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First, determine the oxidation state of Mn in $MnO_4^{2-}$. Let the oxidation state of Mn be x. Then, x + 4(-2) = -2, so x = +6.
In a disproportionation reaction, the same element is both oxidized and reduced. This means Mn(+6) will be oxidized to a higher oxidation state and reduced to a lower oxidation state.
Consider the options:
The correct disproportionation products are $MnO_4^-$ (where Mn is in +7 oxidation state) and $MnO_2$ (where Mn is in +4 oxidation state). Therefore, the correct option is (B).
Correct Answer: $MnO_4^-, MnO_2$
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