Question

An electroplating unit plates $3g$ of silver on a brass plate in $3\min$ . What is the current used by the unit?
The electrochemical equivalent of silver is $1.12\times {{10}^{-6}}kg/C$ .

Answer 1

This is a problem of electrolysis. We can solve it easily using Faraday’s first law of electrolysis. It states that the amount of reaction taking place in terms of mass of the ions discharged from the electrolyte, is directly proportional to the electric current passing. Here we came across one term Chemical equivalent which is a constant.
We use Faraday’s first law: $m=Zit$ , where Z is the chemical equivalent.

Complete step by step solution:
Mass of silver, $m=3g=\dfrac{3}{1000}kg$
Time, $t=3\min =3\times 60=180s$
Z for silver is $1.12\times {{10}^{-6}}kg/C$ , substituting them,
\Rightarrow 0.003=1.12\times {{10}^{-6}}\times i\times 180 \\\ \Rightarrow i=\dfrac{0.003}{1.12\times {{10}^{-6}}\times 180} \\\ \therefore i=14.88A \\\.

Additional information:
When a body loses some electrons, then it becomes positively charged, but opposite of this that body cannot lose the protons. This happens because the number of protons is now more than the number of electrons. The net effect is positive and hence, the body becomes positively charged. We know that electrons have mass and the mass of one electron is $9.1\times {{10}^{-31}}kg$ .

Note:
While solving such problems we have to keep in mind all the values to be taken in standard SI units. The value of the electrochemical equivalent is dependent upon the material used. For silver it was given, had we needed to use gold, then Z would have changed. Since, the unit of Z was kg/C, we had converted the mass given in grams to kilogram. Also, the time is always taken in seconds unless specified.