10.5 Electrical Conduction in Electrolyte Solutions 483ADDITIONAL PROBLEMS
10.58The thermal conductivity, viscosity, and self-diffusion
coefficient of argon gas are listed for one or more
temperatures in Tables A.16, A.18, and A.19 of the
appendix.
a.Calculate the effective hard-sphere diameter of argon
atoms at 0◦C from the viscosity and self-diffusion
coefficient values. Compare your two values with each
other and with the value in Table A.15. Comment on
any discrepancies.
b.Calculate the effective hard-sphere diameter of argon
atoms at 20◦C from the thermal conductivity and
viscosity values. Compare your two values with each
other and with the value in Table A.15. Comment on
any discrepancies.
c.Calculate the value of the self-diffusion coefficient of
argon at 20◦C and 1.00 atm, using Eq. (10.3-9) and the
value of the effective hard-sphere diameter from
Table A.15.
d.Calculate the self-diffusion coefficient of argon at
1.00 atm and 20◦C by interpolation in Table A.19. To
do the interpolation, divide each value in the table by
T^3 /^2 and do a linear least-squares fit to the resulting
values. Comment on the closeness of your fit. Why is
T^3 /^2 the correct factor to use?
e.Using your least-squares fit from part d, find the value
of the self-diffusion coefficient of argon at 473 K and
1.00 atm.
f.Using your value from part c, calculate the effective
hard-sphere diameter of argon atoms at 473 K and
compare it with the value in Table A.15.
10.59The diffusion coefficient of urease (an enzyme) in water
at 25◦C is equal to 3. 5 × 10 −^11 m^2 s−^1.
a.Calculate the rms distance diffused in one direction
in 1.000 hour by urease molecules in water
at 20◦C.
b.Estimate the molecular radius, assuming spherical
molecules.
c.Assuming a density of 1.25 g mL−^1 for the enzyme,
estimate the molar mass.
d.Estimate the sedimentation coefficient.
e.A solution of urease is placed in an ultracentrifuge in
which the same cell is 10.0 cm from the axis of
rotation. If the ultracentrifuge is turning at 100000
revolutions per minute, calculate the time needed for
urease molecules to sediment a distance of 2.00 mm.
10.60Calculate the root-mean-square distance diffused in three
dimensions in 30.0 minutes in a self-diffusion experiment
at 273 K and 1.00 atm for each of the following gaseous
substances:
a.Argon
b.Carbon dioxide
c.Hydrogen
d.Methane
10.61a.Derive an equation for the flow of heat that is
analogous to Fick’s second law of diffusion, Eq.
(10.2-11). Assume a constant heat capacity and a
constant thermal conductivity.
b.Assume that two pieces of aluminum have been
machined so that they fit together perfectly. Assume
that one piece is initially at 30◦C and the other is
initially at 20◦C and that they are suddenly placed in
contact. Write a formula for the temperature profile as
a function of time and of the perpendicular distance
from the junction of the pieces.
10.62.Give verbal explanations for each of the following:
a.Each of the formulas for the transport coefficients in a
hard-sphere gas is proportional toλand to〈v〉.
b.The viscosity of a gas increases with temperature.
c.The diffusion coefficient is inversely proportional
toN.
d.The thermal conductivity and viscosity of a
hard-sphere gas are independent ofN.
10.63Identify each statement as either true or false. If a
statement is true only under certain circumstances, label it
as false.
a.An irreversible process always raises the entropy of
the universe.
b.An irreversible process always raises the entropy of
the system.
c.A temperature gradient can cause a diffusion flow to
occur.
d.Ohm’s law is exactly obeyed by electrolyte solutions.