What this calculator does
Each reaction order has its own integrated rate law, and the rate constant follows from a concentration measured at a known time. A drop from 1 to 0.5 mol/L over 100 seconds gives 0.005 for zero order, 0.00693 for first and 0.01 for second.
Those three numbers are not comparable, because the units differ: mol/(L·s), per second, and L/(mol·s) respectively. That is the first clue to which order applies. A rate constant only means something once you know the order it belongs to.
The formula
Zero order takes the concentration difference over time. First order takes the log of the concentration ratio over time. Second order takes the difference of reciprocal concentrations over time. Each comes from integrating the corresponding differential rate law, which is where the name comes from.
| Term | Meaning |
|---|---|
| Zero order | Rate independent of concentration. A plot of [A] against t is linear. |
| First order | Rate proportional to concentration. A plot of ln[A] against t is linear. |
| Second order | Rate proportional to concentration squared. A plot of 1/[A] against t is linear. |
| Half-life | Constant for first order, but concentration-dependent for zero and second order. |
The inputs explained
| Field | What to enter |
|---|---|
| Reaction order | The reaction order. If unknown, try each and see which gives a consistent constant across several time points. |
| Initial concentration [A]₀ (mol/L) | Starting concentration. |
| Concentration at time t [A] (mol/L) | Concentration at the later time. |
| Elapsed time (s) | Elapsed time between the two measurements. |
When to use it
Determining a rate constant
Two concentration measurements and a known order are enough.
Identifying the reaction order
Computing k at several time points under each assumption shows which one gives a consistent value.
Predicting remaining concentration
Once k and the order are known, the concentration at any later time follows.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does k change with the extent of reaction?
A range of remaining concentrations after the same elapsed time.
| Concentration remaining | Rate constant k | Concentration consumed | Order used |
|---|---|---|---|
| 0.9 mol/L | 0.00105361 /s | 0.1000 mol/L | First |
| 0.5 mol/L | 0.00693147 /s | 0.5000 mol/L | First |
| 0.25 mol/L | 0.01386294 /s | 0.7500 mol/L | First |
| 0.1 mol/L | 0.02302585 /s | 0.9000 mol/L | First |
Questions
How do I find the reaction order?
Calculate k at several time points under each assumption and see which gives a consistent value. The correct order produces the same rate constant throughout; the wrong ones produce a drifting value. Graphically, this is the plot that comes out as a straight line.
Why do the rate constants have different units?
Because the rate must come out in mol/(L·s) whatever the order, so the constant units adjust to compensate. Zero order is mol/(L·s), first order per second, second order L/(mol·s). The units alone identify the order, which is a useful check.
Is half-life constant?
Only for first order reactions, where it is ln2 over k regardless of starting concentration. That is why radioactive decay, which is first order, has a fixed half-life. For zero and second order the half-life depends on where you start.
What makes a reaction zero order?
Usually a saturated catalyst or surface. When every active site is occupied, adding more reactant cannot increase the rate, so it becomes independent of concentration. Enzyme reactions at high substrate concentration behave this way.
For temperature dependence, see the Arrhenius equation calculator. For the rate constant at a different temperature, see the activation energy calculator.