Page 222 - Modern physical chemistry

9.5 Ohm's Law 215

[, and if the average velocity at which they move is proportional to [, and to the perti-
nent potential gradient, then the total current 1 is also proportional to [. We then have

1=1[=& [9.35]
R
with conductance L and resistance R constant. When 1 is in amperes and e in volts, L is
in mhos and R in ohms.
Consider a uniform conductor of length l and cross sectional area A. Since voltages
in series add, resistances in series add and the resistance of the conductor is propor-
tional to its length. Since charges add, parallel currents add. So conductances in paral-
lel add and the conductance of the conductor is proportional to its cross sectional area.
Se have
R=p~. [9.36]
A
The constant of proportionality p is called the specific resistance. The reciprocal of the
specific resistance is the specific conductance

1 lIA
1\.=-=--. [9.37]
P R
To measure the conductance of an electrolytic solution, one fills a conductivity cell
with the solution and inserts it in a Wheatstone bridge circuit. See figures 9.3 and 9.4.
Direct current is not used because transference in the solution and reactions at the elec-
trodes would then polarize the cell very rapidly, changing its apparent resistance. An

FIGURE 9.3 Conductivity cell.

FIGURE 9.4 Wheatstone bridge circuit for measuring the
resistance of electrolytes.