Please enter valid numerical values greater than zero.
Calculated Rate Constant
0.00
Units
M⁻¹ s⁻¹
Reaction Details
Total Reaction Order: 2
How to Calculate Rate Constants (k) in Chemical Kinetics
In chemical kinetics, the Rate Constant (k) is a proportionality constant that establishes the relationship between the rate of a chemical reaction and the concentrations of the reacting substances. Understanding how to calculate rate constants is fundamental for determining reaction mechanisms and predicting how fast a reaction will proceed under specific conditions.
The Rate Law Equation
To calculate the rate constant, one must first understand the experimental rate law. For a general reaction involving reactants A and B:
Rate = k [A]ᵐ [B]ⁿ
Where:
Rate: The speed of the reaction (usually in M/s or mol·L⁻¹·s⁻¹).
k: The rate constant (units vary based on order).
[A] and [B]: The molar concentrations of the reactants.
m and n: The reaction orders with respect to A and B (determined experimentally).
Rearranging for k
To solve for the rate constant, we rearrange the formula:
k = Rate / ([A]ᵐ [B]ⁿ)
Determining the Units of k
Unlike other constants in physics or chemistry, the units of k change depending on the overall order of the reaction. The overall order is the sum of the individual exponents (m + n).
Reaction Order
Rate Law
Units of k
Zero Order (0)
Rate = k
M · s⁻¹
First Order (1)
Rate = k[A]
s⁻¹
Second Order (2)
Rate = k[A]² or k[A][B]
M⁻¹ · s⁻¹
Third Order (3)
Rate = k[A]²[B] etc.
M⁻² · s⁻¹
The general formula for the units of k is M-(order-1) · s-1, where "order" is the total reaction order.
Example Calculation
Let's look at a practical example. Suppose you have the following experimental data for the reaction 2NO + O₂ → 2NO₂:
Rate: 0.05 M/s
Concentration [NO]: 0.1 M
Concentration [O₂]: 0.1 M
Reaction Order: 2nd order for NO, 1st order for O₂ (Total Order = 3)
Step 1: Set up the equation.
k = Rate / ([NO]² [O₂]¹)
Step 2: Plug in the numbers.
k = 0.05 / ((0.1)² × (0.1)¹)
k = 0.05 / (0.01 × 0.1)
k = 0.05 / 0.001
Step 3: Calculate.
k = 50
Step 4: Determine Units.
Total order is 3. Units are M⁻² · s⁻¹. Answer: k = 50 M⁻² · s⁻¹
Factors Affecting the Rate Constant
It is important to note that while k is constant with respect to concentration, it is temperature-dependent. According to the Arrhenius equation, as temperature increases, the rate constant increases, leading to a faster reaction rate. Catalysts also affect k by lowering the activation energy.
function toggleReactantB() {
var container = document.getElementById('reactantBContainer');
var checkbox = document.getElementById('hasReactantB');
if (checkbox.checked) {
container.style.display = 'block';
} else {
container.style.display = 'none';
}
}
function calculateRateConstant() {
// 1. Get DOM elements
var rateInput = document.getElementById('reactionRate');
var concAInput = document.getElementById('concA');
var orderAInput = document.getElementById('orderA');
var hasB = document.getElementById('hasReactantB').checked;
var concBInput = document.getElementById('concB');
var orderBInput = document.getElementById('orderB');
var resultArea = document.getElementById('result-area');
var errorMsg = document.getElementById('errorMsg');
var kDisplay = document.getElementById('kValue');
var unitDisplay = document.getElementById('kUnits');
var orderDisplay = document.getElementById('totalOrderDisplay');
// 2. Parse values
var rate = parseFloat(rateInput.value);
var concA = parseFloat(concAInput.value);
var orderA = parseFloat(orderAInput.value);
var concB = 1; // Default multiplier identity
var orderB = 0;
// 3. Validation
var isValid = true;
if (isNaN(rate) || rate < 0) isValid = false;
if (isNaN(concA) || concA <= 0) isValid = false; // Conc cannot be 0 or neg for division
if (isNaN(orderA)) isValid = false;
if (hasB) {
concB = parseFloat(concBInput.value);
orderB = parseFloat(orderBInput.value);
if (isNaN(concB) || concB <= 0) isValid = false;
if (isNaN(orderB)) isValid = false;
}
if (!isValid) {
resultArea.style.display = 'none';
errorMsg.style.display = 'block';
return;
}
errorMsg.style.display = 'none';
// 4. Calculation Logic
// Formula: k = Rate / ([A]^m * [B]^n)
var denominator = Math.pow(concA, orderA);
if (hasB) {
denominator = denominator * Math.pow(concB, orderB);
}
if (denominator === 0) {
resultArea.style.display = 'none';
errorMsg.innerText = "Mathematical Error: Division by zero. Check concentrations.";
errorMsg.style.display = 'block';
return;
}
var k = rate / denominator;
var totalOrder = orderA + orderB;
// 5. Unit Determination Logic
// General: M^(-(totalOrder – 1)) * s^-1
// Or: M^(1 – totalOrder) * s^-1
var unitString = "";
// Handle common integer orders for cleaner display
if (totalOrder === 0) {
unitString = "M · s⁻¹";
} else if (totalOrder === 1) {
unitString = "s⁻¹";
} else if (totalOrder === 2) {
unitString = "M⁻¹ · s⁻¹";
} else {
// General case for non-standard or higher orders
var mExponent = 1 – totalOrder;
unitString = "M" + mExponent + " · s⁻¹";
}
// 6. Output Results
// Format numbers nicely (up to 4 scientific digits if very small or large)
var displayK = k;
if (k 10000) {
displayK = k.toExponential(4);
} else {
displayK = parseFloat(k.toFixed(5)); // Remove trailing zeros
}
kDisplay.innerText = displayK;
unitDisplay.innerHTML = unitString;
orderDisplay.innerText = totalOrder;
resultArea.style.display = 'block';
}