Question

$$\begin{gathered} \mathbf{\text{Question:Asampleofsolution50.00}}\mathbf{ }{\mathbf{\text{mLcontainingFe}}}^{\mathbf{\text{2 +}}}\mathbf{\text{ionsistitratedwithasolution0.0216}}\mathbf{ }\mathbf{\text{M}}\mathbf{ }{\mathbf{\text{KMnO}}}_{\mathbf{\text{4}}}\mathbf{\text{.}} \\ \mathbf{\text{Itrequired20.62}}\mathbf{ }\mathbf{\text{mL}}\mathbf{ }\mathbf{\text{of}}\mathbf{ }{\mathbf{\text{KMnO}}}_{\mathbf{\text{4}}}\mathbf{\text{solutionto}} \\ {\mathbf{\text{oxidizealltheFe}}}^{\mathbf{\text{2 +}}}{\mathbf{\text{ionstoFe}}}^{\mathbf{\text{3+}}}\mathbf{\text{ionsbythereaction}} \\ \mathbf{Mn}{{\mathbf{O}}_{\mathbf{4}}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{F}{\mathbf{e}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\stackrel{\mathbf{Acidic}}{\mathbf{\to }}{\mathbf{Mn}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{F}{\mathbf{e}}^{\mathbf{3}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{ }\mathbf{\left(}\mathbf{unbalanced}\mathbf{\right)} \\ {\mathbf{\text{aWhatastheconcentrationofFe}}}^{\mathbf{\text{2 +}}}\mathbf{\text{ionsinthesamplesolution?0}} \\ \mathbf{\text{b.Whatvolumeof0.0150}}\mathbf{ }\mathbf{\text{M}}\mathbf{ }{\mathbf{\text{K}}}_{\mathbf{\text{2}}}{\mathbf{\text{Cr}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{7}}}\mathbf{\text{solutionwouldittaketodothesametitration?}} \\ \mathbf{\text{Thereactionis}}{\mathbf{Cr}}_{\mathbf{2}}{{\mathbf{O}}_{\mathbf{7}}}^{\mathbf{2}\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{F}{\mathbf{e}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\stackrel{\mathbf{Acidic}}{\mathbf{\to }}{\mathbf{Cr}}^{\mathbf{3}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{F}{\mathbf{e}}^{\mathbf{3}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{\left(}\mathbf{unbalanced}\mathbf{\right)} \end{gathered}$$

Short answer

Answer

1. The concentration of ${\text{Fe}}^{\text{2 +}}$ ions in the solution is $4.46\times {10}^{-2} \text{M} {\text{Fe}}^{\text{2 +}}$
2. The volume of ${\text{K}}_{\text{2}}{\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}$ solution is 24.8mL

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

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

The balanced equation is

${\text{8H}}^{\text{+}}\text{(aq)}+{\text{MnO}}_{\text{4}}^{\text{-}}\text{(aq)}+{\text{5Fe}}^{\text{2 +}}\text{(aq)}\to {\text{5Fe}}^{\text{3 +}}\text{(aq)}+{\text{Mn}}^{\text{2 +}}\text{(aq)}+{\text{4H}}_{\text{2}}\text{O(l)}$

The molarity of the equation is:

$$\begin{gathered} \text{Molarity}=\frac{2.23\times {10}^{-3}\text{mol} {\text{Fe}}^{2+}}{50.00\times {10}^{-3}\text{L}} \\ =4.46\times {10}^{-2}\text{M} {\text{Fe}}^{\text{2 +}} \end{gathered}$$

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

b) The titration reaction

The titration reaction is:

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

The balanced equation is ${\text{6Fe}}^{\text{2 +}}+\text{14H}+{\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}\to {\text{6Fe}}^{\text{3 +}}+{\text{2Cr}}^{\text{3 +}}+{\text{7H}}_{\text{2}}\text{O}$

To calculate the volume of ${\text{K}}_{\text{2}}{\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}$:

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

The volume of the ${\text{K}}_{\text{2}}{\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}$ solution is 24.8mL .