Start by identifying the oxidation state for each of the element:
stackrel(color(navy)(bb(+2)))("Fe")stackrel(color(purple)(bb(+6)))("S")stackrel(-2)("O")_4 to stackrel(color(navy)(bb(+3)))("Fe"_2)stackrel(-2)("O")_3 + stackrel(color(purple)(bb(+4)))("S")stackrel(-2)("O")_2+stackrel(color(purple)(+6))("S")stackrel(-2)("O")_3color(white)(-)color(grey)("NOT BALANCED")
Only three of the four chemicals- "FeSO"_4, "Fe"_2"O"_3, and "SO"_2 are directly involved in the redox reaction.
The oxidation state of iron "Fe" has increased from
- color(navy)(+2) in stackrel(color(navy)(bb(+2)))(bb("Fe"))stackrel(color(purple)(+6))("S")stackrel(-2)("O")_4 to
- color(navy)(+3) in stackrel(color(navy)(bb(+3)))(bb("Fe")_2)stackrel(-2)("O")_3 by one
and therefore "Fe" is oxidized.
The oxidation state of sulfur "S" has declined from
- color(purple)(+6) in stackrel(color(navy)(+2))("Fe")stackrel(color(purple)(bb(+6)))(bb("S"))stackrel(-2)("O")_4 to
- color(purple)(+4) in stackrel(color(purple)(bb(+4)))(bb("S"))stackrel(-2)("O")_2 by two
and therefore some of the sulfur atoms have been reduced.
-
The total increases in oxidation numbers shall be the same as the sum of decreases in oxidation numbers in a balanced redox reaction.
-
The oxidation number increases by 1 for each mole of "Fe" atom oxidized and decreases by 2 for each mole of "S" oxidized.
-
Therefore for each mole of "S" reduced, two moles of "Fe" atoms shall be oxidized.
Note that sulfur dioxide, stackrel(color(purple)(bb(+4)))(bb("S")) stackrel(-2)("O")_2, is the only species containing sulfur atoms of oxidation state color(purple)(+4). Thus all of the reduced sulfur atoms would end up in "SO"_2.
The number of moles of sulfur atoms reduced shall therefore equal to the number of "SO"_2 molecules produced. This number would be slightly smaller than that of stackrel(color(navy)(+2))("Fe")stackrel(color(purple)(bb(+6)))(bb("S"))stackrel(-2)("O")_4 given that sulfur atoms that were not reduced got eventually into stackrel(color(purple)(+6))("S")stackrel(-2)("O")_3.
Add coefficients 2 and 1 in front of "FeSO"_4 and "SO"_2, respectively:
color(green)(2)color(white)(l)stackrel(color(navy)(bb(+2)))("Fe")stackrel(color(purple)(bb(+6)))("S")stackrel(-2)("O")_4 to stackrel(color(navy)(bb(+3)))("Fe"_2)stackrel(-2)("O")_3 + color(green)(1)color(white)(l)stackrel(color(purple)(bb(+4)))("S")stackrel(-2)("O")_2+stackrel(color(purple)(+6))("S")stackrel(-2)("O")_3color(white)(-)color(grey)("NOT YET BALANCED")
Deduce coefficients for the rest of the species based on the conservation of iron and sulfur atoms.
color(darkgreen)(2)color(white)(l)stackrel(color(navy)(bb(+2)))("Fe")stackrel(color(purple)(bb(+6)))("S")stackrel(-2)("O")_4 to color(green)(1)color(white)(l)stackrel(color(navy)(bb(+3)))("Fe"_2)stackrel(-2)("O")_3 + color(darkgreen)(1)color(white)(l)stackrel(color(purple)(bb(+4)))("S")stackrel(-2)("O")_2+color(green)(1)color(white)(l)stackrel(color(purple)(+6))("S")stackrel(-2)("O")_3color(white)(-)color(grey)("BALANCED")
Take coefficients "1" out of the expression:
2color(white)(l)"FeSO"_4 to "Fe"_2"O"_3 + "SO"_2 + "SO"_3
