A zinc-copper battery is constructed as follows at 25°C.
Zn|Zn^2+ (0.15 M)||Cu2+(3.00 M)|Cu
The mass of each electrode is 200. g.
a) Calculate the cell potential when this battery is first connected.
- i got this to be 1.14V
b.) Calculate the cell potential after 10.0 A of current has flowed for 10.0 h
(c) Calculate the mass of each electrode after 10.0 h.
d) How long can this battery deliver a current of 10.0 A before it goes dead?
please help! i just can't seem to figure out how to calculate the concentrations of the Zn^2+ and Cu^2+ after the current has flowed through.
-thanks.
To calculate the concentrations of Zn^2+ and Cu^2+ after the current has flowed through the battery, you need to use Faraday's laws of electrolysis.
b) Calculate the cell potential after 10.0 A of current has flowed for 10.0 h:
To calculate the cell potential after the current has flowed, we need to use Faraday's law of electrolysis and the Nernst equation.
1. Determine the moles of electrons transferred:
Since each mole of electrons corresponds to one mole of charge, we can calculate the moles of electrons transferred using the formula: moles of electrons = Coulombs of charge / Faraday's constant.
Charge (Coulombs) = current (A) * time (s)
Here, current = 10.0 A, and time = 10.0 h * 60 min/h * 60 s/min = 36000 s.
Charge (Coulombs) = 10.0 A * 36000 s = 360000 C
Faraday's constant (F) = 96485 C/mol (charge on one mole of electrons)
Moles of electrons = 360000 C / 96485 C/mol ≈ 3.73 mol electrons.
2. Determine the change in concentration of Zn^2+ and Cu^2+:
Since each mole of electrons corresponds to one mole of Zn^2+ ions being reduced and one mole of Cu^2+ ions being oxidized, the change in concentration of Zn^2+ and Cu^2+ can be calculated using the stoichiometry of the balanced equation.
The balanced equation is: Zn + Cu^2+ → Zn^2+ + Cu
The ratio of moles of Zn^2+ to Cu^2+ is 1:1.
Therefore, the change in concentration for both Zn^2+ and Cu^2+ is equal to the change in moles of electrons.
3. Calculate the new concentrations of Zn^2+ and Cu^2+:
To calculate the new concentrations, we need to know the initial concentrations of Zn^2+ and Cu^2+.
From the given information, the initial concentration of Zn^2+ is 0.15 M, and the initial concentration of Cu^2+ is 3.00 M.
The new concentration of Zn^2+ = initial concentration of Zn^2+ - change in concentration of Zn^2+
= 0.15 M - 3.73 mol * (1 mol Zn^2+ / 1 mol e-)
= 0.15 - 3.73 M
The new concentration of Cu^2+ = initial concentration of Cu^2+ + change in concentration of Cu^2+
= 3.00 M + 3.73 mol * (1 mol Cu^2+ / 1 mol e-)
= 3.00 + 3.73 M
Now, you can calculate the cell potential after 10.0 A of current has flowed for 10.0 h using the Nernst equation.
(c) Calculate the mass of each electrode after 10.0 h:
To calculate the mass of each electrode after 10.0 h, you need to use Faraday's laws of electrolysis and the molar mass of Zn and Cu.
The molar mass of Zn = atomic mass of Zn = 65.38 g/mol
The molar mass of Cu = atomic mass of Cu = 63.55 g/mol
The moles of Zn deposited = change in moles of electrons (from part b) * (1 mol Zn / 1 mol e-)
The moles of Cu consumed = change in moles of electrons (from part b) * (1 mol Cu / 1 mol e-)
The mass of Zn deposited = moles of Zn deposited * molar mass of Zn
The mass of Cu consumed = moles of Cu consumed * molar mass of Cu
(d) How long can this battery deliver a current of 10.0 A before it goes dead:
To calculate the time until the battery goes dead, you need to use Faraday's laws of electrolysis and the molar mass of Zn and Cu.
The moles of Zn needed = moles of Zn deposited (from part c)
The moles of Cu needed = moles of Cu consumed (from part c)
The charge required to deposit these moles of Zn = moles of Zn needed * Faraday's constant
The charge required to consume these moles of Cu = moles of Cu needed * Faraday's constant
The time until the battery goes dead = (charge required to deposit Zn + charge required to consume Cu) / current
I hope this helps you calculate the concentrations, masses, and lifetime of the battery!