Question

Arsenic(III) oxide $\mathbf{\left(}{\mathbf{As}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\mathbf{\right)}$is available in pure form and is a useful (but carcinogenic) primary standard for oxidizing agents such as ${\mathbf{MnO}}_{\mathbf{4}}^{\mathbf{-}}$.The $\mathbf{\left(}{\mathbf{As}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\mathbf{\right)}$is dissolved in base and then titrated with in acidic solution. A small amount of iodide${\mathbf{MnO}}_{\mathbf{4}}^{\mathbf{-}}$or iodate$\left({\mathrm{IO}}_3^{-}\right)$ is used to catalyze the reaction between ${\mathbf{H}}_{\mathbf{3}}{\mathbf{AsO}}_{\mathbf{3}}$and${\mathbf{MnO}}_{\mathbf{4}}^{\mathbf{-}}$.

${\mathbf{As}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\mathbf{+}\mathbf{4}\mathbf{OH}\mathbf{}\mathbf{\square }\mathbf{}\mathbf{2}{\mathbf{HAsO}}_{\mathbf{3}}^{\mathbf{2}\mathbf{-}}\mathbf{+}{\mathbf{H}}_{\mathbf{2}}{\mathbf{OHAsO}}_{\mathbf{3}}^{\mathbf{2}\mathbf{-}}\mathbf{+}\mathbf{2}{\mathbf{H}}^{\mathbf{+}\mathbf{}}\mathbf{\square }\mathbf{}\mathbf{}{\mathbf{H}}_{\mathbf{3}}{\mathbf{AsO}}_{\mathbf{3}}\mathbf{5}{\mathbf{H}}_{\mathbf{3}}{\mathbf{AsO}}_{\mathbf{3}}\mathbf{+}\mathbf{2}{\mathbf{MnO}}_{\mathbf{4}}^{\mathbf{-}}\mathbf{+}\mathbf{6}{\mathbf{H}}^{\mathbf{+}}$

$\mathbf{\to }\mathbf{5}{\mathbf{H}}_{\mathbf{3}}{\mathbf{AsO}}_{\mathbf{4}}\mathbf{+}\mathbf{2}{\mathbf{Mn}}^{\mathbf{2}}\mathbf{+}\mathbf{3}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}$

(c) It was found that 0.1468 g of ${\mathbf{As}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}$required 29.98 mL of ${\mathbf{KMnO}}_{\mathbf{4}}$solution for the faint color of unreacted ${\mathbf{MnO}}_{\mathbf{4}}^{\mathbf{-}}$to appear. In a blank titration, 0.03 mL of${\mathbf{MnO}}_{\mathbf{4}}^{\mathbf{-}}$ was required to produce enough color to be seen. Calculate the molarity of the permanganate solution.

Short answer

The molarity of the permanganate solution$0.01982\mathrm{MMn}{o}_4^{-}$

Step-by-step solution

Define the molarity.

The total number of moles of solute per litre of solution is known as a solution's molarity. Because, unlike mass, the volume of a system fluctuates with changes in physical conditions, the molality of a solution is affected by changes in physical parameters of the system such as pressure and temperature. Molarity is represented by the letter M, which stands for molar.

The molarity of a solution is defined as one gramme of solute dissolved in one liter of solution.

Step 2: Calculate the molarity of MMNO4- 

The mass of ${\mathrm{As}}_2{\mathrm{O}}_3=0.1468\mathrm{g}$

The volume of ${\mathrm{KMnO}}_4$solution required for the faint colour of unreacted ${\mathrm{MnO}}_4^{-}$

to appear =29.98 mL = 0.02998 L

volume of ${\mathrm{MnO}}_4^{-}$required to produce enough colour to be seen (blank titration)

=0.03 mL=0.00003 L

Now calculate the molarity by using the mole concept formula.

${\mathrm{M}}_{\mathrm{MN}}{\mathrm{o}}_4^{-}=\frac{0.1468{\mathrm{gAs}}_2{\mathrm{O}}_3\left({\displaystyle \frac{1{\mathrm{molAs}}_2{\mathrm{O}}_3}{197.84{\mathrm{gAs}}_2{\mathrm{O}}_3}}\right)\left({\displaystyle \frac{2{\mathrm{molAs}}_2{o}_3^{2-}}{1{\mathrm{molAs}}_2{\mathrm{O}}_3}}\right)\left({\displaystyle \frac{1{\mathrm{molH}}_3{\mathrm{AsO}}_3}{1{\mathrm{molHAsO}}_3^{2-}}}\right)\left({\displaystyle \frac{2{\mathrm{molMnO}}_4^{-}}{5{\mathrm{molH}}_3{\mathrm{AsO}}_3}}\right)}{\left(0.02998-0.00003\right)\mathrm{L}}$

$$\begin{gathered} =0.01982\frac{{\mathrm{molMnO}}_4^{-}}{\mathrm{L}} \\ =0.01982{\mathrm{molMnO}}_4^{-} \end{gathered}$$

Thus, the molarity of the permanganate solution$=0.01982{\mathrm{molMnO}}_4^{-}$