Library / Solution chemistry, equilibria and kinetics / SCH-36
Solution chemistry, equilibria and kinetics
Reaction rate from one species’ concentration change
Average reaction rate per reaction as written, from the change in one species’ concentration Δc over the time Δt and its signed stoichiometric coefficient ν (negative for reactants, positive for products).
- Ref
- SCH-36
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- r̄ [mol/(L·s)]
For a reaction written with stoichiometric coefficients νᵢ (negative for reactants, positive for products), the rate per reaction as written is r = (1/νᵢ) dcᵢ/dt. Over a finite interval, the average is r̄ = Δcᵢ/(νᵢ Δt). Dividing by ν puts the rates of different species on the same basis: a reactant with ν = −2 falling by 0.08 mol/L gives a reaction extent of 0.04 mol/L.
Average reaction rate per reaction as written, from the change in one species’ concentration Δc over the time Δt and its signed stoichiometric coefficient ν (negative for reactants, positive for products). Closed constant-volume batch.
Calculator
- Average rate of change of the species, Δc/Δt−0.004 mol/(L·s)
- Extent of reaction per litre, Δc/ν0.04 mol/L
- Rate in mol/(L·min)0.12 mol/(L·min)
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.
- The reaction proceeded by 0.04 mol/L in 20 s, an average rate of 0.002 mol/(L·s) as written.
- A species with a different coefficient changes at a different speed: here the species itself changes at 0.004 mol/(L·s), which is |ν| times the reaction rate.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (mol/(L·s)) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Δt Time interval | 0.01 to 1,000,000 s | 4e-8 | 4 | 4 | +10% | −9.09 % |
| Δc Change in concentration (final − initial) | −5 to 5 mol/L | −0.125 | 0.125 | 0.25 | +0.2 mol/L | −250 % |
| ν Signed stoichiometric coefficient (negative for reactants) | −4 to −1 | 0.001 | 0.004 | 0.003 | +1 | +100 % |
Sweep of Time interval
| Time interval (s) | Average reaction rate (mol/(L·s)) |
|---|---|
| 0.01 | 4 |
| 0.1 | 0.4 |
| 1 | 0.04 |
| 10 | 0.004 |
| 100 | 4e-4 |
| 1,000 | 4e-5 |
| 10,000 | 4e-6 |
| 100,000 | 4e-7 |
| 1,000,000 | 4e-8 |
Sweep one variable
Variables and how each one contributes
Average reaction rate
What the equation gives you. Everything else feeds it.
Change in concentration (final − initial)
The change in the species’ concentration (final minus initial), in mol/L. Raises the rate in direct proportion. Raising it by 10 % (to −0.088) moves the result by +10 %, from 0.002 to 0.0022 mol/(L·s).
Signed stoichiometric coefficient (negative for reactants)
The signed stoichiometric coefficient: negative for reactants, positive for products. A larger coefficient divides the change among more units, so the rate falls in inverse proportion. Raising it by 10 % (to −2.2) moves the result by −9.09 %, from 0.002 to 0.001818 mol/(L·s).
Time interval
The time interval, in s. A longer interval spreads the same change out, so the rate falls in inverse proportion. Raising it by 10 % (to 22) moves the result by −9.09 %, from 0.002 to 0.001818 mol/(L·s).
Worked example with the values above
- Extent of reaction: Δc/ν = −0.08 / −2 = 0.04 mol/L.
- Divide by the time 20 s.
- r̄ = 0.002 mol/(L·s).
Assumptions and limits
- Constant volume, a well-mixed closed batch at fixed temperature.
- The simple rate law stated, with the same mechanism over the range studied.
Common mistakes
- Giving the stoichiometric coefficient of a reactant a positive sign.
- Using the change over a long interval as an instantaneous rate.
- Forgetting to divide by the coefficient.
Statistics and uncertainty
Rate constants are normally known to 5 % to 10 % and change by about 7 % per kelvin near room temperature for a typical activation energy, so temperature control matters.
Where it is used
- Finding reaction orders and rate constants from experiments.
- Predicting selectivity and relaxation to equilibrium.
Maths you need
- Rate law: rate = k[A]^m[B]^n
- Stoichiometric coefficient: ν, negative for reactants
- First-order decay: c = c₀ e^(−kt)