Answer:
a) ΔG∘ > 0
b) K < 1
c) The electrochemical cell based on this reaction cannot accomplish work on its surroundings.
Explanation:
The Gibb's free energy, ΔG∘, is related to the potential of the cell, E∘ through
ΔG∘ = -nFE∘
where n = number of electrons being gained or lost in the electric cell
F = Amount of Faraday's electricity
a) If E∘ < 0, that is, negative,
ΔG∘ = positive (Since n and F cannot be negative)
That is, ΔG∘ > 0
b) Will the equilibrium constant for the reaction be larger or smaller than 1?
The Gibb's free energy is also related to the equilibrium constant through
ΔG∘ = - nRT In K
where n = number of moles = always positive
R = molar gas constant = always positive
T = absolute temperature in Kelvin = almost always positive too.
Recall that ΔG∘ > 0, that is positive too,
Hence,
- nRT In K = ΔG∘
In K = -(ΔG∘/nRT)
Since all of the quantities on the right hand side are positive parameters,
In K = a negative number
Meaning that K is less than 1.
The equilibrium constant is less than 1.
K < 1
c) Can an electrochemical cell based on this reaction accomplish work on its surroundings?
The Gibb's free energy determines spontaneity.
A process with a negative Gibb's free energy is said to be spontaneous and gives off the free energy as the process proceeds.
A process with a positive Gibb's free energy is said to be non-spontaneous. This one cannot give free energy (work) out to the environment.
For this question, the Gibb's free energy is positive, hence, the electrochemical cell based on this reaction cannot accomplish work on its surroundings.
Hope this Helps!!!
An electrochemical cell based on this reaction can not accomplish work on its surroundings.
We know that we can obtain the value of the standard free energy change from the value of the standard cell potential follows;
ΔG∘ = -nFE∘
Where;
ΔG∘ = standard free energy change
n = Number of electrons transferred
F = Faraday's constant
E∘ = Standard cell potential
We can see that if E∘ is negative, then ΔG∘ will be positive. Also, ΔG∘ = -RTlnK so if ΔG∘ is positive, K is less than zero. As such, an electrochemical cell based on this reaction can not accomplish work on its surroundings.
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