Library / Solution chemistry, equilibria and kinetics / SCH-38
Solution chemistry, equilibria and kinetics
Pseudo-first-order rate constant
Effective first-order rate constant for the rate k[A][B]ᵐ when B is in large excess or buffered, so that its concentration stays constant.
- Ref
- SCH-38
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- kobs [1/s]
When the rate is k[A][B]ᵐ and B is in large excess or buffered, its concentration stays almost constant, so A decays as a first-order process with kobs = k Bᵐ. Plot ln[A] against time to get kobs, then repeat at different B to find m and k. Check that B changes by less than about 5 % during the run, or the pseudo-first-order treatment fails.
Effective first-order rate constant for the rate k[A][B]ᵐ when B is in large excess or buffered, so that its concentration stays constant. Check that B changes little over the time window.
Calculator
- Half-life of A, ln 2/kobs13.86 s
- Time for 90 % conversion, ln 10/kobs46.05 s
- kobs if B is doubled, 2ᵐ kobs0.2 1/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.
- With 0.5 mol/L of B the effective first-order constant is 0.05 1/s, a half-life of 13.86 s for A.
- Doubling B would raise kobs by 4, which is how the order m is read from the slope of ln kobs against ln B.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (1/s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| k Rate constant | 1e-6 to 1,000,000 (L/mol)^m/s | 2.5e-7 | 250,000 | 250,000 | +10% | +10 % |
| B Concentration of the excess reactant | 1e-4 to 10 mol/L | 2e-9 | 20 | 20 | +10% | +21 % |
| m Order in B | 0 to 4 | 0.0125 | 0.2 | 0.1875 | +10% | −12.9 % |
Sweep of Concentration of the excess reactant
| Concentration of the excess reactant (mol/L) | Pseudo-first-order constant (1/s) |
|---|---|
| 1e-4 | 2e-9 |
| 4.217e-4 | 3.557e-8 |
| 0.001778 | 6.325e-7 |
| 0.007499 | 1.125e-5 |
| 0.03162 | 2e-4 |
| 0.1334 | 0.003557 |
| 0.5623 | 0.06325 |
| 2.371 | 1.125 |
| 10 | 20 |
Sweep one variable
Variables and how each one contributes
Pseudo-first-order constant
What the equation gives you. Everything else feeds it.
Rate constant
The rate constant of the full rate law. Raises kobs in direct proportion. Raising it by 10 % (to 0.22) moves the result by +10 %, from 0.05 to 0.055 1/s.
Concentration of the excess reactant
The concentration of the excess reactant, in mol/L. Raises kobs, with a power set by the order m. Raising it by 10 % (to 0.55) moves the result by +21 %, from 0.05 to 0.0605 1/s.
Order in B
The order in B. A higher order makes kobs more sensitive to B (and smaller if B is below 1 mol/L). Raising it by 10 % (to 2.2) moves the result by −12.9 %, from 0.05 to 0.04353 1/s.
Worked example with the values above
- Power of B: Bᵐ = 0.5^2 = 0.25.
- Multiply by k = 0.2.
- kobs = 0.05 1/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
- Using the wrong sign of the stoichiometric coefficient for reactants and products.
- Forgetting that a pseudo-first-order constant includes the excess reactant’s concentration.
- Using rates from different times in a method of initial rates.
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)