The method of balancing redox equations is described here,
1: Separate into two half-reactions.
#"CH"_3"CH"_2"CH"_2"CH"_2"OH" → "CH"_3"CH"_2"CH"_2"COOH"#
#"Cr"_2"O"_7^"2-" → "Cr"^"3+"#
2: Balance all atoms other than H and O.
#"CH"_3"CH"_2"CH"_2"CH"_2"OH" → "CH"_3"CH"_2"CH"_2"COOH"#
#"Cr"_2"O"_7^"2-" → color(red)(2)"Cr"^"3+"#
3: Balance #"O"#
#"CH"_3"CH"_2"CH"_2"CH"_2"OH" + "H"_2"O" → "CH"_3"CH"_2"CH"_2"COOH"#
#"Cr"_2"O"_7^"2-" → color(red)(2)"Cr"^"3+"+ color(blue)(7)"H"_2"O"#
4: Balance H.
#"CH"_3"CH"_2"CH"_2"CH"_2"OH" + "H"_2"O" → "CH"_3"CH"_2"CH"_2"COOH" + color(brown)(4)"H"^+#
#"Cr"_2"O"_7^"2-" + color(brown)(14)"H"^+ → color(red)(2)"Cr"^"3+"+ color(blue)(7)"H"_2"O"#
5: Balance charge.
#"CH"_3"CH"_2"CH"_2"CH"_2"OH" + "H"_2"O" → "CH"_3"CH"_2"CH"_2"COOH" + color(brown)(4)"H"^+ + color(magenta)(4)e^"-"#
#"Cr"_2"O"_7^"2-" + color(brown)(14)"H"^+ + color(magenta)(6)e^"-" → color(red)(2)"Cr"^"3+"+ color(blue)(7)"H"_2"O"#
6: Equalize electrons transferred.
#3 × ["CH"_3"CH"_2"CH"_2"CH"_2"OH" + "H"_2"O" → "CH"_3"CH"_2"CH"_2"COOH" + color(brown)(4)"H"^+ + color(magenta)(4)e^"-"]#
#2 × ["Cr"_2"O"_7^"2-" + color(brown)(14)"H"^+ + color(magenta)(6)e^"-" → color(red)(2)"Cr"^"3+"+ color(blue)(7)"H"_2"O"]#
7: Add the two half-reactions.
#3"CH"_3"CH"_2"CH"_2"CH"_2"OH" + 2"Cr"_2"O"_7^"2-" + color(brown)(16)"H"^+ → 3"CH"_3"CH"_2"CH"_2"COOH" + color(red)(4)"Cr"^"3+"+ color(blue)(11)"H"_2"O"#
8: Check mass balance.
#"Atom"color(white)(m)"On the left"color(white)(m)"On the right"#
#color(white)(m)"C"color(white)(mmmm)12color(white)(mmmmml)12#
#color(white)(m)"H"color(white)(mmmm)46color(white)(mmmmml)46#
#color(white)(m)"O"color(white)(mmmm)17color(white)(mmmmml)17#
#color(white)(m)"Cr"color(white)(mmmml)4color(white)(mmmmmll)4#
9: Check charge balance.
#color(white)(mm)"On the left"color(white)(mm)"On the right"#
#color(white)(m)"4- + 16+ = 12+"color(white)(mml)"12+"#
The balanced equation is
#3"CH"_3"CH"_2"CH"_2"CH"_2"OH" + 2underbrace(color(orange)("Cr"_2"O"_7^"2-"))_color(orange)("orange") + 16"H"^+ → 3"CH"_3"CH"_2"CH"_2"COOH" + 4underbrace(color(green)("Cr"^"3+"))_color(green)("green") + 11"H"_2"O"#
The #color(orange)("orange dichromate ion"# is converted to the #color(green)("green chromium(III) ion")#.
