Lecture 2 - Rate Laws And Reaction Order

Question 1

Definition for instantaneous rates: as an equation

Answer 1

Rate = - d[reactant) / dt

Rate = d[product] / dt

Therefore when you plot a graph of y axis: [product] against time the gradient = rate

Question 2

Stoichometry - what would be the rate eq for a reaction of:
A -> 2P

Give the general case for aA + bB —> cC + dD

Answer 2

Rate = -d[A]/dt = 1/2(d[P]/t)
(As you are making twice as many products)

For a general case of aA + bB —> cC + dD:

Rate = -1/a(d[A]/dt) = -1/b(d[B]/dt) = 1/c(d[C]/dt) = 1/d(d[D]/dt)

Question 3

Rate laws - describing the dependence of reaction rates on the conc of the reactants

What is the differential rate expression for the reaction of A + B -> P

What does each part in the dre mean?

Answer 3

Rate = -d[A]/dt = d[P]/dt = k[A]ᵐ[B]ⁿ

k - rate coefficient / rate constant (depends on T)

m and n are usually integers - they give the order of the reaction with respect to A and B

m + n = overall order of reaction

Note: doesn’t depend on [P] as P doesn’t produce more P, only reactants do

Question 4

How can you determine rate laws?

Answer 4

• Rate law is determined experimentally: it cannot be deduced from the stoichiometry of the reaction.

• Multistep reaction mechanisms can give very complex rate laws e.g.

                     k H2(g) +Br2(g) ⇌ 2 HBr (g)
                     k’

So rate = (k[H2][Br2]^1.5) / [Br2] + k’[HBr]) (as forward and backward reaction) can see H2 is 1st order

• cannot define an overall order for the reaction as cannot work out order of Br2

Question 5

How do you work out units of the rate coefficient, k?

Answer 5

Rate has the units mol dm^-3 s^-1
Conc has units mol dm^-3

So for example:

Rate = k[A]^2[B]
k = (mol dm^-3 s^-1) / (mol dm^-3)^3 and then simplify

Question 6

How to determine rate laws experimentally

Answer 6

By determining the order with respect to one reactant at a time using an isolation method

Eg for A + B -> P we expect rate = k[A]ᵐ[B]ⁿ

By making B large in excess to compared to A, [B] is relatively constant during the reaction (typically when [B] > 10[A])
So rate = k’[A]ᵐ where k’ = k[B]ⁿ (if the reaction is 1st order in [A] ie m=1, k’ = the psuedo-first-order rate coefficient)

Question 7

Determining k’ and m by method of initial rates

Answer 7

Measure the initial rate as [A]₀ is known
Initial rate, r₀ = k’[A]₀ᵐ
Take logs: log₁₀r₀ = log₁₀k’ + mlog₁₀[A]₀
y = c m x

Therefore slope gives you order of reaction with respect to A
If flat line, m = 0
If linear line, depending on steepness m=1 or 2

This method can be very inaccurate if r₀ is not measured accurately. Method is also very wasteful in reactants (needs runs at different [A]₀

REMEMBER: logs don’t have units

Question 8

SUMMARY

Answer 8

• slope of a graph of [reactant] or [product] against time = rate

• The rate law is an empirical relation between reaction rate, the rate coefficient and concentrations of reactants: it gives clues about reaction mechanisms. We can define:
– the order of reaction with respect to each reactant.
– an overall order of reaction

• Isolation method simplifies rate-law determination.

• Method of initial rates is one way of determining the rate law – using integrated rate laws is a better way…