#rate-constant-calculator {
font-family: sans-serif;
border: 1px solid #ddd;
padding: 20px;
border-radius: 8px;
max-width: 600px;
margin: 20px auto;
background-color: #f9f9f9;
}
#rate-constant-calculator h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
}
#rate-constant-calculator .form-group {
margin-bottom: 15px;
}
#rate-constant-calculator label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
#rate-constant-calculator input[type="number"],
#rate-constant-calculator input[type="text"] {
width: calc(100% – 22px);
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box;
}
#rate-constant-calculator button {
width: 100%;
padding: 12px 15px;
background-color: #007bff;
color: white;
border: none;
border-radius: 5px;
cursor: pointer;
font-size: 16px;
transition: background-color 0.3s ease;
}
#rate-constant-calculator button:hover {
background-color: #0056b3;
}
#rate-constant-calculator #result {
margin-top: 20px;
padding: 15px;
background-color: #e9ecef;
border: 1px solid #ced4da;
border-radius: 4px;
text-align: center;
font-size: 1.1em;
color: #333;
min-height: 50px;
display: flex;
align-items: center;
justify-content: center;
}
.explanation {
margin-top: 30px;
border-top: 1px solid #ddd;
padding-top: 20px;
}
.explanation h3 {
color: #444;
margin-bottom: 10px;
}
.explanation p, .explanation ul {
line-height: 1.6;
color: #666;
}
.explanation li {
margin-bottom: 8px;
}
function calculateRateConstant() {
var preExponentialFactor = parseFloat(document.getElementById("pre_exponential_factor").value);
var activationEnergy = parseFloat(document.getElementById("activation_energy").value);
var gasConstant = parseFloat(document.getElementById("gas_constant").value);
var temperature = parseFloat(document.getElementById("temperature").value);
var resultDiv = document.getElementById("result");
if (isNaN(preExponentialFactor) || isNaN(activationEnergy) || isNaN(gasConstant) || isNaN(temperature)) {
resultDiv.textContent = "Please enter valid numbers for all fields.";
return;
}
if (gasConstant <= 0) {
resultDiv.textContent = "Gas constant must be a positive value.";
return;
}
if (temperature <= 0) {
resultDiv.textContent = "Temperature must be a positive value (in Kelvin).";
return;
}
var exponent = -activationEnergy / (gasConstant * temperature);
var rateConstant = preExponentialFactor * Math.exp(exponent);
if (isNaN(rateConstant)) {
resultDiv.textContent = "Calculation resulted in an invalid number. Check your inputs.";
} else {
resultDiv.textContent = "Calculated Rate Constant (k): " + rateConstant.toExponential(4) + " (units depend on reaction order)";
}
}
Arrhenius Equation Rate Constant Calculator
Enter values above to see the calculated rate constant.
Understanding the Arrhenius Equation
The Arrhenius equation is a fundamental formula in chemical kinetics that describes the temperature dependence of reaction rates. It relates the rate constant (k) of a chemical reaction to the absolute temperature (T), the pre-exponential factor (A), and the activation energy (Ea). The equation is given by:
k = A * exp(-Ea / (R * T))
Where:
- k is the rate constant (units depend on the reaction order, typically s⁻¹, L·mol⁻¹·s⁻¹, etc.).
- A is the pre-exponential factor or frequency factor. It represents the frequency of collisions between reactant molecules with the correct orientation to react. Its units are the same as the rate constant.
- Ea is the activation energy. This is the minimum amount of energy required for reactant molecules to overcome the energy barrier and form products. It is usually expressed in Joules per mole (J/mol) or kilojoules per mole (kJ/mol).
- R is the ideal gas constant. Its value is approximately 8.314 J/(mol·K).
- T is the absolute temperature in Kelvin (K).
- exp() is the exponential function (e raised to the power of the argument).
How to Use This Calculator
To calculate the rate constant (k) at a specific room temperature (or any other temperature), follow these steps:
- Pre-exponential Factor (A): Input the value of the pre-exponential factor for your specific reaction. This value is often determined experimentally or from theoretical calculations. Ensure its units match the expected units of your rate constant.
- Activation Energy (Ea): Enter the activation energy of the reaction in Joules per mole (J/mol).
- Gas Constant (R): The calculator defaults to the standard value of the gas constant (8.314 J/mol·K). You can change this if necessary, but it's rarely needed for typical calculations.
- Temperature (T): Input the temperature in Kelvin (K). For room temperature, 25°C is approximately 298.15 K.
After entering all the required values, click the "Calculate Rate Constant (k)" button. The result will show the calculated rate constant for the given conditions.
Example Calculation
Let's calculate the rate constant for a reaction at 25°C (298.15 K) with the following parameters:
- Pre-exponential Factor (A) = 5.0 x 1010 s-1
- Activation Energy (Ea) = 60,000 J/mol
- Gas Constant (R) = 8.314 J/mol·K
- Temperature (T) = 298.15 K
Using these values, the calculator would determine the rate constant (k).