What is the reaction between butan-2-ol and potassium permanganate?

Well, you have added a POTENT oxidant to a material that can be oxidized to butanone…

And so we assess the individual redox equations….

[math]underbrace{MnO_{4}+8H^{+} + 5e^{-} longrightarrow Mn^{2+} + 4H_{2}O(l)}_{ ext{reduction of purple permanganate to COLOURLESS Mn(+II) ion}}[/math]

[math]underbrace{H_{3}C-CH_{2}CH_{2}CH_{2}OH+H_{2}O(l) longrightarrow H_{3}C-CH_{2}CH_{2}C(=O)OH+4H^{+}+4e^{-}}_{ ext{oxidation of C(-I) to C(+III) in butyric acid}}[/math]

We add FOUR of the reduction reaction to FIVE of the oxidation reaction to cancel the electrons….

[math]4MnO_{4}+32H^{+} + 20e^{-} +5H_{3}C-CH_{2}CH_{2}CH_{2}OH+5H_{2}O(l) longrightarrow 4Mn^{2+} + 16H_{2}O(l)+5H_{3}C-CH_{2}CH_{2}C(=O)OH+20H^{+}+20e^{-}[/math]

…and cancel away….

[math]underbrace{4MnO_{4}+12H^{+} +5H_{3}C-CH_{2}CH_{2}CH_{2}OH longrightarrow 4Mn^{2+} +5H_{3}C-CH_{2}CH_{2}C(=O)OH+ 11H_{2}O(l)}_{ ext{balanced redox equation}}[/math]

Is this balanced with respect to mass and charge? Don’t trust my arifmetick!

In acidic medium, half reaction for potassium permanganate:

MnO4^- + 8H^+ + 5e → Mn^2+ + 4H2O (reduction half reaction)

for potassium dichromate:

Cr2O7^2- +14H^+ + 6e → 2 Cr^3+ + 7H2O (reduction half reaction)

In neutral medium, or slightly basic medium,

MnO4^- + 2H2O + 3e → MnO2 + 4OH^-

Hope this helps.