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"#

1 Answer
Aug 24, 2014

Answer:

#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.