Quantitative Relationships in Cells

To find the mass of a certain metal that is plated you need to find how many electrons were "consumed", and thus how many atoms of that metal were produced, and thus how many grams of that metal were produced.

To find how many electrons are consumed:

You are supplying 1.50 x 10^3 A for 30.0 minutes. An amp is a Coulomb per second (C/s). So to find the total charge delivered you multiply the amps by the time (in seconds):

(1.50 x 10^3 C/s) x (30.0 minutes) x ( 60 seconds / 1 minute) = 2.7 x 10^6 Coulombs of charge.

Now the charge on one electron is a known number called "the elementary charge". The normal symbol for this is 'e' but to avoid confusion we'll call it Ce (charge of single electron). This value is: 1.60 x 10^-19 Coulombs.

So you can see if we consume 1 electron, we consume 1Ce of charge. If we consume 5 electrons, we consume 5Ce of charge, and so on. So we know how much charge we are consuming (2.7 x 10^6) and we need to find how many Ce this is, to find how many electrons we consume:

(2.7 x 10^6 C) x ( 1 electron / 1.60 x 10^-19 C) = 1.6875 x 10^25 electrons consumed.

From the Nickel equation you can see for every 2 electrons consumed, you get 1 atom of Nickel, so the total number atoms of Nickel produced are:

(1.6875 x 10^25 electrons) x ( 1 Ni(s) / 2e ) = 8.4375 x 10^24 Ni(s)

To find how many grams this is you can either multiply it by the atomic mass of Ni(s), or convert it to moles and multiply that result by the molar mass of Ni(s). I'll do the second method since it is more difficult and better for learning:

(8.4375 x 10^24) x ( 1 mole / 6.02 x 10^23 particles) = 14.015 moles of Ni(s).

The molar mass of Nickel is: 58.71 g / mole, so (14.015 moles) x (58.71 g / mole) = 823 grams of Ni.

Now you do the same thing for Cr, but the only differences are that you consume 12 electrons to produce 2 Cr atoms, and the molar mass of Cr is 52.00 g / mole:

(1.6875 x 10^25 electrons) x (2 Cr / 12 electrons) = 2.8125 x 10^24 Cr(s) atoms
(2.8125 x 10^24) x ( 1 mole / 6.02 x 10^23 particles) = 4.6719 moles of Cr(s)
(4.6719 moles) x (52.00 g / mole) = 243 grams of Cr(s).