A current is passed through two cells connected in series. The half-reactions occurring at the cathode of each cell are
TcO4-(aq) + 8 H+(aq) + 7 e- ===> Tc(s) + 4 H2O(l) and
Cu2+(aq) + 2 e- ===> Cu(s).
If 4.40 g of copper are deposited in the second cell, how much technetium, Tc, is formed in the first cell?
I am not sure what equations or where to begin to solve this.
Use the information from the deposition of Cu to determine the equivalents of Cu deposited, then the number of coulombs. The colulombs will be the same for the Tc half cell and you can use that to determine the mass of Tc deposited.
How can I figure the equivalents of Cu deposited and then the number of coulombs?
You need to recalculate since I have estimated along the way.
1 equivalent of Cu = 63.546/2 = about 32.
96,485 C needed to deposit 32 g Cu.
How many C needed to deposit 4.40 g?
That must be 96,485 C x (4.40/32) = about 13,000 C.
That is the same # C that will ppt Tc or about 13,000 C will ppt Tc.
1 equivalent of Tc = 98/7 = about 14
So 96,485 C will ppt 14 g Tc, how much will 13,000 C ppt?
Check my thinking. Check my arithmetic. Redo all the numbers since I've estimated.
To solve this problem, we need to use the concept of stoichiometry and Faraday's laws of electrolysis.
First, let's write the balanced equations for the half-reactions occurring at the cathode of each cell:
At the cathode in the first cell:
TcO4-(aq) + 8 H+(aq) + 7 e- → Tc(s) + 4 H2O(l)
At the cathode in the second cell:
Cu2+(aq) + 2 e- → Cu(s)
From these reactions, we can see that for every 7 electrons transferred in the first cell, 1 Tc atom is formed. In the second cell, for every 2 electrons transferred, 1 Cu atom is deposited.
Now, let's use Faraday's laws of electrolysis to relate the number of electrons passed during the electrolysis to the amount of substance formed or deposited.
Faraday's First Law states that the mass of a substance formed at an electrode during electrolysis is directly proportional to the quantity of electricity passed through the cell.
The formula for Faraday's First Law is:
Mass (in grams) = (Current (in amperes) × Time (in seconds) × Molar mass (in grams per mole)) / (1 Faraday)
The Faraday constant, F, is the charge of 1 mole of electrons, which is approximately equal to 96,485 coulombs.
To find the amount of Tc formed in the first cell, we need to know the amount of charge passed through the cell and the number of electrons involved in the reaction.
In the first cell, since 7 electrons are required to form 1 Tc atom, we can say that for every mole of Tc formed, 7 moles of electrons are passed.
Now, let's calculate the moles of electrons passed in the second cell, which is equivalent to the moles of Cu deposited.
The molar mass of Cu is 63.55 g/mol.
Given that 4.40 g of Cu are deposited, we can find the moles of Cu:
Moles of Cu = Mass of Cu / Molar mass of Cu
Moles of Cu = 4.40 g / 63.55 g/mol
Once we have the moles of Cu, we know that the same number of electrons are involved in the reaction, so we can convert the moles of Cu to moles of electrons.
Now, you can multiply the moles of electrons by the ratio of 1 mole of Tc to 7 moles of electrons to find the moles of Tc formed in the first cell.
Finally, to find the mass of Tc formed, you can use the molar mass of Tc.
I hope this explanation helps you understand how to solve the problem! Let me know if you have any further questions.