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The current used for measuring generates heat in the electrolyte, and so warms it. Care must be taken to avoid introducing error in this way; the current from the induction coil should not be too strong, and should be broken when not wanted. The arrangement of Fig. 15 is good in this respect, as the current then only flows for a few seconds, while the sliding contact is actually in use, and pressed down on the wire.
Electrolytic polarisation, self-induction, and electrostatic capacity in any of the four arms of the bridge affect the balance to a certain extent. Fortunately, their influence shows itself first in want of sharpness in the telephone minimum; the point of balance is only affected secondarily, so that no error in measurement is to be feared so long as the "minimum" is sufficientle modelini sufficiently definite to observe with precision. The mathematical theory shows that the influence of
Self-induction Polarisation Capacity is great when the
great frequency is s and when the re
great sistance is
Self-induction is diminished, as already mentioned, by double winding the coils of the resistance-box. It may similarly be diminished in the leads, etc., by laying out and return wires close alongside one another. Short straight conductors, such as electrolytic cells, have very little self-induction. With ordinarily good arrangements its effect should be negligible.
Polarisation, of course, exists in the liquid cells only. It may always be made vanishingly small by making the electrodes large enough, and covering them well with platinum or palladium black. If two arms of the bridge are made of liquid conductors it may be made approximately to balance out.
Capacity occurs in high-resistance coils, from which, however, it may be practically eliminated by Chaperon's method of winding; it is also appreciable in electrolytic cells when the electrolyte is of low conductivity, and between the electrolytic cell and a conductor outside the glass, such as the water of the
See Kohlrausch and Holborn, Leitrermogen d. Elektrolyte, p. 70.
thermostat. The last difficulty may be got over by placing the cell in a beaker of non-conducting liquid such as paraffin, and that inside the thermostat. If, despite these precautions, capacity causes trouble, a
small condenser should be inserted in K another arm of the bridge, for the effect \ is always lessened by symmetry. Thus,
if there is too much capacity in the arm
tinfoil or paraffined paper) is placed in the Fig. 24.
adjacent arm d. The resistance balance
is first found as nearly as may be, and the capacity of K then varied until the minimum in the telephone is quite sharp.
§ 6. EQUIVALENT AND IONIC CONDUCTIVITIES.
In order to express the results of conductivity measurements in a convenient form it is necessary to introduce a new definition—that of the equivalent conductivity. This is the conductivity divided by the concentration. We shall use the symbols k for conductivity, and A for equivalent conductivity; then
where n, as before, is the concentration in gram-equivalents per cubic centimetre, and v is the dilution, or volume, in cubic centimetres per gram-equivalent.
We have seen that the conductivity may be expressed in terms of the properties of ions by the equation
K = 96600 yn(UA + Uc) It follows that
A = 96600 y(UA + Uc) We may form a picture of the meaning of equivalent conductivity in this way. Suppose two metal plates of indefinite extent placed parallel and one centimetre apart; place between them I c.c. of solution in the form of a prism or cylinder of 1 sq. cm. base). Then the conductance between
the plates is, according to definition, the conductivity of the solution. Next, if v is the number of cubic centimetres containing one gram-equivalent of the dissolved substance, place V c.c. of solution between the plates; then the conductance is v times as great as before. It is now a measure of the equivalent conductivity.
The most important result of experiment can be summed up by saying that, in general, while the actual conductivity k falls off very much when the solution is diluted, the equivalent conductivity of a salt (acid or base) increases with its dilution, but tends towards a finite limit for indefinitely great dilution. The following example will serve to illustrate the rule; solutions of varying strengths being made up, and their conductivities measured, the values of the equivalent conductivities are
In each case the increase with dilution is obvious. The approach to a finite maximum is clearly marked in the first case, and the limiting value can be obtained by extrapolation with some certainty : Kohlrausch gives it as 131'2. In the second case the limit is fairly obvious, but not calculable with certainty. With acetic acid it is not obvious; but there is indirect evidence that if it were possible to measure still more dilute solutions, it would be found.
Since the laws of dependence of the equivalent conductivity on concentration are not at all simple, it is of interest to draw curves showing the relations between the two quantities. But as measurements have to be taken over a very wide range of concentration, such diagrams would not be convenient to draw
except in the case of strong solutions. Kohlrausch recommends the use of diagrams in which the cube root of the concentration is taken as abscissa, the equivalent conductivity as ordinate ; curves so drawn are often nearly linear (see Fig. 25). It is also often convenient to take the logarithm of the concentration as abscissa.
Since, according to the hypothesis we have used, the conductivity of a solution is the joint effect of convection by anions and cations in it, the next step is to analyse the equivalent conductivities into a part due to the anions and a part due to the cations. These are called the partial or ionic conductivities ; they will be designated by la and lc, so that, using the same symbols as before, we shall expect to have