A polyvalent metal weghing 0.1 g and having atomic weight 51 reacted will dil `H_2SO_4` to give 43.9 " mL of " `H_2` at STP. This solution containing the metal in the lower oxidation state was found to require 58.8 " mL of " 0.1 permanganate for complete oxidation. What are the valencies of the metal.

Explanation

To determine the valencies of the polyvalent metal, we can follow these steps:

### Step 1: Calculate the number of equivalents of KMnO4 used
We know that the volume of KMnO4 used is 58.8 mL and its concentration is 0.1 N (normality).

1. Convert the volume from mL to L:
\[
\text{Volume in L} = \frac{58.8 \, \text{mL}}{1000} = 0.0588 \, \text{L}
...