** Q1:** A proposed mechanism for the reaction 2NO + O

_{2} 2NO

_{2} is

step(1) NO + NO

N

_{2}O

_{2} (k

_{1} E

_{1} = 82kJmol

^{-1})

step(2) N

_{2}O

_{2} NO + NO (k

_{2} E

_{2} = 205kJmol

^{-1})

step(3) N

_{2}O

_{2} + O

_{2} 2NO

_{2} (k

_{3} E

_{3} = 82kJmol

^{-1})

**(a)** Derive the rate law in terms of the rate of formation of NO

_{2} , that is (

*d*[NO

_{2}])/

*dt*. [10]

**(b)**If k

_{2}[N

_{2}O

_{2}] >> k

_{3}[N

_{2}O

_{2}][O

_{2}], show that the rate law reduces to

*d*[NO_{2}]/*dt* = ((2k_{1}k_{3})/k_{2})[N)^{2}][O_{2}]

** (c)** Show that the expression given in (b)is the results obtained by using the rate determining step approximation by deriving the rate law if we assume that steps (1) and (2) are in a rapid equilibrium and step (3) is slow.

**(d)** Using the rate law given in (b), what is the overall activation energy for this reaction?

**Q2:**If

^{234}Pa is the end product of the decay sequence of

^{238}U (actually it’s

^{206}Pb), that is:

^{238}U

^{234}Th

^{234}Pa

where the half-life of

^{238}U to

^{234}Th is 4.5x10

^{9}yr and

^{234}Th to

^{234}Pa is 24.1day

**(a)** If we start with 1 mg of

^{238}U , how much

^{238}U will be present after 60 days?

**(b)** How much

^{234}Th will be present after 60 days?

**(c)** How much

^{234}Pa will be formed after 60 days?

**Q3:**Provided you have sets of initial rate data for enzyme and substrate, explain using words and appropriate equations how to

**(a)** Determine the partial orders and overall order of the reaction.

**(b)** Obtain the value of the pseudo-order rate constant.

**(c)** Obtain the effective rate constant.

**Q4:**For a given reaction the following half-life and initial concentration data was collected. Use this data to determine the reaction’s order and rate constant.

t

_{1/2} / s [A]

_{0} / mol dm

^{-3} 0.160 0.050

0.0841 0.085

**Q5:**A particular enzyme catalyzed reaction was followed and data collected as indicated below. Using the data, determine the Michaelis constant and the maximum velocity of the reaction.

[S(had to include this text to avoid strikeout text effect)]

_{0} / 10

^{-6} mol dm

^{-3} values in order: 31.8, 46.4, 59.3, 118.5, 222.2

v / 10

^{-9} mol dm

^{-3} s

^{-1} corresponding values in order: 0.070, 0.0972, 0.1167, 0.1592, 0.1945

**Q6:****(a)** The half-life for a general nth order reaction is given by the expression t

_{1/2} = (2

^{n-1} - 1)/ k(n-1)[A]

^{n-1}_{0}. Are there any reactions for which the half-life is independent of the initial concentration? If so, what is it and does this expression apply?

**(b)** I discussed the Mechaelis-Menten mechanism of enzyme action in class. What are its limitations?

**(c)** What is the difference between thermodynamic and kinetic control of a reaction.

**(d)** Is it possible for the activation energy of a reaction to be negative? Explain your conclusion and provide a molecular level explanation.

**(e)** Define the terms in and discuss the limitations of the Arrhenius equation?