A zinc-copper battery is constructed as follows at 25 degree C:
Zn | Zn2+(0.15 M) || Cu2+(1.70 M) | Cu
The mass of each electrode is 250. g.
I found the cell potential to be 1.13V and the cell potential after 5.00 A of current has flowed for 8.00 h is 1.11V.
but how do I Calculate the mass of each electrode after 8.00 h. Zn =___g and Cu= ___g
AND How long can this battery deliver a current of 5.00 A before it goes dead?___hrs.
I get 1.069 for Ecell.
In 8 hrs, coulombs = A x seconds.
C = 5A x 8 hrs x (60 min/1 hr) x (60sec/1 min) = about 144,000 coulombs.
That is how much of a Faraday?
144,000/96,485 = about 1.49 F.
1.49 F will dissolve 65.38/2 g Zn and deposit 63.54/2 g Cu. Subtract g Zn from 250 and add g Cu to 250 g to find amount electrodes weigh after 8 hours operation at 5 A.
How long before the battery will go dead delivering 5A? That is done this way.
96,485 C will dissolve 65.38/2 g = 32.69 g Zn. How many seconds will it take to dissolve 250 g (all of the Zn electrode) Zn . That will be
96,485 x (250/32.69 = ?C
5A x seconds = ?C. Solve for seconds and convert to min or hours as desired.
To calculate the mass of each electrode after 8.00 hours of current flow, you will need to consider the stoichiometry of the electrochemical reaction that is taking place at each electrode.
For the zinc electrode (anode):
1. Determine the number of moles of Zn consumed by the electrochemical reaction using Faraday's Law of electrolysis:
moles of Zn = (current × time) / (number of electrons transferred × Faraday's constant)
Given:
Current (I) = 5.00 A
Time (t) = 8.00 hours = 28800 seconds (convert to seconds)
Number of electrons transferred (n) = 2 (since Zn2+ gains 2 electrons in the half-cell reaction)
Faraday's constant (F) = 96485 C/mol (charge per mole)
moles of Zn = (5.00 A × 28800 s) / (2 × 96485 C/mol)
2. Convert the moles of Zn to grams using the molar mass of zinc:
Molar mass of Zn = 65.38 g/mol
mass of Zn = moles of Zn × molar mass of Zn
For the copper electrode (cathode):
1. Determine the number of moles of Cu deposited by the electrochemical reaction using Faraday's Law:
Similarly, the number of moles of Cu = (current × time) / (number of electrons transferred × Faraday's constant)
Given:
Current (I) = 5.00 A
Time (t) = 8.00 hours = 28800 seconds
Number of electrons transferred (n) = 2 (since Cu2+ gains 2 electrons in the half-cell reaction)
Faraday's constant (F) = 96485 C/mol
moles of Cu = (5.00 A × 28800 s) / (2 × 96485 C/mol)
2. Convert the moles of Cu to grams using the molar mass of copper:
Molar mass of Cu = 63.55 g/mol
mass of Cu = moles of Cu × molar mass of Cu
Now, substitute the values to calculate the mass of each electrode (Zn and Cu).
To determine how long the battery can deliver a current of 5.00 A before it goes dead, you will need to use the concept of the charge transferred during the electrochemical reaction.
1. Calculate the total charge transferred by multiplying the current by the time:
Q = I × t
Given:
Current (I) = 5.00 A
Time (t) is unknown
2. The total charge transferred must equal the product of the number of moles of electrons and Faraday's constant:
Total charge transferred (Q) = n × F
Given:
Number of electrons transferred (n) = 2 (same as before)
Faraday's constant (F) = 96485 C/mol
Therefore, Q = 2 × 96485 C/mol
3. Since Q = I × t, you can solve for time (t):
t = Q / I
Substitute the known values into the equation to find the time in hours.
So, to summarize:
- To calculate the mass of each electrode after 8.00 hours:
- Use Faraday's Law to find the moles of Zn and Cu consumed.
- Convert moles to grams using the molar masses of Zn and Cu.
- To determine how long the battery can deliver a current of 5.00 A:
- Use the total charge transferred equation.
- Solve for time (t) by dividing the total charge transferred by the current.