Question

The $ {E^\circ }_{F{e^{2 + }}/Fe} = - 0.44V $ and $ {E^\circ }_{C{r^{3 + }}/Cr} = - 0.74V $ free energy is $ (F = 96500C) $
A. 57,900
B. -57,900
C. -173,700
D. 173,700

Answer 1

Hint :In order to the question, first we have to determine the cathode and anode for the reaction and then find the standard $ {E^\circ } $ value for the formula to find the Standard free energy change.

Complete Step By Step Answer:
In the question, we have the standard $ {E^\circ } $ value or Equilibrium Constant of both Iron and Chromium $ {E^\circ }_{F{e^{2 + }}/Fe} = - 0.44V $ and $ {E^\circ }_{C{r^{3 + }}/Cr} = - 0.74V $ . Here, the standard $ {E^\circ } $ value of Iron is at the higher side, so Iron is acted as a Cathode here and Chromium is acted as an Anode in the given reaction.
Now, we have to calculate the standard $ {E^\circ } $ value of the cell, we have the formula: $ {E^\circ }_{cell} = {E^\circ }_c - {E^\circ }_a $
here, $ {E^\circ }_c $ is the standard $ {E^\circ } $ value of Cathode
 $ {E^\circ }_a $ is the standard $ {E^\circ } $ value of Anode.
And, we already know that Iron and Chromium act as Cathode and Anode respectively. $ \therefore {E^\circ }_{cell} = - 0.44 - ( - 0.74) $ $ = 0.30\,Volt $ .
Now, in the given reaction $ 3F{e^{2 + }}(aq) + 2Cr(s) \Rightarrow 2C{r^{3 + }}(aq) + 3Fe(s) $ , $ 3F{e^{2 + }} $ is converted into $ 3Fe $ and $ 2Cr $ is converted into $ 2C{r^{3 + }} $ . So, here we can see that the n factor is 6 (n=6).
Hence, we have the formula to find the Standard free energy change for the given reaction:-
The standard free energy of a substance represents the free energy change associated with the formation of the substance.
 $ \therefore \Delta G = - nF{E^\circ }_{cell} $
here, $ \Delta G $ is the standard free energy change
 $ n $ is the n-factor of the reaction
 $ F $ is given (F=96500C)
 $ {E^\circ }_{cell} $ , we calculated above
 $ \because \Delta G = - 6 \times 96500 \times 0.30 $ $ = - 173,700 $
So, we now have the Standard free energy change is -173,700.
Hence, the correct option is (C.) -173,500.

Note :
Or in other words, Calculate the change in standard free energy for a particular reaction. The standard free energy of a substance represents the free energy change associated with the formation of the substance from the elements in their most stable forms as they exist under standard conditions.