Library / Foundations: Chemistry / FCH-10
Foundations: Chemistry
Mean rate of reaction
Average speed of a reaction from the amount made or used over time.
- Ref
- FCH-10
- Rev
- v1
- Field
- Foundations: Chemistry
- Result
- rate [cm³/s]
Δq is the amount of reactant used or product formed over the time Δt. The quantity can be a mass, volume, or concentration. The gradient of a tangent to the curve at a time gives the rate at that instant.
Divide how much changed by how long it took.
Calculator
- Rate per minute24 cm³/min
- Time to make 100 cm³ at this rate250 s
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Reactions are fastest at the start and slow down as reactants are used up, so the mean rate underestimates the initial rate.
- Raising temperature, concentration, surface area or adding a catalyst all increase the rate.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (cm³/s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Δt Time taken | 1 to 3,600 s | 0.01333 | 48 | 47.99 | +10% | −9.09 % |
| Δq Quantity formed | 0.1 to 1,000 cm³ | 8.333e-4 | 8.333 | 8.333 | +10% | +10 % |
Sweep of Time taken
| Time taken (s) | Mean rate (cm³/s) |
|---|---|
| 1 | 48 |
| 2.783 | 17.25 |
| 7.746 | 6.197 |
| 21.56 | 2.227 |
| 60 | 0.8 |
| 167 | 0.2874 |
| 464.8 | 0.1033 |
| 1,293 | 0.03711 |
| 3,600 | 0.01333 |
Sweep one variable
Variables and how each one contributes
Mean rate
What the equation gives you. Everything else feeds it.
Quantity formed
Volume of gas collected (or mass lost). Directly proportional.
Time taken
Time over which the quantity changed. Inversely proportional.
Worked example with the values above
- Quantity formed: 48 cm³.
- Time taken: 120 s.
- Mean rate = 48 / 120 = 0.4 cm³/s.
Assumptions and limits
- Constant conditions such as temperature.
- The quantity is measured accurately.
Common mistakes
- Mixing units of time (s and min).
- Reading a time from a curve instead of the amount.
Statistics and uncertainty
Timing by hand has an error of about 0.5 s, which matters most for fast reactions.
Where it is used
- Comparing catalysts and conditions.
- Process control and shelf-life testing.
Maths you need
- Gradient: change over time
- Units: cm³ per second