The reaction between iron and sulfuric acid is: $$ \begin{aligned} \text{Fe} + \text{H}_2\text{SO}_4 &\longrightarrow \text{FeSO}_4 + \text{H}_2 \end{aligned} $$ The redox reaction between $\text{Fe}^{2+}$ and $\text{KMnO}_4$ is: $$ \begin{aligned} 2\text{KMnO}_4 + 8\text{H}_2\text{SO}_4 + 10\text{FeSO}_4 &\longrightarrow \text{K}_2\text{SO}_4 + 2\text{MnSO}_4 + 5\text{Fe}_2(\text{SO}_4)_3 + 8\text{H}_2\text{O} \end{aligned} $$ From the stoichiometry, $1 \text{ mole of KMnO}_4 \equiv 5 \text{ moles of Fe}^{2+}$. Given: $M = 0.02 \text{ M}$, $V = 98.5 \text{ mL} = 0.0985 \text{ L}$. Moles of $\text{KMnO}_4 = 0.02 \times 0.0985 = 0.00197 \text{ mol}$. Moles of $\text{Fe} = 5 \times 0.00197 = 0.00985 \text{ mol}$. Mass of Fe: $$ \begin{aligned} \text{Mass} &= 0.00985 \times 55.85 \text{ g} \\ &= 0.55 \text{ g} \end{aligned} $$ The weight of the iron wire was $0.55 \text{ g}$.