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ANP PROJECT PROGRESS REPORT
the AgCI at the end was
(1) N + m + mNt;l, - Nt;, ,
where m is the AgCI in one mole at the start and
N is the AgCl from the electrode reaction. If m and
N are subtracted from expression 1 and the remainder
is divided by N, the relative transference
of Ag' is seen to be
(2)
ti, = ti, - mtLa .
By a similar argument it may be seen that
(3)
tEl = 1 - rig .
These relative transference numbers are all that
can be obtained unambiguously from the Hittorf
experiment, in which N faradays of electricity are
passed, the electrode compartments are analyzed,
and the AgCI content of the electrode compartment
is compared with that initially present in the same
amount of NaCI. They are also the only numbers
needed for thermodynamic use.
Useful correlations of the relative transference
numbers with electric conductance may also be
made. For these carelations, X (the ionic conductance)
is defined so that, for pure NaCI,
XNo + XcI = dC, where K is the specific conductance
and C is the concentration in equivalents
per cubic centimeter. For the NaCI-ASCI mixture,
';la =
= cNaXNa -+ 'Ag'Ag + CClhCl *
cNaXNa
K
'A gXA g
. K
*
,
and, when these values are substituted in Eq. 2,
it may be seen that
110
'Ag - 'No
= 'Ag K
ern
'Ag - 'No
K'CNa
From Eq. 4 it is evident that the relative transfer
of the silver ion is proportional to the concentration
of the silver ion and to the difference in the
mobilities of Ag+ and of No', and hence the relative
transfer may be either positive or negative. If
it is negative, tk, will be greater than unity.
For application to a concentration cell with
transference, consider the cell
Ag, AgCl in . . AgCI in NaCI,
NaCI; mA mole . Ag; mB mole
AgCl/mole NaCl : . Ag/mole NaCl
t' t'+dt'
At the cathode the opposite processes occur, with
each A replaced by B. In the section with a con-
centration gradient between A and B, in each
element, such as between the dotted lines, the
gain of AgCl is ti and the loss is tig + dtig,
which gives a net foss of dtig mole AgCI in the
element, and
If tr is constant this simplifies to
however, as shown in Eq. 4, t' is not expected to
be constant.
.
.
t