Question

A certain half-reaction has a standard reduction potential E⁰red = +0.63V. An engineer proposes using this half-reaction at the cathode of a galvanic cell that must provide at least 1.30V of electrical power. The cell will operate under standard conditions.

(a) Is there a minimum standard reduction potential that the half-reaction used at the cathode of this cell can have? If so, write "yes" and calculate the minimum. Round your answer to 2 decimal places. If there is no lower limit, write "no".
(b) Is there a maximum standard reduction potential that the half-reaction used at the cathode of this cell can have? If so, write "yes" and calculate the minimum. Round your answer to 2 decimal places. If there is no upper limit, write "no".

Answer 1

a) YES, this is a minimum standard reduction potential and
`E^0_(cathode)= 1.93 V`

b) NO maximum reduction potential of half cell of cathode.

Step-by-step explanation:

Given that the galvanic cell must provide at least 1.30 V of electrical power . that denotes that
`E^0_(cell) =1.30 V`

Here, the standard reduction potential of the half-cell reaction of anode is + 0.63 V

i.e
`E^0_(anode) = +0.63 V`

We know that:

`E^0_(cell) = E^0_(cathode)-E^0_(anode)`

`1.30 V= E^0_(cathode)-(+0.63)V`

`-E^0_(cathode)= - 1.3 V - 0.63 V`

`E^0_(cathode)= 1.30 V +0.63 V`

`E^0_(cathode)= 1.93 V`

If
`E^0_(cathode) > 1.93 V`; then
`E^0_(cell)` > 1.30 V

Also; If
`E^0_(cathode) < 1.93 V`; then
`E^0_(cell)<` 1.30 V

This is because the cell supply minimum electrical power that is 1.30 V , Hence reduction potential of half- cell reaction at cathode will be minimum at 1.93 V

Therefore, from the foregoing, we conclude that: YES, this is a minimum standard reduction potential.

`E^0_(cell) = E^0_(cathode)-E^0_(anode)`

`E^0_(cell) = E^0_(cathode)-(+0.63V)`

So, if reduction potential value of the half-cell reaction used at cathode is greater than 1.93 (V); we get at least 1.30 V or greater than 1.30 V cell emf.

As such, No maximum reduction potential of half cell of cathode.