A current of 5.18 A is pass through a Cr(NO3)2 solution for 1.20 hours. How much chromium is plated out of the solution? __g
I have no idea how to approach this. Here's what I tried to do logically but I'm not sure if it works out:
I know that the conversions are 1 A *s = 1 C and 1 mol e- = 96485 C which is given by my textbook.
one problem im having is I'm not sure whether to use Cr 3+ or Cr 2+ [to know number of electrons. I used 2... for no reason in particular it was just a wild guess]
1.20 hours = 72 minutes = 4320 seconds
96485 x 2 coulombs [or 2e-?] plates 51.9961g/mol Cr
5.18 A x 4320 seconds =
51.9961/(96485 x 2) x 5.18 A x 4320 g Cr = 24.118 g?
First, the 2 is right. You look at Cr(NO3)2 so Cr is +2 (you know NO3 is -1) and it must be going to zero to plate.
You also are right that 96,485 x 2 Coulombs will plate about 52g.
So you have 5.18 x 1.2 x 60 x 60 = about 22,378 C. Therefore, you will plate
52 x (22,378/96,486*2) = about 6 g.
If your equation were
51.996 x 5.18 x 1.2 x 60 x 60/(96485 x 2)= about 6 you would be ok.
Whoops your right I totally calculated "51.9961/(96485 x 2) x 5.18 A x 4320 g Cr = 24.118 g?" incorrectly. Thank you!
To solve this problem, you need to use Faraday's law of electrolysis:
According to Faraday's law, the amount of substance plated out (in this case, chromium) is directly proportional to the charge passed through the solution.
First, you need to calculate the total charge passed through the solution using the formula:
Charge (Coulombs) = Current (Amperes) x Time (Seconds)
Charge = 5.18 A x 4320 s = 22,401.6 C
Next, you need to determine the number of moles of electrons transferred. This can be done by dividing the charge by the Faraday constant, which is 96,485 C/mol e-
Moles of electrons transferred = Charge / Faraday constant
= 22,401.6 C / 96,485 C/mol e-
= 0.2320 mol e-
Since Cr(NO3)2 is an ionic compound, it will dissociate into Cr2+ ions in solution. Each Cr2+ ion corresponds to the transfer of 2 moles of electrons.
Therefore, the number of moles of Cr plated out can be calculated by multiplying the moles of electrons transferred by the stoichiometric ratio:
Moles of Cr plated out = 0.2320 mol e- x (1 mol Cr / 2 mol e-)
= 0.1160 mol Cr
Finally, you need to convert moles of Cr plated out to grams using the molar mass of chromium. The molar mass of Cr is approximately 51.9961 g/mol.
Mass of Cr plated out = Moles of Cr plated out x Molar mass of Cr
= 0.1160 mol Cr x 51.9961 g/mol Cr
= 6.038 g
Therefore, approximately 6.038 grams of chromium will be plated out of the solution.
To determine how much chromium is plated out of the solution, you can use Faraday's law of electrochemistry, which relates the amount of substance produced in an electrolytic reaction to the amount of electric charge passed through the solution.
First, let's determine the number of moles of electrons that have passed through the solution. Since Cr(NO3)2 is a salt, it dissociates into Cr2+ ions in solution. Each Cr2+ ion requires 2 moles of electrons to be reduced to solid chromium (Cr).
The equation is:
2 Cr2+ + 2e- → 2 Cr
Next, calculate the amount of charge passed through the solution using the formula:
Charge (Coulombs) = Current (Amperes) x Time (seconds)
Charge = 5.18 A x 4320 s = 22,401.6 C
Now, apply Faraday's law, which states that 1 mole of electrons corresponds to 1 Faraday of charge (96,485 C). Therefore, the number of moles of electrons passed through the solution is:
22,401.6 C / 96,485 C/mol e- = 0.232 mol e-
Since 2 moles of electrons are required to plate 1 mole of chromium, the number of moles of chromium plated out of the solution is:
0.232 mol e- / 2 mol Cr = 0.116 mol Cr
Finally, calculate the mass of chromium by multiplying the moles of chromium by its molar mass:
Mass (g) = 0.116 mol Cr x 51.9961 g/mol Cr ≈ 6.03 g
Therefore, approximately 6.03 grams of chromium would be plated out of the solution.