Calculate the Value of Rate Constant

Rate Constant (k) Calculator

Calculate the value of the rate constant using the Arrhenius Equation

Frequency of collisions (s⁻¹ or M⁻¹s⁻¹)
Energy barrier for reaction
Absolute temperature (K = °C + 273.15)
J/(mol·K) – Standard Value

Resulting Rate Constant (k):

Understanding the Rate Constant Calculation

The rate constant (k) is a fundamental coefficient in chemical kinetics that quantifies the speed of a chemical reaction. The value of the rate constant depends heavily on the temperature and the activation energy required for the reaction to proceed.

The Arrhenius Equation

This calculator utilizes the Arrhenius Equation, which is the most widely used mathematical model for describing how temperature affects reaction rates:

k = A * e(-Ea / RT)
  • k: The Rate Constant.
  • A: Pre-exponential factor (frequency factor), representing the frequency of collisions with correct orientation.
  • Ea: Activation Energy (input in kJ/mol, converted to J/mol for the calculation).
  • R: The Universal Gas Constant (8.314 J/mol·K).
  • T: Absolute Temperature in Kelvin.

Example Calculation

Suppose you have a reaction with the following parameters:

  • Pre-exponential Factor (A): 1.0 × 1013 s⁻¹
  • Activation Energy (Ea): 50 kJ/mol (50,000 J/mol)
  • Temperature (T): 300 K

Plugging these into the formula:
k = 1.0e13 * exp(-50000 / (8.314 * 300))
k = 1.0e13 * exp(-20.046)
k ≈ 1.98 × 104 s⁻¹

Why is the Rate Constant Important?

Calculating the rate constant allows chemists to predict how long a reaction will take to reach completion under specific environmental conditions. It is essential in industrial chemistry for optimizing reactor yields and in pharmacology for determining drug shelf-life and metabolic rates.

function calculateRateConstant() { var a = parseFloat(document.getElementById('preExpA').value); var ea_kj = parseFloat(document.getElementById('actEnergy').value); var t = parseFloat(document.getElementById('tempK').value); var r = 8.314; var error = false; if (isNaN(a) || a <= 0) { alert("Please enter a valid positive Pre-exponential Factor (A)."); error = true; } else if (isNaN(ea_kj)) { alert("Please enter a valid Activation Energy (Ea)."); error = true; } else if (isNaN(t) || t <= 0) { alert("Please enter a valid Temperature in Kelvin (must be greater than 0)."); error = true; } if (!error) { // Convert Ea from kJ/mol to J/mol var ea_j = ea_kj * 1000; // Arrhenius calculation: k = A * exp(-Ea / (R * T)) var exponent = -ea_j / (r * t); var k = a * Math.exp(exponent); // Result formatting var displayK = k; if (k 10000) { displayK = k.toExponential(4); } else { displayK = k.toFixed(6); } document.getElementById('kValueDisplay').innerText = displayK; document.getElementById('kFormulaDisplay').innerText = "Calculation: " + a + " * e^(-" + ea_j + " / (8.314 * " + t + "))"; document.getElementById('kResultContainer').style.display = 'block'; // Scroll to result document.getElementById('kResultContainer').scrollIntoView({ behavior: 'smooth', block: 'nearest' }); } }

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