How to Calculate Units of Rate Constant

Rate Constant (k) Units Calculator

Enter the sum of the exponents in the rate law.
Seconds (s) Minutes (min) Hours (h) Days Years (yr)

Resulting Units for k:


How to Calculate Units of Rate Constant

In chemical kinetics, the rate constant (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 always has units of concentration divided by time (usually M/s), the units of the rate constant change depending on the overall reaction order.

The General Formula

To find the units for any order n, you can use the following universal derivation:

Units of k = M(1 – n) · t-1

Where:

  • M = Molarity (mol/L)
  • n = Overall order of the reaction
  • t = Time (seconds, minutes, etc.)

Common Reaction Orders and Their Units

Order (n) Rate Law Example Units of k
0 (Zero Order) Rate = k M · s-1 or mol/(L·s)
1 (First Order) Rate = k[A] s-1
2 (Second Order) Rate = k[A]2 M-1 · s-1 or L/(mol·s)
3 (Third Order) Rate = k[A]2[B] M-2 · s-1 or L2/(mol2·s)

Practical Example Calculation

Suppose you have a reaction that is 1.5 order overall. What are the units of k if time is measured in minutes?

  1. Identify n = 1.5 and t = min.
  2. Apply the formula: M(1 – 1.5) · min-1.
  3. Simplify: M-0.5 · min-1.
  4. Expanded: (mol/L)-0.5 · min-1 = L0.5 · mol-0.5 · min-1.
function calculateRateUnits() { var nInput = document.getElementById("reactionOrder").value; var timeUnit = document.getElementById("timeUnit").value; var resultArea = document.getElementById("resultArea"); var unitOutput = document.getElementById("unitOutput"); var formattedOutput = document.getElementById("formattedOutput"); if (nInput === "") { alert("Please enter a reaction order."); return; } var n = parseFloat(nInput); var molExponent = 1 – n; var lExponent = n – 1; var displayStr = ""; var expandedStr = ""; // Molarity based notation if (n === 1) { displayStr = timeUnit + "⁻¹"; expandedStr = "Reciprocal " + timeUnit; } else { var mExpStr = (1 – n) === 1 ? "" : (1 – n); displayStr = "M" + formatSuperscript(mExpStr) + " · " + timeUnit + "⁻¹"; // Expansion into mol and L var molStr = ""; if (molExponent !== 0) { molStr = "mol" + formatSuperscript(molExponent); } var literStr = ""; if (lExponent !== 0) { literStr = "L" + formatSuperscript(lExponent); } expandedStr = (literStr + " " + molStr + " " + timeUnit + "⁻¹").trim().replace(/ +/g, ' · '); } unitOutput.innerHTML = displayStr; formattedOutput.innerHTML = "Equivalent to: " + expandedStr; resultArea.style.display = "block"; } function formatSuperscript(num) { if (num === "" || num === 1) return ""; var str = num.toString(); var map = { '0': '⁰', '1': '¹', '2': '²', '3': '³', '4': '⁴', '5': '⁵', '6': '⁶', '7': '⁷', '8': '⁸', '9': '⁹', '-': '⁻', '.': '˙' }; var result = ""; for (var i = 0; i < str.length; i++) { result += map[str[i]] || str[i]; } return result; }

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