RESISTANCE (CONDUCTIVITY).

THE three electrical quantities which the physical chemist has most frequently to measure are resistance or its reciprocal, conductivity, current strength, and electromotive force. In other words, the three quantities involved in the equation :

I = E / R

Conductors of electricity are usually divided into two classes, though there is much doubt as to whether there is any true distinction between them: (1) those which conduct the current without suffering chemical decomposition, and (2)those which undergo chemical change when traversed by the electric current. To the first class belong the metals and carbon, while to the second belong the solutions of many substances which undergo decomposition at the poles. It is with the second class of conductors that we are chiefly concerned. These conductors are known as electrolytes, and include chiefly the solutions of acids, bases, and salts. There are many substances which in solution do not conduct the electric current, and these are known as non-electrolytes; among these may be mentioned the alcohols, the ketones, and the hydrocarbons.

Specific and Molecular Conductivity. The specific resistance of a conductor is the electrical resistance of a centimeter cube of it when the current flows through it from one face to the face opposite. Specific resistance is wholly dependent upon the nature of the conductor. Denoting the specific resistance by s', and the length and cross-sectional area of the conductor by I and a respectively, then the resistance is

Since conductivity is the reciprocal of resistance, it follows that the specific conductivity of the conductor is

 Conductors of the second class, as has been said, consist of solutions of an electrolyte in some solvent, and since liquids have no definite form it is obvious that the above definition of specific conductivity does not apply. Since the conductivity of solutions depends upon the dissolved electrolyte, we select the gram-molecular weight of dissolved substance in a litre as the basis of a definition which shall render the resistances of all solutions comparable. Consider a litre of solution containing a gram-molecular weight placed between two electrodes which are separated by a distance of 1 cm. The cross-section will be 1000 cm². This will have 1/1000 the resistance or 1000 times the conductivity of a centimetrecube of the same solution.

If v denotes the number of cubic centimetres of any solution containing a gram-molecule of dissolved substance, and s represents the specific conductivity of a centimeter cube of the solution, the molecular conductivity µ is

Where g gram-molecules of dissolved substance are contained in a litre of solution, we have as a perfectly general expression

If the specific conductivity be referred to a cylinder of solution 100 cms. in length and 0.1 cm. in cross-section, then obviously (1) and (2) become

Thus when solutions of the same concentration are employed their molecular conductivities are directly comparable.

Wheatstone's Bridge.

For the measurement Of all but very high or very low resistances the Wheatstone's bridge

 

is the most convenient. It consists of a combination of resistances. It is obvious that in the divided circuit from C to A there must be a point on the branch CDA which will have the same potential as a point on the branch CEA. Let us imagine that by means of the galvanometer G two such points have been found, and let these points be denoted by D and E. Then we have the following proportion:

From this equation it is evident that if the values of any three of the four resistances are known the other one is determined. Let us imagine the resistance-box to be inserted hi the arm R and the unknown resistance to be placed in the arm X; then we can alter the position of the point E until the galvanometer shows no deflection, and thus determine the lengths of CE and AE. Since resistance is directly proportional to the length of the conductor, it follows that the values of r₃ and r₄ are proportional to the lengths AE=l₁ and CE=l₂, or

The most convenient form of the Wheatstone 's bridge is the slide-wire-metre bridge, Fig. 67. In this form of bridge

the conductor AEC, corresponding to the similarly lettered portion of Fig. 66, is made of a thin uniform wire one metre long, the point E being determined by a sliding contact which moves over a millimetre scale. The arms CD and DA of the bridge consist of heavy copper straps which offer inappreciable resistance. The lettering in the two diagrams being the same, theMatter becomes self-explanatory. A single determination of the position of the index is not reliable owing to variations in the size of the wire and to lack of precision hi determining the point of balance. For these reasons the mean of a series of observations should be taken. When a direct current is passed through the solution of an electrolyte bubbles of gas appear on the electrodes after a very short time, or, as we say, polarization sets in. Polarization causes a counter E.M.F., which makes the accurate measurement of conductivity an impossibility. This difficulty has been overcome by Kohlrausch, who introduced the use of the alternating current.

The alternating current is furnished by a small inductorium, the wires from the secondary of which are connected with the ends of the bridgewire. Since the galvanometer cannot be used with the alternating current, it is replaced by a telephone. The inductorium is best placed in another room from that in which the bridge is placed, so that the sound of the coil can only be heard through the telephone. The sliding contact is then moved along the bridge-wire until a point is found where the sound of the coil either entirely vanishes or attains a minimum of intensity. This point is the position of balance between the arms of the bridge.

Before the Wheatstone's bridge is used the wire should be carefully calibrated. Of the several methods in use for this, that of Strouhal and Barus is best adapted to the physico-chemical laboratory.

LABORATORY EXERCISES PHYSICAL CHEMISTRY

BY

FEEDEKICK H. GETMAN, PH.D.,

Fellow by Courtesy of The Johns Hopkins University,

Carnegie Research Assistant.