Question #c7688

1 Answer
Jun 11, 2017

Answer:

Here's what I got.

Explanation:

The trick here is to realize that peroxydisulfuric acid contains the peroxydisulfate anion, #"S"_2"O"_8^(-)#, which has a particularly interesting Lewis structure.

https://en.wikipedia.org/wiki/Peroxydisulfate

Notice that two oxygen atoms are bonded via a single bond--this is known as a peroxide linkage. This will influence the average oxidation state of oxygen in this anion.

More specifically, the two oxygen atoms that are bonded to each other will have a #color(blue)(-1)# oxidation state, the same oxidation state that oxygen has in peroxides (hence the name peroxide linkage).

The other six oxygen atoms will have a #color(blue)(-2)# oxidation state, which implies that the average oxidation state of oxygen in the peroxydisulfate anion is

#(6 xx color(blue)(-2) + 2 xx color(blue)(-1))/8 = -7/4#

This means that instead of using two different oxidation states for the oxygen atoms, you can use an average oxidation state of #color(blue)(-7/4)# for all #8# atoms of oxygen present in the anion.

This implies that you have--keep in mind that hydrogen has a #color(blue)(+1)# oxidation state in this compound

#stackrel(color(blue)(+1))("H")_ 2 stackrel(color(blue)(?))("S") _ 2 stackrel(color(blue)(-7/4))("O")_ 8#

Now, peroxydisulfuric acid is a neutral compound, which implies that the sum of the oxidation states of all the atoms that make up a molecule of peroxydisulfuric acid must be equal to #0#.

This means that you have

#overbrace(2 xx color(blue)((+1)))^(color(red)("2 atoms of H")) + overbrace( 2 xx ?)^(color(red)("2 atoms of S")) + overbrace(8 xx color(blue)((-7/4)))^(color(red)("8 atoms of O")) = 0#

Solve to find the oxidation state of sulfur

#2 * 2 * ? - 14 = 0#

#2 * ? = 12 implies ? = +6#

Therefore, you can say that sulfur has a #color(blue)(+6)# oxidation state in peroxydisulfuric acid

#stackrel(color(blue)(+1))("H")_ 2 stackrel(color(blue)(+6))("S")_ 2stackrel(color(blue)(-7/4))("O")_ 8#

#color(white)(a/a)#
Now, here's an example of how NOT to answer this question.

#color(white)(a)#
#darr darrcolor(red)("Incorrect solution below")darr darr#

#color(white)(a/a)#
Your ultimate goal here is to figure out the oxidation state of sulfur in peroxydisulfuric acid, #"H"_2"S"_2"O"_8#, because you should already know the oxidation states for hydrogen and oxygen in this compound.

More specifically, hydrogen has a #color(blue)(+1)# oxidation state and oxygen has a #color(blue)(-2)# oxidation state.

This means that you have

#stackrel(color(blue)(+1))("H")_ 2 stackrel(color(blue)(?))("S")_ 2stackrel(color(blue)(-2))("O")_ 8#

Now, peroxydisulfuric acid is a neutral compound, which implies that the sum of the oxidation states of all the atoms that make up a molecule of peroxydisulfuric acid must be equal to #0#.

This means that you have

#overbrace(2 xx color(blue)((+1)))^(color(red)("2 atoms of H")) + overbrace( 2 xx ?)^(color(red)("2 atoms of S")) + overbrace(8 xx color(blue)((-2)))^(color(red)("8 atoms of O")) = 0#

Solve to find the oxidation state of sulfur

#2 + 2 * ? - 16 = 0#

#2 * ? = 14 implies ? = 14/2 = 7#

Therefore, sulfur is in a #color(blue)(+7)# oxidation state in peroxydisulfuric acid.

#stackrel(color(blue)(+1))("H")_ 2 stackrel(color(blue)(+7))("S")_ 2stackrel(color(blue)(-2))("O")_ 8#