Enter the sum of exponents in the rate law (e.g., 1st order = 1, 2nd order = 2).
Seconds (s)
Minutes (min)
Hours (h)
Days
Calculation Result
For a reaction of order , the units of the rate constant k are:
Molarity Form:
Expanded Form (mol & L):
How to Calculate the Unit of Rate Constant
In chemical kinetics, the rate constant (k) is a proportionality constant in the rate law equation that links the rate of a chemical reaction to the concentrations of the reacting substances. Unlike other physical constants, the units of k are not fixed; they depend entirely on the overall order of the reaction.
This calculator helps students and chemists quickly determine the correct dimensional analysis for the rate constant based on the reaction order and time units provided.
The General Formula
To determine the units of k manually, we start with the general rate law:
Rate = k [A]n
Where:
Rate is typically measured in concentration over time (M/s or mol·L-1·s-1).
[A] is the concentration (Molarity, M or mol/L).
n is the overall order of the reaction.
Rearranging the equation to solve for k:
k = Rate / [A]n
Substituting the units:
Units of k = (M · s-1) / (M)n
This simplifies to the general formula used by this calculator:
Units of k = M1-n · s-1
Expanded Units (mol and L)
Often, especially in academic questions, you are required to express Molarity (M) as mol/L (or mol·L-1). When we expand the formula, it becomes:
Units of k = (mol/L)1-n · s-1
Which can be rewritten as:
Ln-1 · mol1-n · s-1
Common Reaction Orders and Units
Here is a reference table for the most common integer reaction orders using seconds as the time unit:
Reaction Order (n)
Molarity Form
Expanded Form
Zero Order (0)
M · s-1
mol · L-1 · s-1
First Order (1)
s-1
s-1
Second Order (2)
M-1 · s-1
L · mol-1 · s-1
Third Order (3)
M-2 · s-1
L2 · mol-2 · s-1
Why Unit Consistency Matters
Calculating the unit of the rate constant is often the first step in verifying if a proposed reaction mechanism is plausible. If the units of k derived from experimental data do not match the expected units for the proposed reaction order, there is likely an error in determining the order or the mechanism involves complex intermediate steps.
function calculateRateUnits() {
// Get inputs
var orderInput = document.getElementById('reactionOrder').value;
var timeUnit = document.getElementById('timeUnit').value;
var resultBox = document.getElementById('resultBox');
var displayOrder = document.getElementById('displayOrder');
var molarityResult = document.getElementById('molarityResult');
var expandedResult = document.getElementById('expandedResult');
// Validate Input
if (orderInput === "" || isNaN(orderInput)) {
alert("Please enter a valid numeric Reaction Order.");
return;
}
var n = parseFloat(orderInput);
// Calculation Logic
// General Formula: M^(1-n) * time^(-1)
// Expanded: mol^(1-n) * L^(n-1) * time^(-1)
var exponentM = 1 – n;
var exponentL = n – 1;
var exponentMol = 1 – n;
// Construct Molarity String
var mString = "";
if (exponentM === 0) {
// M^0 is 1, so it disappears. Just time^-1
mString = timeUnit + "-1";
} else if (exponentM === 1) {
mString = "M · " + timeUnit + "-1";
} else {
mString = "M" + exponentM + " · " + timeUnit + "-1";
}
// Construct Expanded String (mol, L, time)
// Order usually: L, then mol, then time (for positive L exponents) or mol, L, time
// Standard convention usually puts positive exponents first, but let's stick to consistent mol L time or L mol time based on standard text.
// Often seen as L^(n-1) mol^(1-n) s^-1 for order >= 2
var expandedStr = "";
if (n === 1) {
// Special case First Order: units cancel out
expandedStr = timeUnit + "-1";
} else {
var parts = [];
// Liter part
if (exponentL !== 0) {
if (exponentL === 1) parts.push("L");
else parts.push("L" + exponentL + "");
}
// Mole part
if (exponentMol !== 0) {
if (exponentMol === 1) parts.push("mol");
else parts.push("mol" + exponentMol + "");
}
// Time part (always -1 for rate constant k usually)
parts.push(timeUnit + "-1");
expandedStr = parts.join(" · ");
}
// Update UI
displayOrder.innerHTML = n;
molarityResult.innerHTML = mString;
expandedResult.innerHTML = expandedStr;
resultBox.style.display = "block";
}