How to Calculate Initial Rate of Reaction

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Initial Rate of Reaction Calculator

Understanding and Calculating the Initial Rate of Reaction

The rate of a chemical reaction is a measure of how quickly reactants are converted into products. The initial rate of reaction specifically refers to the instantaneous rate of the reaction at time zero, when the concentrations of reactants are at their highest and the concentrations of products are zero. This is often the easiest rate to measure experimentally because it minimizes the influence of product accumulation, which can sometimes inhibit the reaction.

The rate of a reaction is typically determined by an experimentally derived rate law. For a general reaction such as:

aA + bB → Products

The rate law is expressed as:

Rate = k[A]m[B]n

Where:

  • Rate is the speed of the reaction (often in units of mol L-1 s-1).
  • k is the rate constant, a proportionality constant specific to the reaction and temperature. Its units depend on the overall order of the reaction.
  • [A] and [B] are the molar concentrations of reactants A and B, respectively.
  • m and n are the reaction orders with respect to reactants A and B, respectively. These orders are not necessarily the stoichiometric coefficients (a and b) and must be determined experimentally.

The initial rate is calculated using the initial concentrations of the reactants and the experimentally determined rate law. If the reaction orders are known, you can plug the initial concentrations directly into the rate law equation to find the initial rate.

How to Use the Calculator:

  1. Initial Concentration of Reactant A (mol/L): Enter the starting molar concentration of reactant A.
  2. Initial Concentration of Reactant B (mol/L): Enter the starting molar concentration of reactant B.
  3. Reaction Order with respect to A: Enter the experimentally determined order (m) for reactant A.
  4. Reaction Order with respect to B: Enter the experimentally determined order (n) for reactant B.
  5. Rate Constant (k): Enter the value of the rate constant (k) for the reaction at the given temperature. Ensure the units of k are consistent with the units of concentration and time you are using.

Clicking "Calculate Initial Rate" will provide you with the calculated initial rate of the reaction.

Example Calculation:

Consider the reaction: 2NO(g) + O2(g) → 2NO2(g)

The experimentally determined rate law is: Rate = k[NO]2[O2]

Let's say the rate constant (k) is 7.5 x 103 M-2s-1, the initial concentration of NO is 0.020 M, and the initial concentration of O2 is 0.030 M.

  • Initial Concentration of Reactant A (NO): 0.020 mol/L
  • Initial Concentration of Reactant B (O2): 0.030 mol/L
  • Reaction Order with respect to A (NO): 2
  • Reaction Order with respect to B (O2): 1
  • Rate Constant (k): 7500 M-2s-1 (or 7.5e3 M-2s-1)

Using the calculator with these values, you would find the initial rate.

Mathematical Formula:

Initial Rate = k * (Initial Concentration of A)Order of A * (Initial Concentration of B)Order of B

function calculateInitialRate() { var initialConcentrationA = parseFloat(document.getElementById("initialConcentrationA").value); var initialConcentrationB = parseFloat(document.getElementById("initialConcentrationB").value); var reactionOrderA = parseFloat(document.getElementById("reactionOrderA").value); var reactionOrderB = parseFloat(document.getElementById("reactionOrderB").value); var rateConstant = parseFloat(document.getElementById("rateConstant").value); var resultDiv = document.getElementById("result"); resultDiv.innerHTML = ""; // Clear previous result if (isNaN(initialConcentrationA) || isNaN(initialConcentrationB) || isNaN(reactionOrderA) || isNaN(reactionOrderB) || isNaN(rateConstant)) { resultDiv.innerHTML = "Please enter valid numbers for all fields."; return; } if (initialConcentrationA < 0 || initialConcentrationB < 0 || rateConstant < 0) { resultDiv.innerHTML = "Concentrations and rate constant cannot be negative."; return; } // Calculate the initial rate var initialRate = rateConstant * Math.pow(initialConcentrationA, reactionOrderA) * Math.pow(initialConcentrationB, reactionOrderB); // Display the result resultDiv.innerHTML = "The calculated initial rate of reaction is: " + initialRate.toExponential(4) + " mol L-1 time unit-1"; // time unit depends on k }

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