Rate Law Constant Calculator

by

Rate Law Constant (k) Calculator

Calculation Results:

Rate Constant (k):

Overall Reaction Order:

Standard Units:

function calculateRateConstant() { var rate = parseFloat(document.getElementById('reactionRate').value); var ca = parseFloat(document.getElementById('concA').value); var oa = parseFloat(document.getElementById('orderA').value); var cb_input = document.getElementById('concB').value; var ob_input = document.getElementById('orderB').value; var cb = cb_input === "" ? 1 : parseFloat(cb_input); var ob = ob_input === "" ? 0 : parseFloat(ob_input); if (isNaN(rate) || isNaN(ca) || isNaN(oa)) { alert("Please fill in at least the Reaction Rate, Concentration A, and Order A."); return; } if (ca <= 0 || (cb_input !== "" && cb <= 0)) { alert("Concentrations must be greater than zero."); return; } // Calculation: k = Rate / ([A]^m * [B]^n) var denominator = Math.pow(ca, oa) * Math.pow(cb, ob); var k = rate / denominator; var totalOrder = oa + ob; // Determine Units var unitStr = ""; if (totalOrder === 0) { unitStr = "M·s⁻¹"; } else if (totalOrder === 1) { unitStr = "s⁻¹"; } else if (totalOrder === 2) { unitStr = "M⁻¹·s⁻¹"; } else if (totalOrder === 3) { unitStr = "M⁻²·s⁻¹"; } else { unitStr = "M^(" + (1 – totalOrder) + ")·s⁻¹"; } document.getElementById('kValue').innerText = k.toExponential(4); document.getElementById('overallOrder').innerText = totalOrder; document.getElementById('kUnits').innerText = unitStr; document.getElementById('rateResult').style.display = "block"; }

Understanding the Rate Law Constant (k)

In chemical kinetics, the rate law constant (or specific rate constant), denoted by k, is a proportionality constant that relates the molar concentration of reactants to the rate of a chemical reaction. Unlike the reaction rate itself, which changes as reactants are consumed, the rate constant k remains constant for a specific reaction at a fixed temperature.

The Rate Law Equation

For a general reaction: aA + bB → Products, the rate law is typically expressed as:

Rate = k [A]m [B]n

Where:

  • Rate: The speed of the reaction (usually in M/s).
  • k: The rate law constant.
  • [A], [B]: Molar concentrations of the reactants.
  • m, n: The partial orders of reaction (determined experimentally).

How to Calculate the Rate Constant

To find the value of k, you must rearrange the rate law equation:

k = Rate / ([A]m [B]n)

Units of the Rate Constant (k)

The units of k vary depending on the overall reaction order (the sum of m + n). This is a common point of confusion in chemistry exams. Here is a quick reference guide:

Overall Order Units of k
0 M/s (or mol·L⁻¹·s⁻¹)
1 s⁻¹ (per second)
2 M⁻¹·s⁻¹ (or L·mol⁻¹·s⁻¹)
3 M⁻²·s⁻¹ (or L²·mol⁻²·s⁻¹)

Example Calculation

Suppose you have a first-order reaction where Reactant A has a concentration of 0.20 M and the measured initial rate is 0.0050 M/s. What is the rate constant?

  1. Identify values: Rate = 0.0050, [A] = 0.20, Order = 1.
  2. Apply formula: k = 0.0050 / (0.20)1
  3. Solve: k = 0.025
  4. Determine Units: Since it is first order, the units are s⁻¹.
  5. Final Result: k = 0.025 s⁻¹.

Factors Affecting the Rate Constant

While k is constant for a given reaction at a specific temperature, it will change if certain conditions are altered:

  • Temperature: According to the Arrhenius equation, as temperature increases, k increases significantly because more molecules have the kinetic energy required to overcome the activation energy.
  • Catalysts: Adding a catalyst provides an alternative reaction pathway with a lower activation energy, which effectively increases the rate constant k.
  • Surface Area: In heterogeneous reactions, increasing surface area can affect the observed rate, though k itself is usually defined by the intrinsic chemistry.

Leave a Comment