A zinc-copper battery is constructed as follows.
Zn | Zn2+ (0.70 M) || Cu2+ (2.30 M) | Cu
The mass of each electrode is 200. g.
(a) Calculate the cell potential when this battery is first connected.
1 V
(b) Calculate the cell potential after 10.0 A of current has flowed for 10.0 h. (Assume each half-cell contains 1.00 L of solution).
please tell me which equations to use?
Calculate the half cell with Zn using the Nernst equation.
Calculate the half cell with Cu using the Nernst equation.
Now put the two equations together with the equation and determine the cell potential.
Part 2. Use Faraday's Law to determine the coulombs of electricity used in the cell, convert that to grams Zn^+2 and grams Cu^+2 used, calculate the new concns of the cells, and redo part 1 the same way.
i don't kno
To calculate the cell potential for this zinc-copper battery, you can use the Nernst equation. The Nernst equation relates the cell potential to the standard cell potential, the reaction quotient, and the temperature. The equation is as follows:
Ecell = E°cell - (RT / nF) * ln(Q)
Where:
- Ecell is the cell potential
- E°cell is the standard cell potential at 25°C (298 K)
- R is the gas constant (8.314 J/mol·K)
- T is the temperature in Kelvin
- n is the number of moles of electrons transferred in the balanced redox equation
- F is Faraday's constant (96485 C/mol)
- Q is the reaction quotient
Using the given information, the balanced equation for the cell reaction is:
Zn + Cu2+ → Zn2+ + Cu
Since Zn is oxidized and Cu2+ is reduced, the number of moles of electrons transferred (n) is 2.
(a) To calculate the cell potential when the battery is first connected, you need to find the reaction quotient Q. At the start, when the battery is connected, the concentrations of Zn2+ and Cu2+ are equal to their initial values. Thus, Q = [Zn2+] / [Cu2+].
Given that both half-cells contain 1.00 L of solution, the concentrations are:
- [Zn2+] = (0.70 M)
- [Cu2+] = (2.30 M)
Substituting the values into the Nernst equation, you can calculate the cell potential when the battery is first connected.
(b) To calculate the cell potential after 10.0 A of current has flowed for 10.0 h, you need to consider the change in concentrations of Zn2+ and Cu2+ due to the flow of current. The change in concentration can be determined using Faraday's law:
Δn = (I * t) / (n * F)
Where:
- I is the current in amperes
- t is the time in seconds
- Δn is the change in moles of electrons
- n is the number of moles of electrons transferred in the balanced redox equation
- F is Faraday's constant (96485 C/mol)
After calculating Δn, you can use it to adjust the concentrations of Zn2+ and Cu2+ in the Nernst equation to find the new cell potential.
In both cases, you'll need to convert the temperature to Kelvin before using the Nernst equation.