19.24.The vapor pressure of Hg at room temperature (taken
as 22.0° C) is 0.001426 mmHg. What is the average collision
frequency of gaseous Hg atoms in a system that contains only
Hg? Use d2.4 Å, and use the ideal gas law to determine
the density of Hg vapors under these conditions.
19.25.A 1.00-mole sample of Xe gas is kept at a tempera-
ture of 298 K. What volume must it have in order to have an
average collision frequency of 1 per second? Assume that the
collision diameter is 4.00 Å.
19.26.What is the total number of collisions per second per
unit volume for the gas system described in the previous
exercise?
19.27.What is the total number of collisions per second for
the gas system described in the previous exercise? (Note how
this question is different from the earlier one.)
19.28.Determine (a)the mean free paths, (b)the average
collision frequencies, and (c)the total number of collisions be-
tween nitrogen and oxygen molecules in air. Assume standard
thermodynamic conditions (273 K and 1 atm) and use d
3.15 and 2.98 Å for nitrogen and oxygen, respectively.
19.29.Consider a gas mixture containing equal concentra-
tions of argon and helium. Without performing any calcula-
tions, determine which is higher: the number of collisions be-
tween helium and helium, the number of collisions between
argon and argon, or the number of collisions between helium
and argon?
19.5 Effusion and Diffusion
19.30.In what ways are effusion and diffusion different? In
what ways are they similar?
19.31.Estimate the rate at which Hg effuses out a hole of
area 0.10 mm^2 at 295 K. The vapor pressure of Hg at this tem-
perature is 0.0014 mmHg.
19.32.Knudsen effusion cells are used to determine vapor
pressures of high-temperature materials. For example, a
Knudsen cell is filled with tungsten and heated to 4500 K in a
vacuum. Measurements show that the cell loses mass—
assumed to be W vapor—at the rate of 2.113 grams per hour
out of a hole that is 1.00 mm^2 in area. Calculate the vapor
pressure of W at 4500 K.
19.33.Knudsen effusion can be used to estimate the amount
of gas entering into a vacuum system from an aperture. If ar-
gon gas at 300 K and 0.100 torr is introduced into a vacuum
system via a tube that had an inner diameter of 0.01625 inches,
how many grams per second of argon are entering the vac-
uum system? (Watch your units on this one!)
19.34.If an atomically clean metal surface is generated in a
vacuum system whose pressure is kept at 1.00 10 ^12 torr,
how many atoms of oxygen per second are colliding with
each square centimeter of the surface? Assume that any resid-
ual gas in the system has the same composition as air, and a
temperature of 295K.
19.35.Using equation 19.54, determine the units of D 12.
19.36.Determine Dfor (a)He and (b)Xe at standard pres-
sure and 25.0°C. Use d2.65 and 4.00 Å, respectively.
19.37.Use Fick’s first law to demonstrate why diffusion stops
when a solute (that is, minor component) gas is evenly spread
in a system of solvent (that is, major component) gas.
19.38.Verify the approximate value for D 12 in Example 19.9,
using hard-sphere radii of 1.6 Å for ammonia and 1.9 Å as an
estimate for air molecules.
19.39.Calculate the total distance traveled by an ammonia
molecule in 1 minute using the definition of average velocity
from classical mechanics and using an average velocity defined
by kinetic theory. Assume T295K.
19.40.Use the Dvalues from exercise 19.36 to determine
how far away from its original position an average atom trav-
els in 1 second if it is He or if it is Xe.
19.41.Consider a variation from the conditions in Example
19.9. Assume that the ammonia is diffusing through an at-
mosphere of (a)helium, or (b)SF 6. Will diffusion be faster or
slower than through air?
19.42.Use Graham’s law to determine the ratio of diffusion
through air of HCl and NH 3 vapors. First, use only the masses
of HCl and NH 3. Then, determine the reduced masses of
(HCl air) and (NH 3 air) and determine the ratio of diffu-
sion. Compare the ratios to the experimentally determined
ratio of about 0.7. Which ratio represents the better model of
reality?
19.43.A recent educational paper claimed that rather than
using HCl or NH 3 or other vapors to illustrate diffusion, one
can use soluble salts dropped on either sides of a petri dish
filled with water. As the salts dissolve, their ions “diffuse” and,
with the correct selection of salts, form a precipitate when
cation and anion diffuse to the same point. The ratio of dis-
tances that the ions travel could be related to their masses,
much as Graham’s law does for gases. Critique this “demon-
stration” of diffusion.19.44.For 1 mole of He at 298 K, compare graphs of gxver-
sus vxand G(v) versus v. What are the similarities and differ-ences in the graphs?
19.45.Use the graph of G(v) from exercise 19.44 to deter-
mine what percentage of atoms have a velocity within 1% of
(a)the root-mean-square speed; (b)the most probable speed;
and (c)the mean speed. Are the percentages similar?Exercises for Chapter 19 679Symbolic Math Exercises