Introduction:
In this question, we are required to calculate the time required to prepare 12% by weight candium by electrolysis of a solution of candium chloride using mercury cathode.

Given:
- Weight of mercury cathode = 2.0g
- Current = 5A

Calculation of amount of candium deposited:
The amount of candium deposited can be calculated using Faraday's Law of Electrolysis which states that the amount of substance deposited at an electrode is directly proportional to the amount of charge passed through the electrode.

The formula for the amount of substance deposited is given by:
Amount of substance = (Current x Time x Atomic weight) / (1 x Faraday's constant)

The atomic weight of candium is 112.41 g/mol and the Faraday's constant is 96500 C/mol.

Substituting the given values in the formula, we get:
Amount of substance = (5 x t x 112.41) / (96500)
Amount of substance = 0.058t

Calculation of weight of candium deposited:
The weight of candium deposited can be calculated using the formula:
Weight = Amount of substance x Atomic weight

Substituting the value of amount of substance in the formula, we get:
Weight of candium deposited = 0.058t x 112.41
Weight of candium deposited = 6.54t

Calculation of time required:
From the given problem, we know that the weight of candium deposited should be 12% of the final weight. Therefore, we can write the equation:
Weight of candium deposited = 0.12 x Final weight

Substituting the value of weight of candium deposited in the equation, we get:
6.54t = 0.12 x Final weight

Solving for Final weight, we get:
Final weight = 54.5t

Substituting the value of Final weight in the equation, we get:
6.54t = 0.12 x 54.5t

Solving for t, we get:
t = 70.3 seconds

Conclusion:
Therefore, the time required to prepare 12% by weight candium by electrolysis of a solution of candium chloride using mercury cathode is 70.3 seconds.