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Question: Given these standard reduction potential, what is the standard reduction potential for: \[C{o^{3 +...

Given these standard reduction potential, what is the standard reduction potential for:
Co3+ (aq) → Co(s) ;   Eo  =?C{o^{3 + }}\,(aq)\, \to \,Co(s)\,;\,\,\,{E^o}\,\, = ?
Given: Co3+ (aq)   +   e−→ Co2+(aq) ;   Eo  =1.82 VC{o^{3 + }}\,(aq)\,\,\, + \,\,\,{e^ - } \to \,C{o^{2 + }}(aq)\,;\,\,\,{E^o}\,\, = 1.82\,V
Co2+ (aq)   +   2e−→ Co (s) ;   Eo  =−0.28 VC{o^{2 + }}\,(aq)\,\,\, + \,\,\,2{e^ - } \to \,Co\,(s)\,;\,\,\,{E^o}\,\, = - 0.28\,V
A.2.10 V2.10\,V
B.1.54 V1.54\,V
C.0.57 V0.57\,V
D.0.42 V0.42\,V

Explanation

Solution

In the given question, we have to calculate the standard reduction potential so here, we can take the standard hydrogen electrode (SHE) as a reference electrode. The reduction potential reduces the reducing tendency for a species. Standard reduction potentials are measured under standard conditions such as temperature should be 25oC{25^o}C , concentration is 1M1M for each ion and pressure is 1 atm1\,atm.

Complete answer:
Standard reduction potentials is the reduction potential of molecules under standard conditions and are used for the measurement of molecules' tendency to reduce. Reduction means the addition of electrons.
Standard reduction potential is related to the standard hydrogen electrode (SHE) which is taken as a reference electrode. The arbitrary value of the potential of SHE is taken as 0.00 V0.00\,V. The reduction potential measures the reducing tendencies for a species. By comparing the two reduction potentials for two reactions, we will be able to determine how a reaction will proceed.
According to the question, we have given two standard reduction potentials.
Co3+ (aq)   +   e−→ Co2+(aq) C{o^{3 + }}\,(aq)\,\,\, + \,\,\,{e^ - } \to \,C{o^{2 + }}(aq)\,
When Co3+C{o^{3 + }} is reduced toCo2+C{o^{2 + }}. Here, the number of electron (n1)({n_1}) transferred is equal to11 and standard reduction value is E1o = 1.82  V{E_1}^o\, = \,1.82\,\,V
Co2+ (aq)   +   2e−→ Co (s) C{o^{2 + }}\,(aq)\,\,\, + \,\,\,2{e^ - } \to \,Co\,(s)\,
When Co2+C{o^{2 + }} is reduced toCoCo. Here, the number of electrons (n2)({n_2}) transferred is equal to22 and the standard reduction value isE2o = −0.28  V{E_2}^o\, = \, - 0.28\,\,V.
We have to calculate,
Co3+ (aq) → Co(s) ;   E3o  =?    n3  = 3C{o^{3 + }}\,(aq)\, \to \,Co(s)\,;\,\,\,{E_3}^o\,\, = ?\,\,\,\,{n_3}\,\, = \,3
Co3+ (aq)  →1.82 V1e−→ Co2+(aq) →−0.28  V2e− Co (s) C{o^{3 + }}\,(aq)\,\,\xrightarrow[{1.82\,V}]{{1{e^ - }}} \to \,C{o^{2 + }}(aq)\,\xrightarrow[{ - 0.28\,\,V}]{{2{e^ - }}}\,Co\,(s)\,
We use this formula,
E3on3  = E1on1 + E2on2 {E_3}^o{n_3}\,\, = \,{E_1}^o{n_1}\, + \,{E_2}^o{n_2}\,
Substituting all the values,
E3o  × 3  =   1×1.82   +   2 × (−0.28) {E_3}^o\,\, \times \,3\,\, = \,\,\,1 \times 1.82\,\,\, + \,\,\,2\, \times \,( - 0.28)\,
E3o  = 1.82  ×  0.563{E_3}^o\,\, = \,\dfrac{{1.82\,\, \times \,\,0.56}}{3}
We get, E3o  = 0.42 V{E_3}^o\,\, = \,0.42\,V
So, the standard reduction potential for Co3+ (aq) → Co(s)C{o^{3 + }}\,(aq)\, \to \,Co(s) is E3o  = 0.42 V{E_3}^o\,\, = \,0.42\,V
Hence, the correct answer is option (D).

Note:
Standard reduction potential is useful in determining the direction of the reaction and how a reaction proceeds. If in some questions, the oxidation potential is given, then convert the oxidation potential into reduction potential. Always remember that the reduction potential of a given species is considered to be the negative of the oxidation potential.