Calculate the n-factor in the following chemical changes.
(i) `KMnO_(4) overset(H^(+)) to Mn^(2+)`
(ii) `KMnO_(4) overset(H_(2)O) to Mn^(4+)`
(iii) `KMnO_(4) overset(OH^(-)) to Mn^(6+)`
(iv) ` K_(2)Cr_(2)O_(7) overset(H^(+)) to Cr^(3+)`
(v) ` C_(2)O_(4)^(2-) to CO_(2)`
(vi) `FeSO_(4) to Fe_(2)O_(3)`
(vii) `Fe_(2)O_(3) to FeSO_(4)`

Explanation

To calculate the n-factor for each of the given chemical changes, we will follow a systematic approach to determine the change in oxidation states of the elements involved.

### Step-by-Step Solution:

**(i) KMnO₄ in acidic medium to Mn²⁺:**
1. Determine the oxidation state of Mn in KMnO₄:
- Mn = x, O = -2 (4 O atoms contribute -8), K = +1
- Equation: x - 8 + 1 = 0 → x = +7
...