Confusing electrolysis questions

[cccc]

So originally I thought when you are doing electrolysis, for the aqueous solutions, you always consider between H+ and the metal cation ? So for both of the solutions, hydrogen gas should be discharged preferentially due to a less negative E value number? But why is the answer comparing it to H2O???

Please help

[Seung Hun Han]

It is Ecell value of H2O that you have to compare. In the data booklet, Ecell values of water when it is oxidized/reduced are provided. In this case, you will have to compare Ecell value of water when it is reduced as the reaction occurs separately.

Ecell of Water (reduction)= -0.83V. Since Ecell of Cd2+ is bigger than that of water, Cd will be reduced. 

In a same logic, Cr+2 has smaller value, hence oxidized. Note that as water undergoes reduction, H2 gas is formed. When it undergoes oxidation, it will produce O2. 

 

[kw0573]

Always make a list of what can be oxidized/reduced
Potential oxidizing agents: Cd²⁺, Cr²⁺, H₂O (E = -0.83), H⁺ (E = 0.00)
Potential reducing agents: OH^- (E_reduction = 0.40), H₂O (E = 1.23)
Note that electrolysis of water can be in 3 cases
1) H⁺ is oxidizing agent. H₂O is reducing agent. (favored in strongly acidic conditions)
2) H₂O is oxidizing agent. OH^- is reducing agent. (favored in strongly basic conditions)

3) H₂O is both oxidizing agent and reducing agent. 
We don't know whether either cation is acidic or basic, so by assuming neutral pH, the presence and effects of H⁺ and OH^- can be ignored. H₂ can still be produced alongside Cd in electrolysis of Cd²⁺ because of the large number of water molecules (by route 3 above). On the other hand, there are so much water molecules that if the reduction potential is less than -0.83, the cation is never going to be oxidized. 

Analogy:
It's like lottery tickets. Let the crowd be the abundant water molecules. Someone may buy 100 lottery tickets, and say over 10⁷ tickets are sold in total, the chances are that person will not win the lottery in a continuous drawing (this is H⁺ being negligible). But say that only 500 tickets are sold (500 others each bought a ticket), then in a continuous drawing there is a very good chance that she will win (Cd²⁺ can be displaced). But suppose if she buys only 1 lottery ticket, and 1000 others each buy 1000 tickets, that one person may never win (Cr²⁺ won't be displaced). 

 

Edited May 7, 2016 by kw0573
added a weird analogy