Give reasons for the following:
`Mn_(2)O_(3)` is basic whereas `Mn_(2)O_(7)` is acidic.

Explanation

To explain why \( \text{Mn}_2\text{O}_3 \) is basic while \( \text{Mn}_2\text{O}_7 \) is acidic, we can analyze the oxidation states of manganese in both compounds and their electronic configurations.

### Step 1: Determine the oxidation state of manganese in \( \text{Mn}_2\text{O}_3 \)

1. The formula for manganese(III) oxide is \( \text{Mn}_2\text{O}_3 \).
2. Oxygen typically has an oxidation state of -2.
3. In \( \text{Mn}_2\text{O}_3 \), there are 3 oxygen atoms, contributing a total of \( 3 \times (-2) = -6 \).
4. Let the oxidation state of manganese be \( x \). The equation for the oxidation states is:
...