Concise Physical Chemistry

c10 JWBS043-Rogers September 13, 2010 11:26 Printer Name: Yet to Come

162 CHEMICAL KINETICS

Problem 10.1

Assume that the reaction

A

k

→products

is a simple first-order decay. If the amount of A drops from an initial value att= 0

of 0.5000 mols to 0.0625 mol in exactly 1.0 hour, what is the rate constantkand half

time for the reaction?

Problem 10.2

The curie (Ci) is a measure of radioactive decay frequency 1 Ci= 3. 7 × 1010 s−^1 .A

1.50 mg sample of theβemitter technetium-99 has an activity of 5. 66 × 107 cpm

(counts per minute). Recall that technetium is^9944 Tc and theβparticle is an electron.

(a) What are the products of the reaction? Write the reaction.

(b) Find the frequency in units of Ci.

(c) Find the rate constant (decay constant)k, in whatever unit you choose, and

find the half-life in units of years for^9944 Tc.

Problem 10.3

In population ecology, an exponential growth curve

P(t)=Aekt

is often assumed for the uncontrolled growth of a newly introduced species where

P(t) is the population at timetandAis a parameter. A new crab was accidentally

introduced into San Francisco bay several years go. Routine trapping and systematic

population monitoring found 12 crabs at the beginning of the survey; two years later,

24 crabs were found at the same location by the same trapping and sampling method.

What was the doubling time of the species? FindkandA. What is the estimated crab

sample after 10 years fromt=0?

Problem 10.4

Further spot checks of the population increase of the invasive species showed the

following results:

t(years) 0 2 3 5 8 10

P(t) 12 24 39 59 167 300

Reevaluate the parametersAandkusing a linear least-squares method. What is the

predicted sample at the 12 year survey?