Okay. I'm very, very confused.

The initial question is: predict the products of the electrolysis of a 1 mol/L solution sodium chloride.

This is my work:

The four different possible equations are:
2H2o + 2e- -------> H2 + 2OH- (V= -0.83)
O2 + 4H+ + 4e- -------> 2H2O (V= 1.23)
Na+ + e- ---------> Na (V= -2.71)
Cl2 + 2e- -----> 2Cl- (V= 1.36)

So the reaction of O2 and the reaction of Cl2 are the reduction reactions, and the reaction of 2H20 and Na are the oxidation reactions.

[ could someone tell me if I'm using the right 2 equations for water? ]

Then I combine the pairs of half reactions:

Cl2 reaction with the 2H2o reaction: (2.19)
Cl2 reaction with the Na reaction: (4.07)
O2 reaction with the 2H2o reaction: (2.06)
O2 reaction with the Na reaction: (3.94)

[i used the equation E cell= Ecathode-Eanode. However, I'm confused because its an electrolysis reaction, and I'm supposed to get negative numbers.]

And then I know that the reaction of 02 with 2H2O requires the least amount of energy, so...

O2 + 4H+ + 4e- ---------> 2H2O (v=1.23)
H2 + 2OH- -----> 2H2O + 2e- (flipped) (V= +0.83)
_____________________________________________________

2H2 + o2 + 4OH- ----------> 6H2O (+0.40)

ANNNDDD that what I did. And I don't get the right answer, as my products are supposed to be hydrogen and oxygen. Could someone PLEASE correct my work?

Water is reduced in preference to Na^+ at the cathode. Water is also prreferentially oxidized relative to the chloride at the anode.
2H2O + 2e ==> H2 + 2OH^-
2H2O ==> O2 + 4H^+ + 4e

Multiply equation 1 by 2 and add.
4H2O + 4e ==> 2H2 + 4 OH^- (cathode)
2H2O ==> O2 + 4H^+ + 4e (anode)
--------------------------
6H2O ==>2H2 + 4 OH^- + 4H^+ + O2
combine ions
6H2O ==> 2H2 + 4H2O + O2
net equation: 2H2O ==> 2H2 + O2

I just reread your answer and although you did a lot of unnecessary work I think your error was that you didn't multiply the equations involving water (the last set you wrote) to make the electons equal. Therefore, the final equation wasn't balanced and that's why the H^+ and OH^- didn't combine and add out to give 2H2O on the left.

To predict the products of the electrolysis of a 1 mol/L solution of sodium chloride, you need to consider the possible oxidation and reduction reactions.

First, let's go through the half-reactions involving water (H2O) and their standard reduction potentials (E⦵):

1. Oxidation half-reaction: 2H2O → O2 + 4H+ + 4e- (E⦵ = +1.23 V)
2. Reduction half-reaction: 2H2O + 2e- → H2 + 2OH- (E⦵ = -0.83 V)

Now, let's consider the half-reactions involving sodium (Na) and chlorine (Cl2):

1. Reduction half-reaction: Na+ + e- → Na (E⦵ = -2.71 V)
2. Oxidation half-reaction: Cl2 + 2e- → 2Cl- (E⦵ = +1.36 V)

To determine the overall reaction that will occur during electrolysis, you need to combine these half-reactions in pairs, with the reduction reaction and oxidation reaction properly balanced in terms of electrons.

Here are the pairs:

1. Cl2 reduction with 2H2O oxidation:
- Cl2 + 2H2O + 4e- → 2Cl- + 4OH- (+ 4H+)

2. Na+ reduction with 2H2O oxidation:
- Na+ + 2H2O + 2e- → Na + 2OH- (+ 2H+)

To balance the electrons, you may need to multiply one or both half-reactions by certain coefficients. In this case, multiplying the second pair by 2 will give you balanced electrons:

- 2Na+ + 4H2O + 4e- → 2Na + 4OH- (+ 4H+)

Now, combine the two pairs of half-reactions:

- Cl2 + 2Na+ + 6H2O → 2Cl- + 4OH- + 2Na + 2H+

Finally, simplify the equation by eliminating spectator ions, which are the common ions present on both sides:

- Cl2 + 2Na+ + 6H2O → 2Cl- + H2 + 2Na + 2OH-

The resulting net equation is:

2H2O → H2 + O2

Therefore, the products of the electrolysis of a 1 mol/L solution of sodium chloride are hydrogen gas (H2) and oxygen gas (O2).