A zinc-copper battery is constructed as follows at 25°C:
Zn | Zn2+(0.15 M) || Cu2+(1.70 M) | Cu
The mass of each electrode is 150. g.
The cell potential when the cell is first attached is 1.13V
How long can this battery deliver a current of 5.00 A before it goes dead?
I tried using the method posted from a previous user, but it doesnt work!! i keep getting 24.6 hrs after using factor label. Maybe the Molarties play a part, but I don't know how...please help me!
Let's get on the same page. What Eo values are you using for Cu and Zn. Is that 1.13 v given in the problem or did you calculate that?
i've calculated it and its right (this is a webassign problem) so i know that's right...the masses were given
If I'm to help I need to know the Eo values you used. I don't want to go through this calculation using values from my book when you use values from some other book. Using my numbers I don't get 1.13 v; that's why I need the Eo values.
ok ..so the Eo value for Zn is -0.763 and for Cu its +0.337
To find out how long the battery can deliver a current of 5.00 A before going dead, we need to consider the balanced redox reaction that occurs in the battery and calculate the number of moles of electrons transferred in the reaction.
The balanced redox reaction occurring in this battery is:
Zn + Cu2+ -> Zn2+ + Cu
From the reaction, we can see that each mole of Zn reacts with one mole of Cu2+ to produce one mole of Zn2+ and one mole of Cu. Therefore, we need to calculate the number of moles of Cu2+ or Zn that will be consumed to deliver a current of 5.00 A.
The current (I) is related to the number of moles of electrons (n) transferred by the equation:
I = nF / t
Where I is the current in amperes, n is the number of moles of electrons, F is the Faraday constant (96485 C/mol), and t is the time in seconds.
Since 1 mole of Cu2+ reacts with 2 moles of electrons, we can calculate the number of moles of Cu2+ required for the given current:
n = I * t / (2 * F)
Substituting the given values:
n = 5.00 A * t / (2 * 96485 C/mol)
Now, we need to convert the number of moles of Cu2+ to moles of Zn using the stoichiometric coefficients of the balanced redox reaction. From the reaction, we see that 1 mole of Zn reacts with 1 mole of Cu2+. Therefore, the number of moles of Zn required is also given by n.
Now we can use the molar mass of Zn (65.38 g/mol) to calculate the mass of Zn required:
mass = n * molar mass
In this case, the mass of each electrode is given as 150 g. Therefore, the total mass of Zn required is twice the mass of one electrode:
total mass of Zn = 2 * 150 g
Finally, the time (t) can be calculated by solving the equation:
mass of Zn = n * molar mass
t = (2 * 150 g) / (5.00 A * molar mass * 96485 C/mol)
Substitute the given molar mass of Zn (65.38 g/mol) into the equation to get the final result.
Note: Make sure to convert the final time from seconds to hours if necessary.
I hope this explanation helps! Let me know if you need any further assistance.