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In my book, under the topic of redox reactions, it is given,

In all redox reactions, the total increase in oxidation number must be equal to the total decrease in oxidation number.

Is this a consequence of "Charges can never be created. The total charge of a system remains constant", or something else?

For the reaction, $$\ce{ 10 \color{red}{FeSO4} + 2 \color{red}{KMnO4} + 8 H2SO4 -> 5\color{red}{Fe2(SO4)3} + 2\color{red}{MnSO4} + K2SO4 + 8 H2O }$$

(Reactants and products in red undergo oxidation or reduction)

For the above reaction, I tried whether the property stated above works or not.

The oxidation state of Fe and Mn in the reactants side are +2 and +7 respectively. The oxidation states of these elements in the product side are +3 and +2 respectively. The increase in OS is 1 and the decrease is 5.

Finally, the increase and decrease in oxidation states are not equal.

Kindly give an explanation for this fact.

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    $\begingroup$ In any balanced redox equation, there are no free electrons on either side of the reaction. So whatever electrons were gained by the one or several oxidizing agents must have come from the one or several reducing agents. The total number of electrons gained must equal the total number of electrons lost. Now think about what happens to oxidation numbers when electrons are gained or lost. And look over on the right side for examples of redox reactions, etc. $\endgroup$ – Ed V Aug 17 '19 at 15:36
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    $\begingroup$ Can you please explain how you arrived at the statement "Finally, the increase and decrease in oxidation states were not equal." You might have made a mistake calculating that. $\endgroup$ – Martin - マーチン Aug 18 '19 at 6:40
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    $\begingroup$ Please add a citation for the quote you are using, otherwise this can be considered plagiarism. $\endgroup$ – Martin - マーチン Aug 18 '19 at 6:42
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    $\begingroup$ @Martin-マーチン, The statement is from the book Physical Chemistry for JEE Mains and Advanced - Resonance DLPD. It's just a book from one of the coaching institutes in India. $\endgroup$ – Guru Vishnu Aug 18 '19 at 7:07
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    $\begingroup$ The 'total' is the key word in the given statement. You have to sum up all the oxidation states. Hence 10 times +1 is +10, and 2 times -5 is -10. The decrease therefore equals the increase. Thank you for editing in your thoughts, this makes the problem a lot more understandable. $\endgroup$ – Martin - マーチン Aug 18 '19 at 8:24
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The reaction is with an advantage written in the simplified ion form:

$$\ce{5 Fe^2+ + MnO4- + 8 H+ -> 5 Fe^3+ + Mn^2+ + 4 H2O}$$

Total oxidation numbers $+17=+17$

The oxidation number is formally the net charge an atom within a molecule would have held, if we had broken all bonds and bond electrons had sticked to atoms according the atom electronegativity.

Therefore, the constant total sum of oxidation numbers across all involved atoms directly relates to the constant total sum of valence electrons and to the law of charge conservation.

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