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_3CH_2CH_2CH_2OH CH_3CH_2CH_2COOH##
##Cr_2O_7^2- Cr^3+##
2: Balance all atoms other than H and O.
##CH_3CH_2CH_2CH_2OH CH_3CH_2CH_2COOH##
##Cr_2O_7^2- color(red)(2)Cr^3+##
3: Balance ##O##
##CH_3CH_2CH_2CH_2OH + H_2O CH_3CH_2CH_2COOH##
##Cr_2O_7^2- color(red)(2)Cr^3++ color(blue)(7)H_2O##
4: Balance H.
##CH_3CH_2CH_2CH_2OH + H_2O CH_3CH_2CH_2COOH + color(brown)(4)H^+##
##Cr_2O_7^2- + color(brown)(14)H^+ color(red)(2)Cr^3++ color(blue)(7)H_2O##
5: Balance charge.
##CH_3CH_2CH_2CH_2OH + H_2O CH_3CH_2CH_2COOH + color(brown)(4)H^+ + color(magenta)(4)e^-##
##Cr_2O_7^2- + color(brown)(14)H^+ + color(magenta)(6)e^- color(red)(2)Cr^3++ color(blue)(7)H_2O##
6: Equalize electrons transferred.
##3 [CH_3CH_2CH_2CH_2OH + H_2O CH_3CH_2CH_2COOH + color(brown)(4)H^+ + color(magenta)(4)e^-]##
##2 [Cr_2O_7^2- + color(brown)(14)H^+ + color(magenta)(6)e^- color(red)(2)Cr^3++ color(blue)(7)H_2O]##
7: Add the two half-reactions.
##3CH_3CH_2CH_2CH_2OH + 2Cr_2O_7^2- + color(brown)(16)H^+ 3CH_3CH_2CH_2COOH + color(red)(4)Cr^3++ color(blue)(11)H_2O##
8: Check mass balance.
##Atomcolor(white)(m)On the leftcolor(white)(m)On the right##
##color(white)(m)Ccolor(white)(mmmm)12color(white)(mmmmml)12##
##color(white)(m)Hcolor(white)(mmmm)46color(white)(mmmmml)46##
##color(white)(m)Ocolor(white)(mmmm)17color(white)(mmmmml)17##
##color(white)(m)Crcolor(white)(mmmml)4color(white)(mmmmmll)4##
9: Check charge balance.
##color(white)(mm)On the leftcolor(white)(mm)On the right##
##color(white)(m)4- + 16+ = 12+color(white)(mml)12+##
The balanced equation is
##3CH_3CH_2CH_2CH_2OH + 2underbrace(color(orange)(Cr_2O_7^2-))_color(orange)(orange) + 16H^+ 3CH_3CH_2CH_2COOH + 4underbrace(color(green)(Cr^3+))_color(green)(green) + 11H_2O##
The ##color(orange)(orange dichromate ion## is converted to the ##color(green)(green chromium(III) ion)##.