20.21.Use equation 20.24 to determine the time it takes for
a zeroth-order reaction to come to completion.
20.22.When ionic compounds crystallize from a supersatu-
rated solution, the crystallization front (that is, the barrier be-
tween the crystalline solid and the supersaturated solution)
typically travels at a constant speed through the solution un-
til it reaches the boundaries of the system, then stops. What
order of rate law is described by this behavior?
20.23.An aqueous reaction that uses the solvent H 2 O as a re-
actant has a given rate law of
rate k[H 2 O][A]where A is the other reactant species. Explain why, in most cir-
cumstances, this reaction can be defined in terms of pseudo
first-order kinetics. What are the units on the rate constant?
20.24.If a reaction has the same rate constant, what time
does it take for a reactant to decrease by 5% (that is, still near
the beginning of the reaction process) if the kinetics are
zeroth-order, first-order, and second-order with respect to that
reactant?
20.25.List at least four experimentally determined parame-
ters that you, an experimenter, can define when exploring the
hydrolysis of ethyl benzoate by aqueous sodium hydroxide.
20.26.Will a plot of the base-10 logarithm of the concentra-
tion, log [A]t, versus time give a straight-line plot for a first-
order reaction? If so, what does the slope of this line equal?
20.4 & 20.5 Equilibrium, Parallel, and
Consecutive Reactions
20.27.Explain why a zeroth-order reaction probably won’t
be zeroth-order for two complete half-lives.
20.28.For the reaction A B C D, various initial rate
measurements were run using A and B only, and C and D only.
From the data below, calculate the equilibrium constant for
the reaction.
Rate (M/s) [A] [B]
1.081 10 ^5 0.660 1.23
6.577 10 ^5 4.01 1.23
6.568 10 ^5 4.01 2.25
Rate (M/s) [C] [D]
7.805 10 ^7 2.88 0.995
1.290 10 ^6 2.88 1.65
1.300 10 ^6 1.01 1.6520.29.Show how equation 20.33 reduces to a simpler form
of an integrated first-order rate law when the reverse reaction
of an equilibrium is negligible.
20.30.Write expressions like equation 20.37 for a set of three
parallel reactions from the same reactant. Use k 1 , k 2 , and k 3
for the three rate constants.
20.31.A trisaccharide is a carbohydrate that is composed of
three sugar (“saccharide”) molecules. Consider a trisaccharide
composed of three different sugars and represented by A-B-C.
In acidic solution, the carbohydrate will hydrolyze in two pos-
sible ways:
QPk 1
A–B–C →A B–C
k 2
A–B–C →A–B C
If k 1 4.40 10 ^5 s^1 and k 2 3.95 10 ^4 s^1 , what is
the ratio A–B/B–C initially? Can you determine the ratio
A–B/B–C when the reaction reaches equilibrium?
20.32.Show that the set of three equations 20.44 satisfies
the law of conservation of matter for the stoichiometry of the
general chemical reaction that is used. (Hint:consider that the
initial amount of material is given by [A] 0 , and show that at
equilibrium the amount of material is still [A] 0 .)
20.33.For a simple set of two parallel reactions, the decrease
of the initial species A is easy to follow graphically by taking
the logarithm of equation 20.38. What is the slope of this
straight-line graph? Is there an easy way to determine the in-
dividual values from this plot alone?
20.34.Can one determine the forms of straight-line graphs
for equations 20.41 and 20.42, keeping in mind that time, t,
is usually the variable that is plotted on the ordinate (that is,
the x-axis)? Why or why not?
20.35.Consider the answers to the two previous questions.
Nowcan the two individual rate constants k 1 and k 2 be de-
termined? How would that be done?
20.36.In Example 20.7, we showed that there will be a “mo-
mentary” buildup of the intermediate product,^210 Po.
(a)Use the [B]texpression in equation 20.47 to derive an ex-
pression for the time it takes for the maximumamount of^210 Po
to be present. Here’s what to do: take the derivative of the ex-
pression for [B]twith respect to time, set it equal to zero (since
if the amount is at a maximum, the plot of the amount versus
time has a slope of zero), and solve for time t.
(b)Use this value for time and equations 20.47 to determine
the specific amounts of^210 Bi,^210 Po, and^206 Pb when the
amount of^210 Po is at a maximum.
20.37.For what values of time, t, will^210 Bi and^206 Pb be at
a maximum? (See exercise 20.36.)
20.38.An interesting pair of consecutive reactions involve the
absorption of ethyl alcohol by the body, which is a first-order
process, and the consequent oxidation of alcohol to acetalde-
hyde by liver alcohol dehydrogenase (LADH), which is a zeroth-
order process. The differential changes in the three states of
ethanol can therefore be described asdd[At]k 1 [A]tdd[Bt]k 1 [A]tk 2dd[Ct]k 2which are slightly modified from equations 20.46. The inte-
grated form of the first equation is the same as for two con-
secutive first-order reactions, but for the second and third re-
actions, they will not be.
(a)What do A, B, and C stand for in this example?Exercises for Chapter 20 727