Question

How do you balance this chemical equation? `"KMnO"_4 + "Na"_2"C"_2"O"_4 + "H"_2"SO"_4 → "K"_2"SO"_4 + "Na"_2"SO"_4 + "MnSO"_4 + "CO"_2 + "H"_2"O"`

Answer 1

`color(blue)("2KMnO"_4 + "5Na"_2"C"_2"O"_4 + "8H"_2"SO"_4 → "K"_2"SO"_4 + "5Na"_2"SO"_4 + "MnSO"_4 + "10CO"_2 + "8H"_2"O")`

Explanation:

One method is to balance equations by the oxidation number method.

Step 1. Calculate the oxidation numbers of every atom:

`stackrelcolor(blue)(+1)("K")stackrelcolor(blue)(+7)("Mn")stackrelcolor(blue)("-2")("O")_4 + stackrelcolor(blue)(+1)("Na")_2stackrelcolor(blue)(+3)("C")_2stackrelcolor(blue)("-2")("O")_4 + stackrelcolor(blue)(+1)("H")_2stackrelcolor(blue)(+6)("S")stackrelcolor(blue)("-2")("O")_4 → stackrelcolor(blue)(+1)("K")_2stackrelcolor(blue)(+6)("S")stackrelcolor(blue)("-2")("O")_4 + stackrelcolor(blue)(+1)("Na")_2stackrelcolor(blue)(+6)("S")stackrelcolor(blue)("-2")("O")_4 + stackrelcolor(blue)(+2)("Mn")stackrelcolor(blue)(+6)("S")stackrelcolor(blue)("-2")("O")_4 + stackrelcolor(blue)(+4)("C")stackrelcolor(blue)("-2")("O")_2 + stackrelcolor(blue)(+1)("H")_2stackrelcolor(blue)("-2")("O")`

Step 2. Identify the atoms that change oxidation number.

`"Mn: +7 → +2; Change = -5"`
`"C: +3 → +4; Change = +1"`

Step 3. Equalize the changes in oxidation number.

You need `"1 atom of Mn"` for every `"5 atoms of C"` or `"2 atoms of Mn"` for every `"10 atoms of C"`. This gives us total changes of `+10` and `"-10"`.

Step 4. Insert coefficients to get these numbers.

`color(red)(2)"KMnO"_4 + color(red)(5)"Na"_2"C"_2"O"_4 + "H"_2"SO"_4 → "K"_2"SO"_4 + "Na"_2"SO"_4 + color(red)(2)"MnSO"_4 + color(red)(10)"CO"_2 + "H"_2"O"`

Step 5 Balance `"K"`.

`color(red)(2)"KMnO"_4 + color(red)(5)"Na"_2"C"_2"O"_4 + "H"_2"SO"_4 → color(blue)(1)"K"_2"SO"_4 + "Na"_2"SO"_4 + color(red)(2)"MnSO"_4 + color(red)(10)"CO"_2 + "H"_2"O"`

Step 6 Balance `"Na"`.

`color(red)(2)"KMnO"_4 + color(red)(5)"Na"_2"C"_2"O"_4 + "H"_2"SO"_4 → color(blue)(1)"K"_2"SO"_4 + color(orange)(5)"Na"_2"SO"_4 + color(red)(2)"MnSO"_4 + color(red)(10)"CO"_2 + "H"_2"O"`

Step 7. Balance `"S"`.

`color(red)(2)"KMnO"_4 + color(red)(5)"Na"_2"C"_2"O"_4 + color(olive)(8)"H"_2"SO"_4 → color(blue)(1)"K"_2"SO"_4 + color(orange)(5)"Na"_2"SO"_4 + color(red)(2)"MnSO"_4 + color(red)(10)"CO"_2 + "H"_2"O"`

Step 8. Balance `"O"`.

`color(red)(2)"KMnO"_4 + color(red)(5)"Na"_2"C"_2"O"_4 + color(olive)(8)"H"_2"SO"_4 → color(blue)(1)"K"_2"SO"_4 + color(orange)(5)"Na"_2"SO"_4 + color(red)(2)"MnSO"_4 + color(red)(10)"CO"_2 + color(brown)(8)"H"_2"O"`

Every substance now has a coefficient, so the equation should be balanced.

Step 9. Check that all atoms balance.

`bb"Atom"color(white)(m) bb"Left Hand Side"color(white)(m) bb"Right Hand Side"`
`color(white)(m)"K"color(white)(mmmmm) 2 color(white)(mmmmmmmmmm)2`
`color(white)(m)"Mn" color(white)(mmmml)2 color(white)(mmmmmmmmmm)2`
`color(white)(m)"O"color(white)(mmmmll)60 color(white)(mmmmmmmmml)60`
`color(white)(m)"Na" color(white)(mmmm)10 color(white)(mmmmmmmmml)10`
`color(white)(m)"C"color(white)(mmmmll)10 color(white)(mmmmmmmmml)10`
`color(white)(m)"H"color(white)(mmmmll)16color(white)(mmmmmmmmml)16`
`color(white)(m)"S"color(white)(mmmmml)8color(white)(mmmmmmmmmm)8`

The balanced equation is

`"2KMnO"_4 + "5Na"_2"C"_2"O"_4 + "8H"_2"SO"_4 → "K"_2"SO"_4 + "5Na"_2"SO"_4 + "MnSO"_4 + "10CO"_2 + "8H"_2"O"`

Here's a video on balancing equations by the oxidation number method.