Question

For the reduction of silver ions with copper metal, the standard cell potential is 0.46 V at 25 degree Celsius. The value of standard Gibbs energy \[\Delta {{G}^{\circ }}\] will be:
A. -89.0 kJ
B. -89.0 J
C. -44.5 kJ
D. -98.0 kJ

Answer 1

Hint: Gibbs energy is a measure of the capacity of any system to do useful work. Standard Gibbs energy is dependent on the standard cell potential and the number of electron changes taking place in an electrolytic reaction.

Complete step by step answer:
According to the question, there is a reaction between silver ions and copper metal, in which silver ions get reduced. So, we can write the reaction as –
\[Cu(s)+2A{{g}^{+}}(aq)\to C{{u}^{2+}}(aq)+2Ag(s)\]
The equation of standard Gibbs energy is given as –
\[\Delta {{G}^{\circ }}=-nF{{E}^{\circ }}\]; where,
\[\Delta {{G}^{\circ }}\] = Standard Gibbs energy
n = total electron change
\[{{E}^{\circ }}\] = standard cell potential = 0.46 V (given)
F = Faraday’s constant = 96500 C/ mol
We can write the half reactions as –
\[Cu(s)\to C{{u}^{2+}}(aq)+2{{e}^{-}}\]
\[2(A{{g}^{+}}+{{e}^{-}}\to Ag)\]
As we can see, there is a net change of 2 electrons.
Therefore, n= 2.
Now, putting all the values in the equation for Gibbs energy, we get –
\[\Delta {{G}^{\circ }}\]= - 2 mol x 96500 C/mol x 0.46 V
\[\Delta {{G}^{\circ }}\]= - 88700 J [Since, CV = J]
\[\Delta {{G}^{\circ }}\]= - 88.7 kJ = - 89 kJ (approx.)

Therefore, the answer is – option (a) –
The value of standard Gibbs energy \[\Delta {{G}^{\circ }}\] is -89kJ.

Additional Information:
Gibbs free energy can also be calculated by the formula - \[\Delta {{G}^{\circ }}=-2.303RT\log K\].

Note: Gibbs free energy is a thermodynamic quantity which is used to calculate the maximum reversible work that can be performed by a thermodynamic system at a constant temperature and pressure.