Identifying if reaction is reduction or oxidation. Is there an error in this question? I am looking at this reaction:


I am trying to determine if it is reduction or oxidation.

In the initial molecule I calculate the overall oxidation numbers as:

ox(Cl)*6 + ox(H)*6 + ox(C)*6 = 0
-6 + 6 +ox(c)*6 = 0
hence, ox(c) = 0


In the subsequent molecule, I calculated the oxidation numbers as:

ox(Cl)*4 + ox(H)*6 + ox(C)*6 = 0
-4 + 6 +ox(c)*6 = 0
hence, ox(c) = 6/2 = 1/3


However, my textbook says the oxidation number of ALL carbon in the second molecule is 2. I am very confused by this, since if all the carbons have an oxidation number of 2 then the molecule would be charged overall? Then I am unsure if my oxidation numbers can be fractional. Is my textbook wrong, and I wrong or are we both wrong?

Overall, what I am really trying to get at is if the molecule is being oxidized or reduced, and how many electrons are being transferred. Is there a better way of doing this?

Thank you kindly
Before the reaction, every carbon is attached to to other carbon atoms, one hydrogen atom and one chlorine atom. So oxidation state of each carbon = 0+0+-1(due to C-H bond) +1(due to C-Cl bond)= 0; average oxidation state of carbon is also zero.
In the product only two carbon atoms suffer a change in bondings; now each of these two carbon atoms is attached to one carbon through double bond, another carbon through single bond and a hydrogen atom; so O.S. of this carbon = 0+0+-1 = -1; so to conclude four carbon atoms remain in zero oxidation states, where as the doubly bonded carbon atoms are in -1 oxidation state. so average oxidation state of carbon = -2/6 = -1/3

P.S.:Fractional oxidation state results only when we take average, and that too in some cases