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Concept 01 / 06Chemical Kinetics
Rate of a Chemical Reaction: Average and Instantaneous Rates
Definition of reaction rate in terms of reactants and products, average versus instantaneous rate from concentration-time graphs, expressing rate for reactions with different stoichiometric coefficients, units of rate, and the factors that influence reaction rates.
Figure 1
Chemical kinetics studies how fast reactions proceed, the factors affecting speed, and the mechanism by which they occur. Thermodynamics tells whether a reaction is feasible; kinetics tells how fast it goes (diamond turning into graphite is feasible but immeasurably slow).
Rate of reaction. The change in concentration of a reactant or product per unit time. For R→P:
average rate =−ΔtΔ[R]=ΔtΔ[P].
The minus sign makes the rate positive, since reactant concentration falls. Units: molL−1s−1 (or atms−1 for gases).
Because rate usually changes with time, the instantaneous rate at a moment t is the limit as Δt→0:
rinst=−dtd[R]=dtd[P],
found as the negative slope of the tangent to the [R]-t curve at that point (see figure).
Stoichiometry. For aA+bB→cC+dD, a single rate is defined by dividing each rate of change by its coefficient:
r=−a1dtd[A]=−b1dtd[B]=c1dtd[C]=d1dtd[D].
Example: 2N2O5→4NO2+O2: r=−21dtd[N2O5]=41dtd[NO2]=dtd[O2].
Factors affecting rate. Concentration (or pressure) of reactants; temperature; nature of reactants (ionic reactions are fast; those breaking strong covalent bonds are slow); surface area (powdered solids react faster); catalysts; and for some reactions, light (photochemical reactions).
Key Takeaways:
- Rate =−a1dtd[A]=c1dtd[C].
- Instantaneous rate = negative slope of the tangent to the reactant curve.
- Units of rate: molL−1s−1.
- Rate generally decreases as reactants are used up.
- Pitfall: the rate of disappearance of a reactant is not the same as the rate of the reaction unless its coefficient is 1.
Brain-Teaser 1: For 2N2O5→4NO2+O2, NO2 forms at 5.2×10−3molL−1s−1. Find the rate of reaction and the rate of disappearance of N2O5.
Solution: r=41×5.2×10−3=1.3×10−3molL−1s−1. −dtd[N2O5]=2r=2.6×10−3molL−1s−1.
Brain-Teaser 2: In N2+3H2→2NH3, the rate of formation of ammonia is 2×10−4molL−1s−1. Find the rates of consumption of N2 and H2.
Solution: r=21×2×10−4=10−4. N2: 10−4; H2: 3×10−4molL−1s−1.
Brain-Teaser 3: In the reaction R→P, the concentration of R falls from 0.03M to 0.02M in 25min. Find the average rate in seconds.
Solution: −ΔtΔ[R]=25×600.01=6.67×10−6molL−1s−1.
