A sample of pyrolusite `(MnO_2)` weighs 0.5 g. To its solution, 0.6674 g of `As_2O_3` and dilute, acid are added. After the reaction has ceased, arsenic `(As^(3+))` in `As_2O_3` is titrated with `45mL` of `(M)/(50)` `KMnO_4` solution. Calculate the percentage of `MnO_2` in pyrolusite. (Atomic weight of As is 74.9 and that of Mn is 55.)

Explanation

To solve the problem step by step, we will calculate the percentage of `MnO_2` in the pyrolusite sample based on the provided data.

### Step 1: Calculate the moles of KMnO₄ used
The molarity of the KMnO₄ solution is given as \( \frac{1}{50} \) M, and the volume used is 45 mL.

\[ \text{Moles of KMnO}_4 = \text{Molarity} \times \text{Volume (L)} = \frac{1}{50} \times 0.045 = 0.0009 \text{ moles} \]
...