skddod (DjoaosOosm JOHN J. ALEXANDER University of Cincinnati Cincinnati, 45221
Collision Theory
volume
=
2.5 mi3 X (1.6 X 103
total number
J. Chem. Educ. 1978.55:243. Downloaded from pubs.acs.org by KAROLINSKA INST on 01/23/19. For personal use only.
Given the following information, what is the maximum number of “monsters” which could inhabit Loch Ness? The loch is 24 mi long and 1 mi wide with an average depth of 540 ft. 2) A rough estimate of the swimming velocity is 3 m sec-1. 3) The frequency of sightings by underwater stroboscopic photography in 1975 was once every 104-105 sec. 4) Because of the loch’s turbidity, the visibility range is only about 1)
10 m.
Hints collision. with a stationary and dissimilar target time of collision t {nav)-1 where
a mean
=
n
number of density of objects
=
collision cross-section
=
a
v
3) Consider
a
a
=
-nr2
where
r
=
visibility around the tar-
get.
culation.
Literature Cited (1) Sagan, C., Nature 264, 497 (1976).
mean
time for collision is t
=
as
104-105 sec. Assume t cr
v
=
3 m sec
=
tit2
=
t(JU 5 X 104 sec =
3.1 X 102 m2
(5 X 104 sec)(3.1 X 102 m2)(3
=
=
6.12
m
sec-1)
=
-log [H30+]
[H30+] 10-6-12 7.6 X 10-7 M (b) In pure H20, [OH-] = [HsO+], so [OH-] = 7.6 X 10-7 M (c) Neutral, since [H30+] [OH-] 10-7 M. Apparently (d) Water has a pH of 7.0 at 25°C since [H30+] the dissociation is more extensive at 100°C producing higher ion concentrations. At this temperature the value of Kw will be different from that at 25° C. =
=
=
10-8 monsters m-3
2 X =
=
volume
(a) Calculate the [H30+] in water at 100°C. (b) Calculate the [OH-] in water at 100° C. (c) Is this water acidic, basic, or neutral? What is the basis for your
=
_1_
total number
ion.
(a) pH
——
1
=
First year students sometimes fail to connect general features of equilibrium theory with the study of ionic equilibria in aqueous solution. This question requires the resolution of a conflict between a common sense notion (How can pure water be anything but neutral?) and an isolated fact (The pH of pure water is 7.). The dilemma is resolved by the realization that Kw, like other equilibrium constants, depends on T. Answering this question requires students to synthesize material which usually has been presented in separated fash-
Satisfactory Answer
=
(3.14)(10 m)2
—
M, J. Steffel Ohio State University Marion Campus Marion, Ohio 43302
—
no v
The number density of creatures is n t is given
Temperature Dependence of Kw
answer? (d) Why is the pH not 7.00?
Satisfactory Answer The
creatures
Question At 100°C the pH of pure water is 6.12.
velocity
is the range of
2 X 102
Biomass calculations, based on assumptions about the diet of these creatures, indicate a population of 102±1 in agreement with this cal-
Question
with
(2 X 10-8 creatures m-3) X (1.0 X 1010 m3) =
Defining an observation as the “collision” of an object with an observation device permits an interesting application of collision theory to a problem of current interest. Depending on the number of hints supplied by the instructor, the following question could be employed in general or physical chemistry courses.
1) Consider a sighting to be 2) A moving object collides
=
1)3
1.0 X 1010 m3
=
Richard S. Myers Department of Physical Sciences Delta State University Cleveland, Mississippi 38733
mi
m
number density X volume n
X volume
24 mi X =
1
mi X
2.5 mi3
540 ft 5280 ft mi-1
Exam Question Exchange offers teachers an opportunity to share prize exam questions with others. Guidelines for preparing exam questions for submission were outlined on page 608 of the October 1977 issue. All questions submitted become the property of the Journal of Chemical Education and will not be returned. Questions shquld be submitted to the column editor.
Volume 55, Number 4, April 1978 / 243
