<u>Answer:</u>
<u>For a:</u> The standard Gibbs free energy of the reaction is -347.4 kJ
<u>For b:</u> The standard Gibbs free energy of the reaction is 746.91 kJ
<u>Explanation:</u>
Relationship between standard Gibbs free energy and standard electrode potential follows:
............(1)
The given chemical equation follows:
![2Ce^{4+}(aq.)+3I^{-}(aq.)\rightarrow 2Ce^{3+}(aq.)+I_3^-(aq.)](https://tex.z-dn.net/?f=2Ce%5E%7B4%2B%7D%28aq.%29%2B3I%5E%7B-%7D%28aq.%29%5Crightarrow%202Ce%5E%7B3%2B%7D%28aq.%29%2BI_3%5E-%28aq.%29)
<u>Oxidation half reaction:</u>
( × 2)
<u>Reduction half reaction:</u> ![3I^_(aq.)+2e^-\rightarrow I_3^-(aq.)](https://tex.z-dn.net/?f=3I%5E_%28aq.%29%2B2e%5E-%5Crightarrow%20I_3%5E-%28aq.%29)
We are given:
![n=2\\E^o_{cell}=+1.08V\\F=96500](https://tex.z-dn.net/?f=n%3D2%5C%5CE%5Eo_%7Bcell%7D%3D%2B1.08V%5C%5CF%3D96500)
Putting values in equation 1, we get:
![\Delta G^o=-2\times 96500\times (+1.80)=-347,400J=-347.4kJ](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D-2%5Ctimes%2096500%5Ctimes%20%28%2B1.80%29%3D-347%2C400J%3D-347.4kJ)
Hence, the standard Gibbs free energy of the reaction is -347.4 kJ
The given chemical equation follows:
![6Fe^{3+}(aq.)+2Cr^{3+}+7H_2O(l)(aq.)\rightarrow 6Fe^{2+}(aq.)+Cr_2O_7^{2-}(aq.)+14H^+(aq.)](https://tex.z-dn.net/?f=6Fe%5E%7B3%2B%7D%28aq.%29%2B2Cr%5E%7B3%2B%7D%2B7H_2O%28l%29%28aq.%29%5Crightarrow%206Fe%5E%7B2%2B%7D%28aq.%29%2BCr_2O_7%5E%7B2-%7D%28aq.%29%2B14H%5E%2B%28aq.%29)
<u>Oxidation half reaction:</u>
( × 6)
<u>Reduction half reaction:</u> ![2Cr^{2+}(aq.)+7H_2O(l)+6e^-\rightarrow Cr_2O_7^{2-}(aq.)+14H^+(aq.)](https://tex.z-dn.net/?f=2Cr%5E%7B2%2B%7D%28aq.%29%2B7H_2O%28l%29%2B6e%5E-%5Crightarrow%20Cr_2O_7%5E%7B2-%7D%28aq.%29%2B14H%5E%2B%28aq.%29)
We are given:
![n=6\\E^o_{cell}=-1.29V\\F=96500](https://tex.z-dn.net/?f=n%3D6%5C%5CE%5Eo_%7Bcell%7D%3D-1.29V%5C%5CF%3D96500)
Putting values in equation 1, we get:
![\Delta G^o=-6\times 96500\times (-1.29)=746,910J=746.91kJ](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D-6%5Ctimes%2096500%5Ctimes%20%28-1.29%29%3D746%2C910J%3D746.91kJ)
Hence, the standard Gibbs free energy of the reaction is 746.91 kJ