Second-Order Reaction Kinetics Calculator
Concentration left after a given time in a second-order reaction, its half-life and the time to reach 90 % conversion.
Results
Concentration left
0.31250
mol/L
Half-life (at this starting concentration)
100.00
s
Time to 90 % conversion
900.00
s
Conversion reached
37.50
%
The dashed line marks the value you entered.
What this tool does
In a second-order reaction the rate depends on the square of the concentration, so it slows down much more than a first-order one as the reactant runs out. The half-life is not constant: each half-life is twice as long as the one before, and it depends on how much you started with. The dashed curve is a first-order reaction with the same first half-life — the two agree at that point and then part ways, which is a quick way to tell them apart in data.
Formula
1 ÷ [A] = 1 ÷ [A]₀ + k t · t½ = 1 ÷ (k [A]₀)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
a0 | Initial concentration | mol/L |
k | Rate constant k | L/(mol·s) |
t | Time | s |
A | Concentration left | mol/L |
HL | Half-life (at this starting concentration) | s |
T9 | Time to 90 % conversion | s |
CV | Conversion reached | % |
Worked example
- Initial concentration0.5 mol/L
- Rate constant k0.02 L/(mol·s)
- Time60 s
- Concentration left0.31250 mol/L
- Half-life (at this starting concentration)100.00 s
- Time to 90 % conversion900.00 s
- Conversion reached37.50 %
Limitations
- 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.