Let's determine the various oxidation states of manganese (Mn) in the given reaction and identify which states are not present.
The reaction is:
\(3MnO_4^{2-} + 4H^+ \rightarrow 2MnO_4^- + MnO_2 + 2H_2O\)
We need to identify the oxidation states of Mn in each compound:
- \(MnO_4^{2-}\): Oxygen typically has an oxidation state of -2. Therefore, for \(MnO_4^{2-}\), let the oxidation state of Mn be \( x \).
x + 4(-2) = -2
- Solving gives \(x = +6\).
- \(MnO_4^{-}\): Again, oxygen is -2, so let the oxidation state of Mn be \( y \).
y + 4(-2) = -1
- Solving gives \(y = +7\).
- \(MnO_2\): Here, with oxygen being -2, the oxidation state of Mn (\( z \)) in \(MnO_2\) is:
z + 2(-2) = 0
- Solving gives \(z = +4\).
The oxidation states of Mn present in the reaction are +6, +7, and +4.
Now, let's look at the options:
- +6 is present, so options including A are incorrect.
- +7 is present, so options including D are incorrect.
- +4 is present, so options including C are incorrect.
- +2 is not present, making option B correct.
- +3 is not present, making option E correct.
Thus, the oxidation states not shown by Mn in the reaction are +2 and +3.
The correct answer is: B and E only.