identifying a metal using electrolysis

Question

When a solution containing M(NO3)2 of an unknown metal M is electrolyzed, it takes 74.1 seconds for a current of 2.00 A to plate out 0.0737 g of the metal. What is the metal?

Answer 1

Let's start with what we know:

1. The current is applied for 74.1 seconds.
2. The current is 2.00 Amperes. An Ampere = 1 Coulomb per second
3. The Faraday constant (96485 C/mol) tells us the number of Coulombs in a mole of electrons.
4. We know the charge on the metal before electrolysis because we are told it is in a M(NO3)2 soltuion, and we know it is neutral once it is plated. This tells us the number of moles of electrons gained by one mole of the metal. (2e- + M+2 --> M)
5. We know the mass of the metal plated.

This is actually a lot of information! Where are we going though? We want to know the identity of a metal. One thing we definitely have access to is a periodic table, and each metal has a unique molar mass.

1. molar mass = mass / number of moles
2. Great! We know the mass of metal plated, that's given.
3. We can use the above info to find the number of moles of metal plated.

So, here we go...

74.1 second x (2.00 Coulombs/second) x (1 mol e-/96485 Coulombs) x (1 mol metal/2 mol e-) = 0.000768 mol metal

We have the number of moles of metal plated! Now to get the molar mass.

molar mass = mass/moles = 0.0737 grams / 0.000768 mol = 95.96 g/mol

This is almost exactly the molar mass for molybdenum, so the metal is molybdenum!