Page:Text-book of Electrochemistry.djvu/24

I. CURRENT DENSITY. 7 P2, which are a cm. apart, is V volts, then at each point a force $$\frac{V}{a}$$ is acting against the displacement of 1 coulomb of positive electricity from the lower to the higher potential. The total work which is done in moving 1 positive coulomb from P2 to P1 is, therefore, $$\frac{V}{a} \times a = V$$, expressed in 10.2 kilogram-centimetres as unit. Usage has led to the adoption of electromotive force as synonymous with potential difference, although the former expression is not quite exact.

Current Density. — The processes which take place at the poles P1 and P2 depend to a great extent on how much gas, or substance in general, is deposited on each square centimetre of the plates per second. If the current strength is A amperes, and if plate P1 has an area of y sq. cms., then the quantity deposited on 1 sq. cm. per second is given by $$\frac{A}{y}$$. The value of this expression is termed the "current density," which obviously is measured in amperes per square centimetre. In the above example, $$\frac{A}{y}$$ must only be regarded as an average value of the current density; but in those cases where the fall of potential in the solution is the same throughout, the current density has the same value at all parts of the plate.

Electrochemical Equivalents. — It has already been mentioned that 1 coulomb can bring about the deposition of 1.118 mgram. of silver, 0.3284 mgram. of copper, or 0.0104 mgram. of hydrogen. On this account, therefore, we say that 1.118 mgram. of silver, 0.3284 mgram. of copper, and 0.0104 mgram. of hydrogen are electrochemically equivalent.

The electrochemical equivalents correspond exactly with the chemical equivalents, which represent the weights of two substances capable of replacing each other in chemical compounds (Faraday's law). Thus, for instance, 31.8 grams of copper can replace 1 gram of hydrogen from 49 grams of sulphuric acid, and produce 79.8 grams of copper sulphate.