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The first step in solving this problem is to determine the moles of metal deposited on the cathode. To do this, we use the following equation:

moles of metal = mass of metal / molar mass of metal

The molar mass of the metal is not provided in the question, so we need to look it up. The metal with a relative mass of 27 is cobalt (Co), which has a molar mass of 58.93 g/mol.

Using the given information, we can calculate the moles of cobalt deposited on the cathode as follows:

moles of Co = 0.1769 g / 58.93 g/mol = 0.00300 mol

Next, we need to calculate the charge that was required to deposit this amount of cobalt on the cathode. The charge required can be calculated using Faraday’s law of electrolysis, which relates the amount of substance deposited to the amount of charge passed through the electrolytic cell:

Q = n × F

where Q is the magnitude of the charge in coulombs, n is the number of moles of substance deposited, and F is the Faraday constant, which is equal to 96,485 coulombs per mole of electrons.

Substituting the values we have determined into this equation, we get:

Q = 0.00300 mol × 96,485 C/mol = 289.5 C

Therefore, the magnitude of the charge on the cations of the metal is 289.5 coulombs.

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