What is the equation for the reaction with Butan-1-ol with [o] acidified ##K_2Cr_2O_7##?

The butan-1-ol is oxidized to butanoic acid, and the dichromate ion is reduced to chromium(III) ion.

The method of balancing redox equations is described ,

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")##.