Question

A $\mathbf{50}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{ml}$ sample of solution containing${\mathbf{Fe}}^{\mathbf{2}\mathbf{+}}$ ions is titrated with a$\mathbf{0}\mathbf{.}\mathbf{0216}\mathbf{}\mathbf{M}\mathbf{}{\mathbf{KMnO}}_{\mathbf{4}}$ solution. It required$\mathbf{20}\mathbf{.}\mathbf{62}\mathbf{}\mathbf{ml}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{KMnO}}_{\mathbf{4}}$ solution to oxidize all the${\mathbf{Fe}}^{\mathbf{2}\mathbf{+}}$ ions to${\mathbf{Fe}}^{\mathbf{3}\mathbf{+}}$ ions by the reaction

${\mathbf{MnO}}_{\mathbf{4}}^{\mathbf{-}}\left(\mathrm{aq}\right)\mathbf{+}{\mathbf{Fe}}^{\mathbf{2}\mathbf{+}}\left(\mathrm{aq}\right)\stackrel{\mathbf{Acidic}}{\mathbf{\to }}{\mathbf{Mn}}^{\mathbf{2}\mathbf{+}}\left(\mathrm{aq}\right)\mathbf{+}{\mathbf{Fe}}^{\mathbf{3}\mathbf{+}}\left(\mathrm{aq}\right)\left(\mathrm{unbalanced}\right)$

1. What as the concentration of ${\mathbf{Fe}}^{\mathbf{2}\mathbf{+}}$ions in the sample solution?
2. What volume of $\mathbf{0}\mathbf{.}\mathbf{0150}\mathbf{}\mathbf{M}\mathbf{}{\mathbf{K}}_{\mathbf{2}}{\mathbf{Cr}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{7}}$solution would it take to do the same titration? The reaction is ${\mathbf{Cr}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{7}}^{\mathbf{2}\mathbf{-}}\left(\mathrm{aq}\right)\mathbf{+}{\mathbf{Fe}}^{\mathbf{2}\mathbf{+}}\left(\mathrm{aq}\right)\stackrel{\mathbf{Acidic}}{\mathbf{\to }}{\mathbf{Cr}}^{\mathbf{3}\mathbf{+}}\left(\mathrm{aq}\right)\mathbf{+}{\mathbf{Fe}}^{\mathbf{3}\mathbf{+}}\left(\mathrm{aq}\right)\left(\mathrm{unbalanced}\right)$

Short answer

1. The concentration of ${\mathrm{Fe}}^{2+}$ions in the solution is $4.46\times {10}^{-2}\mathrm{M}{\mathrm{Fe}}^{2+}$.
2. The volume of ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$solution is $24.8\mathrm{ml}$.

Step-by-step solution

Definition of the concentration of solution

A measure of the amount of solute that has been dissolved in a given amount of solvent or solution is defined as the concentration of the solution.

a) Calculation of the concentration of the sample solution

The equation of oxidation and reduction reactions are

$$\begin{gathered} {\mathrm{Fe}}^{2+}\to {\mathrm{Fe}}^{3+}+{\mathrm{e}}^{-} \\ 5{\mathrm{e}}^{-}+8{\mathrm{H}}^{+}+{\mathrm{MnO}}_4^{-}\to {\mathrm{Mn}}^{2+}+4{\mathrm{H}}_2\mathrm{O} \end{gathered}$$

The balanced equation is

$8{\mathrm{H}}^{+}+{\mathrm{MnO}}_4^{-}+5{\mathrm{Fe}}^{2+}\to 5{\mathrm{Fe}}^{3+}+{\mathrm{Mn}}^{2+}+4{\mathrm{H}}_2\mathrm{O}$

The molarity of the equation is:

$\begin{array}{rcl}\mathrm{Molarity}& =& \frac{2.23\times {10}^{-3}\mathrm{mol}{\mathrm{Fe}}^{2+}}{50.00\times {10}^{-3}\mathrm{L}}\\ & =& 4.46\times {10}^{-2}\mathrm{M}{\mathrm{Fe}}^{2+}\end{array}$

The concentration of ${\mathrm{Fe}}^{2+}$ions in the solution is $4.46\times {10}^{-2}\mathrm{M}{\mathrm{Fe}}^{2+}$.

b) The titration reaction

The titration reaction is:

$$\begin{gathered} {\mathrm{Fe}}^{2+}\to {\mathrm{Fe}}^{3+}+{\mathrm{e}}^{-} \\ 6{\mathrm{e}}^{-}+14{\mathrm{H}}^{+}+{\mathrm{Cr}}_2{\mathrm{O}}_7^{2-}\to 2{\mathrm{Cr}}^{3+}+7{\mathrm{H}}_2\mathrm{O} \end{gathered}$$

The balanced equation is

$6{\mathrm{Fe}}^{2+}+14{\mathrm{H}}^{+}+{\mathrm{Cr}}_2{\mathrm{O}}_7^{2-}\to 6{\mathrm{Fe}}^{3+}+2{\mathrm{Cr}}^{3+}+7{\mathrm{H}}_2\mathrm{O}$

To calculate the volume of ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$:

$$\begin{gathered} =2.48\times {10}^{-2}\mathrm{L}\times \frac{{10}^3\mathrm{ml}}{1\mathrm{L}} \\ =24.8\mathrm{ml} \end{gathered}$$

The volume of the ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$solution is $24.8\mathrm{ml}$.