482 10 Transport ProcessesPROBLEMS
Section 10.5: Transport in Electrolyte Solutions
10.50Calculate the transference numbers for H+and Cl−ions
in a dilute aqueous HCl solution at 25◦C.
10.51a.Calculate the force on 1.000 mol of sodium ions
(assumed localized in a small volume) at a distance of
1.000 m in a vacuum from 1.000 mol of chloride ions.
b.Find the mass in kilograms and in pounds on which
the gravitational force at the earth’s surface would
equal the force in part a.
10.52Calculate the effective radii of K+and Cl−ions in dilute
aqueous solution at 25◦C.
10.53Calculate the transference numbers for K+and Cl−ions
in a dilute aqueous KCl solution at 25◦C.
10.54a.Calculate the conductivity of an aqueous solution of
NaCl with molarity 0.100 mol L−^1. Assume that the
infinite-dilution values of the mobilities can be used.
b.A cell with two electrodes of area 1.000 cm^2 and
length between the electrodes of 10.00 cm is filled
with the solution of part a. What is its resistance?
c.What is the transference number of each ion?
10.55A conductance cell has two electrodes 1.00 cm by
1.00 cm, separated by a distance of 2.00 cm. Find the
electrical resistance of this cell if it is filled with a
0.00100 mol L−^1 solution of KCl at 25◦C. Assume that
infinite dilution values can be used at this con-
centration.
10.56Calculate the transference numbers for each ion in an
acetic acid solution, assuming that infinite-dilution values
can be used. Does your answer depend on the extent of
ionization? Explain your assertion.
10.57a.Calculate the transference number of each ion in a
solution with 0.00050 mol L−^1 sodium acetate and
0.00100 mol L−^1 sodium chloride, assuming that
infinite-dilution values can be used. Neglect the
hydrolysis of the acetate ions.
b.Calculate the conductivity of the solution of part a.
c.Find the resistance of a cube-shaped cell with side
equal to 1.000 cm, containing the solution of part
a and having electrodes on two opposite sides.Summary of the Chapter
The three transport processes correspond to the transport of some quantity through
space: Heat conduction is the transport of energy, diffusion is the transport of molecules,
and viscous flow is the transport of momentum. These processes are described by
empirical linear laws in which each rate is directly proportional to a single driving
force. According to Fourier’s law the flow of heat is proportional to the temperature
gradient. According to Fick’s law the diffusion flux is proportional to the concentration
gradient. According to Newton’s law of viscous flow the force per unit area to maintain
a shearing flow is proportional to the rate of shear.
Transport processes in a hard-sphere gas can be analyzed theoretically. A formula
for the self-diffusion coefficient was derived in this chapter, and similar formulas for
thermal conductivities and viscosity coefficients were presented. Each transport coeffi-
cient is proportional to the mean free path and to the mean speed, and thus proportional
to the square root of the temperature.
A molecule in a liquid was pictured as partially confined in a cage made up of its
nearest neighbors. This model and an assumed frictional force were related to diffusion
in liquid solutions, to viscosity in pure liquids, and to sedimentation in solutions of
macromolecular substances.
We presented the consequences of assuming that an ion moving through a solution
experiences a frictional force proportional to its speed with a proportionality constant
called a friction coefficient. It was shown that this assumption leads to Ohm’s law for
an electrolyte solution, with a conductivity contribution for each type of ion that is
inversely proportional to the friction coefficient.