Question

A Co|Co2+ || Sn2+|Sn galvanic cell is constructed in which the standard cell voltage is 0.140 V. Calculate the free energy change at 25°C when 0.852 g of Sn plates out, if all concentrations remain at their standard value of 1 M throughout the process. What is the maximum amount of work that could be done by the cell on its surroundings during this experiment?

ΔG° = ____________J

Maximum work =___________ J

Answer 1

Answer:

In an electrochemical cell, the cell potential E is the chemical potential available from redox reactions (E = μ_ce). E is related to the Gibbs energy change ΔG only by a constant: ΔG = −nFE, where n is the number of electrons transferred and F is the Faraday constant.

The atomic mass of Sn: 118.71 g/mol.

A Co|Co2+ || Sn2+|Sn galvanic cell is constructed in which the standard cell voltage is 0.140 V.

half cell reaction: Co ⇌ Co ²⁺ + 2e^- Sn²⁺ + 2e^-⇌ Sn

Full reaction: Co + Sn²⁺ = Co ²⁺ +Sn

So, n= 2 , ΔG⁰ = −nFE_⁰ , standard cell voltage E_⁰ ,  Standard free energy change ΔG⁰

ΔG° = - 2*96500*0.14 = -27020 J (negative sign indicate contneous reaction process)

(Unit calculation: E=Volt, F = J/(mol-volt) , n= mol of electron )

Also, we used the fact that Gibbs free energy is the maximum amount of work to derive the equation ΔG=− nFE.

Now that the connection has been made between the free energy and cell potentials, nonstandard concentrations follow. Recall that

AG = AGⓇ + RT In Q

where Q is the reaction quotient. Converting to cell potentials:

-n F Ecell = -nFEL + RT In Q or Ecell = Ecell - A In Q

This is the Nernst equation. At standard temperature (298 K), it is possible to write the above equations as

Ecell = E- 0.0257 V In Q or Ecell = E - 0.0592 V log Q

Given Q=( [ Co²⁺] / [ Sn²⁺] ) = 1 , logQ = Log 1 = 0 , So, E = E⁰

Maximum work = = ΔG° = - 2*96500*0.14 = -27020 J

AG = AGⓇ + RT In Q