Instrument 04
Half-life
Order, k and [A]₀ in; the half-life, a countdown of half-lives and [A] at any time out.
This is the instrument’s sample run (demo numbers). Change anything and press Run, or start from an empty form.
Result
t½ = 50.0 min
- Rate law
- rate = k[A]2, k = 0.250 M−1 min−1
- [A] at t = 30 min
- 0.0500 M
- Time to [A] = 0.01 M
- 350 min
Second order: each half-life is twice as long as the one before.
Half-life countdown
| Half-life | Length (min) | Ends at (min) | [A] then (M) |
|---|---|---|---|
| 1 | 50.0 | 50.0 | 0.0400 |
| 2 | 100 | 150 | 0.0200 |
| 3 | 200 | 350 | 0.0100 |
| 4 | 400 | 750 | 5.00 × 10−3 |
| 5 | 800 | 1,550 | 2.50 × 10−3 |
The working
Intermediate values are carried to six significant figures; results are rounded to three at the end.
- t½ = 1/(k[A]0) = 1 / (0.25 × 0.08) = 50.0 min.
- Second order: each half-life starts from half the concentration, so it lasts twice as long as the one before.
- [A] at t = 30 min: 1/[A] = 1/[A]0 + kt = 1/0.08 + (0.25 × 30) = 12.5 + 7.5 = 20 M−1, so [A] = 1/20 = 0.0500 M.
- Time to [A] = 0.01 M: t = (1/[A] − 1/[A]0) / k = (1/0.01 − 1/0.08) / 0.25 = (100 − 12.5) / 0.25 = 350 min.
Keep this run
- Bench Pass
- $1.95 a month or $19.50 a year
- Exam Week Pass
- $1.00 for 7 days
Free during previewCompare the plans