px; } .article-content li { margin-bottom: 5px; } .calculator-form { flex: 1; min-width: 250px; background-color: #fff; padding: 20px; border-radius: 8px; box-shadow: 0 2px 4px rgba(0,0,0,0.1); } .calculator-form h3 { text-align: center; color: #333; margin-bottom: 20px; } .input-group { margin-bottom: 15px; } .input-group label { display: block; margin-bottom: 5px; color: #555; font-weight: bold; } .input-group input[type="number"], .input-group select { width: calc(100% – 12px); padding: 8px; border: 1px solid #ccc; border-radius: 4px; box-sizing: border-box; } .calculator-form button { width: 100%; padding: 10px; background-color: #007bff; color: white; border: none; border-radius: 4px; cursor: pointer; font-size: 16px; transition: background-color 0.3s ease; } .calculator-form button:hover { background-color: #0056b3; } #result { margin-top: 20px; padding: 10px; border: 1px solid #eee; background-color: #f0f0f0; border-radius: 4px; text-align: center; font-size: 1.1em; color: #333; }

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