Concise Physical Chemistry

c21 JWBS043-Rogers September 13, 2010 11:30 Printer Name: Yet to Come

PROBLEMS AND EXAMPLES 357

the left is the same as the number and types of the bonds on the right. One value is

missing from this scheme, that offH^298 fort-butylmethane.

Their calculated enthalpy of reactionrH^298 was

rH^298 =4(− 79 .64672)−(− 197 .35354)−3(− 40 .41828)

= 0 .02150 h= 13 .49 kcal mol−^1 = 56 .44 kJ mol−^1

This enthalpy change is used to calculate the remaining unknown from the experi-

mental values offH^298 for methane and ethane:

rH^298 = 4 fH^298 (ethane)−fH^298 (t-butylmethane)− 3 fH^298 (methane)

13. 5 =4(− 20 .1)−fH 298 (t-butylmethane)−3(− 17 .9)

which leads to

fH^298 (t-butylmethane)=− 40 .2 kcal mol−^1 =− 168 .2kJmol−^1

The experimental value is−39.9±0.2 kcal mol−^1 =− 166 .9kJmol−^1.

Comments:So far, the isodesmic reaction has merely passed the test of reproducing

a known experimental result. Agreement with the experimental value is also good

for the second compound in the series, but experimental work is uncertain and

under debate for the third compound. An experimental value is nonexistent for the

last compound named, which is highly strained and has not yet been synthesized.

The authors carry these calculations on in a logical sequence to obtainfH^298 of

all four compounds di(t-butyl)methane (−59.2), tri(t-butyl)methane (−55.3), and

tetra(t-butyl) methane (−320.7 kcal mol−^1 ). Example 21.2 is a good example of

verification of a method for known compounds followed by extension to unknowns

that are not amenable to experimental work.

Problem 21.1

Chlorine does not react with toluene in the dark. If light is admitted to a chlorine–

toluene mixture, a reaction occurs. Propose a mechanism for this reaction. Propose

an experiment to support or contradict your mechanism.

Problem 21.2

The number density of one mole of methane at 1 bar and 298 K isρ=n/V=

NAp/RT= 2. 43 × 1025 m−^3 under the ideal gas assumption. The collision cross

section is 5. 3 × 10 −^19 m^2 , and the average speed of the methane molecule is〈x〉=

( 8 RT/πM)^1 /^2 =630 m s−^1. What is the collision frequency? Carry all units through

your calculation and demonstrate that the answer is, indeed, a frequency.