Kinetics

Chemical Kinetics Reaction Rates:

Reaction Rate: The change in the concentration of a reactant or a product with time (M/s). Reactant → Products A → B

Average rate =

change in number of moles of B change in time ∆ ( moles of B ) ∆t

=

=

∆[B] ∆t

Since reactants go away with time:

Rate = −

∆[A] ∆t

Consider the decomposition of N2O5 to give NO2 and O2: 2N2O5(g)→ 4NO2(g) + O2(g)

reactants decrease with time

products increase with time

From the graph looking at t = 300 to 400 s

Rate O 2 = 0.0009M = 9 × 10−6 Ms −1 100s 0.0037M = 3.7 × 10−5 Ms −1 Rate NO 2 = 100s 0.0019M = 1.9 × 10−5 Ms −1 Rate N 2 O5 = 100s

Why do they differ? Recall:

2N2O5(g)→ 4NO2(g) + O2(g)

To compare the rates one must account for the stoichiometry.

1 Rate O2 = × 9 × 10−6 Ms −1 = 9 × 10−6 Ms−1 1 1 Rate NO 2 = × 3.7 × 10−5 Ms −1 = 9.2 × 10−6 Ms−1 4 1 Rate N 2O5 = × 1.9 × 10−5 Ms−1 = 9.5 × 10−6 Ms−1 2

Now they agree!

Reaction Rate and Stoichiometry

In general for the reaction:

aA + bB → cC + dD

Rate = − 1 ∆ [A] 1 ∆ [ B] 1 ∆ [C] 1 ∆ [ D] =− = = a ∆t b ∆t c ∆t d ∆t

Rate Law & Reaction Order

The reaction rate law expression relates the rate of a reaction to the concentrations of the reactants. Each concentration is expressed with an order (exponent). The rate constant converts the concentration expression into the correct units of rate (Ms−1). (It also has deeper significance, which will be discussed later) For the general reaction:

aA + bB → cC + dD

x and y are the reactant orders

Rate = k [A]x [B]y

determined from experiment.

x and y are NOT the

stoichiometric coefficients.

The Overall Order of a reaction is the sum of the individual orders: Rate (Ms−1) = k[A][B]1/2[C]2 Overall order: or 1 + ½ + 2 = 3.5 = 7/2

seven−halves order

note: when the order of a reaction is 1 (first order) no exponent is written.

Units for the rate constant:

The units of a rate constant will change depending upon the overall order. The units of rate are always M/s or Ms–1 To find the units of a...