20.2 Rates and Rate Laws
20.1.Write three additional rate relationships like equation 20.5
using the definition of the rates from equations 20.3 or 20.4.
20.2.The oxidation-reduction reaction between iron metal
and aqueous permanganate ions in acidic solution is
16H(aq) 5Fe (s) 2MnO 4 (aq) →
2Mn^2 (aq) 5Fe^2 4H 2 O ()
At some temperature, the reaction proceeds at such a rate that
1.00 millimole of His consumed in 2 minutes 33.8 seconds.
What is the (invariant) rate of this reaction in units of moles
per second?
20.3.The oxidation-reduction reaction between iron metal
and aqueous permanganate ions in acidic solution is
16H(aq) 5Fe (s) 2MnO 4 (aq) →
2Mn^2 (aq) 5Fe^2 4H 2 O ()
At some temperature, the reaction proceeds at such a rate that
1.00 millimole of His consumed in 2 minutes 33.8 seconds.
What is the rate of this reaction in units of moles of each re-
actant per second and moles of each product per second?
How do these answers differ from the answer in the previous
problem?
20.4.Consider the chemical reaction
A B C →productsDetermine the order with respect to A, B, and C, and con-
struct the complete rate law (including the value of the rate
law constant) from the following experimental data.
Initial rate (M/s) [A] [B] [C]
6.76 10 ^6 0.550 0.200 1.15
9.82 10 ^7 0.210 0.200 1.15
1.68 10 ^6 0.210 0.333 1.15
9.84 10 ^7 0.210 0.200 1.7720.5.Explain how a species might be part of a rate law but
not part of a balanced chemical reaction.
20.6.Refer to Example 20.2 and explain whether any useful
information can be obtained by comparing the first and the
third set of data.
20.7.Rate law experiments don’t always give data in the form
of a rate in moles per second. Some of them give an amount
of time necessary for a reaction to proceed to a given point. The
faster the rate, the less time necessary. For the following data,
assume that the time given is to react 0.10 M of A. Determine
the complete rate law for the reaction A B →products.
Time taken (s) [A] [B]
36.8 0.20 0.40
25.0 0.20 0.60
10.0 0.50 0.60(A classic chemical reaction/demonstration called the iodine
clock reactionis usually measured this way.)
20.8.A researcher determined the rate law
rate k[A]^2
for a simple chemical reaction. If the rate was 2.44 10 ^4 M/s
when [A] was 0.167 M, what would [A] be when the rate of
the reaction is 1.55 10 ^6 M/s?
20.9.What must the units on kbe for the following rate law?
rate k[A]^2 [B]^220.3 Characteristics of Rate Laws
20.10.Derive equation 20.15.
20.11.Explain why plotting [A]tversus time, as equation
20.15 might suggest, would notyield a straight-line plot for a
first-order reaction.
20.12.To a very good approximation, the cooling of a hot
body to room temperature follows first-order kinetics. (In this
case, however, the unit that is changing is kelvins, not molar-
ity. This idea is known as Newton’s law of cooling.) If the rate
constant for a body is 0.0344 s^1 , how long would it take for
a piece of matter to go from 1000 K to 298 K?
20.13.Assume that thermal decomposition of mercuric ox-
ide, HgO, follows first-order kinetics. It can be followed by the
production of oxygen gas as a product:
2HgO (s) →2Hg () O 2 (g)
At a particular temperature, k6.02 10 ^4 s^1. If 1.00 gram
of HgO were present initially, how long would it take to pro-
duce (a)1.00 mL of O 2 (g) at STP; (b)10.0 mL of O 2 (g) at
STP? (STP standard temperature and pressure for a gas.)
20.14.Assume that thermal decomposition of mercuric ox-
ide, HgO, follows second-order kinetics with the same numer-
ical value given in exercise 20.13 for k(but different units).
Answer (a)and (b)above under that assumption. Compare
the answers with the ones from above.
20.15.Derive equation 20.20 from equation 20.19.
20.16.Derive equation 20.22.
20.17. (a)Write a rate law and an integrated rate law for a
chemical reaction that follows third-order kinetics in one of the
reactants. (b)What would you have to plot on a graph in or-
der to get a straight line for a reaction that follows third-order
kinetics?
20.18.Derive an expression for the half-life of (a)a third-
order reaction; (b)a reaction whose order is 1; (c)a reac-
tion whose order is ^12 . (In these last two cases, examples are
rare but known.)
20.19.What are the slope and y-intercept of a straight line
plotted for a zeroth-order reaction?
20.20.Rewrite equation 20.27 so that it has the form of a
straight-line equation and identify the expected slope(s) and
intercept(s) of two possible plots.726 Exercises for Chapter 20
EXERCISES FOR CHAPTER 20