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Find the oxidation number of S in K2S2O8

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Let us assume that K is +1 and O is -2 and then we calculate the oxidation state of sulfur. 

We know that, the sum of the oxidation numbers must be zero for a compound. Now evaluating it, we get
K2S2O8 
2(+1) + 2x + 8(-2) = 0 
2x = 14 
x = +7 .... but, Sulfur doesn't exhibit an oxidation state of +7. 

This is commonly called sodium persulfate and two of the oxygen atoms, like the peroxide, are in the -1 oxidation state 
Now, For simplicity we will write the formula as 
K2S2(O2)O6 
2(+1) + 2x + 2(-1) + 6(-2) 
x = +6 .... which is a viable oxidation state for Sulfur (S)

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