Question

A battery is constructed based on the oxidation of magnesium and the reduction of Cu2+. The initial concentrations of Mg2+ and Cu2+ are 1.2×10⁻⁴ M and 1.5 M , respectively, in 1.0-liter half-cells.

A)What is the initial voltage of the battery?   

B)What is the voltage of the battery after delivering 5.0 A for 8.0 h ?

C) What are the concentrations of Mg²⁺ and Cu²⁺ when the cell is dead?

D)  How long can the battery deliver 5.0 A before going dead?

Answer 1

Hi, we first need the standard reduction potentials of both half cells:

  

  

We have to calculate first the standard cell potential which is

Since, the whole reaction is where copper is reduced and magnesium is oxidized.

, using the Nernst equation, we can write:

, so the cell voltage is

B) We have to calculate the number of electrons transferred first

we do this by calculating charge, which is current multiplied by time

No. of faradays are

since the reaction requires two moles of electrons per mole of each specie, take any reaction for example:

, so the change in concentration of each specie is: 1.49/2 = 0.745 M

So we can say that 0.745 mole of Mg2+ ions are produced by oxidation and 0.745 moles of Cu2+ ions are reduced. The new concentrations are

The new voltage is

C) When a battery is dead, we mean the cell reaction is at equilibrium, We have to calculate Keq first

and

suppose the new concentration of is and that of is 1.5-x. We have the equilibrium constant

and , I solved this equation to get the value of x = 1.50

please note that the value of Keq is so large, we can assume that the reaction goes to completion and at the end, all of Cu2+ is used up and the concentration of Mg2+ is which is essentially 1.50 M. If you want, you can always recalculate these values. You might want to calculate values upto more digits after the decimal point.

D) based on C, we can say that battery is dead when it uses 1.50 M of each specie, and since we know the number of electrons transferred are 2. The number of Faradays for the reaction is 3.0 F. We have to calculate the time which we can calculate as:

and , so 57891 s and in hours it is = 16.1 h. I hope it answers you question. If you need more information, please do not hesitate to ask.