What is the sum of all the oxidation numbers in any compound

The sum of all the oxidation numbers for neutral compound = 0

For charged  species sum of oxidation no. of all the elements is not equal to zero either positive or negative.

Explanation:

In case for neutral compounds sum of total oxidation no. of all elements is equal to zero.

Let us consider for

          K₂Cr₂O₇ (Potassium dichromate) the sum of total oxidation state of elements is equal to zero.

Oxidation state of potassium = +1, For Chromium = +6 & for oxygen = -2        

So total oxidation number

                     2 x (+1) + 2 x (+6) + 7 x (-2)

                 = +14 - 14 = 0.

In case for charged species.

Example for

Ammonium ion (NH₄⁺) total charge = +1

∵ O.N for nitrogen = -3 and for hydrogen = +1

∴ Sum of oxidation numbers = 1 x (-3) + 4 x (+1)

                                             = +1

For Carbonate ion (CO₃²⁻) total charge = -2

Oxidation number for carbon = +4 and for oxygen = -2

(∵Oxygen is more electronegative than carbon)

∴  Sum of oxidation numbers = 1 x (+4) + 3 x (-2) = -2

the answer would be a