First-Order Kinetics Calculator
Concentration remaining after a given time, the half-life and the time to reach 90 % conversion.
Results
Concentration
0.548812
mol/L
Percentage
54.8812
%
Half-life
346.574
s
Time
1151.293
s
Reaction rate
0.00109762
mol/(L·s)
What this tool does
In a first-order reaction the half-life does not depend on how much you started with, which is the signature that tells you the order from the data alone. Keep the units of k and t consistent — a rate constant per second needs a time in seconds — and the exponent takes care of the rest.
Formula
[A] = [A]₀ e^(−kt) ; t½ = ln2 ÷ k
Variables
| Symbol | Meaning | Unit |
|---|---|---|
k | Rate constant | 1/s |
c0 | Initial concentration | mol/L |
t | Time | s |
CT | Concentration | mol/L |
PC | Percentage | % |
HL | Half-life | s |
T90 | Time | s |
RT | Reaction rate | mol/(L·s) |
Worked example
- Rate constant0.002 1/s
- Initial concentration1 mol/L
- Time300 s
- Concentration0.548812 mol/L
- Percentage54.8812 %
- Half-life346.574 s
- Time1151.293 s
- Reaction rate0.00109762 mol/(L·s)
Limitations
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.