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:
In an electrochemical cell, the cell potential E is the chemical potential available from redox reactions (E = μce). 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 = −nFE0 , standard cell voltage E0 , 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
where Q is the reaction quotient. Converting to cell potentials:
This is the Nernst equation. At standard temperature (298 K), it is possible to write the above equations as
Given Q=( [ Co2+] / [ Sn2+] ) = 1 , logQ = Log 1 = 0 , So, E = E0
Maximum work = = ΔG° = - 2*96500*0.14 = -27020 J
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