Chapter 6 - Chemical kinetics: the rates of reactions

The average reaction rate

The average rate of change of the concentration in a time interval adjusted for differences in the stoichiometric coefficients

Instantaneous reaction rate

• the rate of change of the concentration of a species involved in the reaction, divided by the stoichiometric coefficient

• Can be obtained from the slope of the graph of concentration [A] versus time, again corrected for the stoichiometric coefficient.

Rate law

The proportionality constant k is called the rate constant. It depends on the temperature.

r = k[A]^p[B]^q

Reaction order

The powers p and q are the reaction order.

• Shows how the reaction rate depends on the concentration of the species involved.

• The relation between the reaction rate and the reactant concentrations must be obtained from experiment.

Overall order

The sum p + q = overall order

Graph rate vs. concentration [A] zero order

Graph concentration [A] against Time zero order

graph rate against concentration [A] first order

Graph concentration [A] against time first order

graph ln [A]₀/[A] against time first order

Graph rate against concentration [A] second order

Graph concentration [A] against time second order

Graph 1/[A] against time t second order

What does the differential form give us?

• Expresses the rate of change of the concentration of a reactant with respect to time

• Shows how the reaction rate depends on the concentration of the reactant

What does the integrated form give us?

• This is derived from the differential rate law by integrating with respect to time

• Provides a direct relationship between the concentration of the reactant and time.

What does the half-life equation give us?

• This is the time required for the concentration of the reactant to decrease to half of its initial value.

• It is derived from the integrated rate law and depends on the order of the reaction.

Determining the rate law from the integrated rate law graph.

• If a plot of [A] versus time gives a straight line, then the reaction is zeroth order with respect to A

• If a plot of ln[A] versus time gives a straight line, then the reaction is first order with respect to A

• If a plot of 1/[A] versus time gives a straight line, then the reaction is second order with respect to A.

How to determine reaction order from half-life

• Plot ln t_1/2 against ln[A]₀ which should give a straight line.

• The slope equals -(p-1) with p being the reaction order.