The standard potential change of a reaction can be calculated as the difference between the standard potential of the reduction half-reaction and the standard potential of the oxidation half-reaction. In this case, if we want to oxidize Cr(OH)3, this has to be the oxidation reaction and the permanganate has to be reduction reaction, so we have:
The relation between this change in potential and the change in Gibbs free energy, which determines if the process is spontaneous, is given by:
Which means that if ΔE° is positive, ΔG° is negative and the reaction is spontaneous. This means that yes, Cr(OH)3 can be oxidized with permanganate.
b) If HCrO4- is formed, we will be obtaining the most toxic form of Cr. If this filters into groundwaters, the health hazard is enormous, since we will be adding a toxic species to water that can be used for cropping, consumption, etc. So yes, there is a potential adverse effect when using permanganate in aquifers which might contain Cr(III).
Some engineers recommend addition of the strong oxidant potassium permanganate (KMnO4) for remediating aquifers contaminated with...