0.01 M KMnO$$_4$$ solution was added to 20.0 mL of 0.05 M Mohr's salt solution through a burette. The initial reading of 50 mL burette is zero. The volume of KMnO$$_4$$ solution left in the burette after the end point is ______ mL. (nearest integer)

We need to find the volume of KMnO$$_4$$ solution left in the burette after titration with Mohr's salt.

KMnO$$_4$$ solution concentration = 0.01 M, Mohr's salt (FeSO$$_4$$(NH$$_4$$)$$_2$$SO$$_4$$ · 6H$$_2$$O) solution is 20.0 mL of 0.05 M, and the burette capacity is 50 mL with an initial reading of 0.

In acidic medium: $$\text{MnO}_4^- + 5\text{Fe}^{2+} + 8\text{H}^+ \rightarrow \text{Mn}^{2+} + 5\text{Fe}^{3+} + 4\text{H}_2\text{O}$$ So 1 mole of KMnO$$_4$$ reacts with 5 moles of Fe$$^{2+}$$.

$$\text{mmol of Fe}^{2+} = 0.05 \times 20.0 = 1.0 \text{ mmol}, \quad \text{mmol of KMnO}_4 = \frac{1.0}{5} = 0.2 \text{ mmol}$$

$$V = \frac{\text{mmol}}{M} = \frac{0.2}{0.01} = 20 \text{ mL}$$

Volume left = Total volume − Volume used = 50 − 20 = 30 mL. Hence, the answer is 30 mL.