Chapter 4, Problem 128CP

Chromium has been investigated as a coating for steelcans. The thickness of the chromium film is determinedby dissolving a sample of a can in acid and oxidizing theresulting ${\text{Cr}}^{\text{3+}}{\text{to Cr}}_{\text{2}}{\text{O}}_{\text{7}}{}^{\text{2–}}$ with the peroxydisulfate ion:

$\begin{array}{l}{\text{S}}_{\text{2}}{\text{O}}_{\text{8}}{}^{\text{2–}}\text{(}aq{\text{)+Cr}}^{\text{3+}}\text{(}aq{\text{)+H}}_{\text{2}}\text{O(}l\text{)}\to {\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}{}^{\text{2–}}\text{(}aq\text{)}\\ {\text{+SO}}_{\text{4}}{}^{\text{2–}}\text{(}aq{\text{)+H}}^{\text{+}}\text{(}aq\text{) }\left(\text{Unbalanced}\right)\end{array}$

After removal of unreacted ${\text{S}}_{\text{2}}{\text{O}}_{\text{8}}{}^{\text{2–}}$ , an excess of ferrousammonium sulfate ${\text{[Fe(NH}}_{\text{4}}{\text{)}}_{\text{2}}{{\text{(SO}}_{\text{4}}\text{)}}_{\text{2}}\cdot {\text{6H}}_{\text{2}}\text{O]}$ is added,reacting with ${\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}{}^{\text{2–}}$ produced from the first reaction.The unreacted ${\text{Fe}}^{\text{2+}}$ from the excess ferrous ammoniumsulfate is titrated with a separate ${\text{K}}_{\text{2}}{\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}$ solution. Thereaction is:

$\begin{array}{l}{\text{H}}^{\text{+}}\text{(}aq{\text{)+Fe}}^{\text{2+}}\text{(}aq{\text{)+Cr}}_{\text{2}}{\text{O}}_{\text{7}}{}^{\text{2–}}\text{(}aq\text{)}\to {\text{Fe}}^{\text{3+}}\text{(}aq\text{)}\\ {\text{+Cr}}^{\text{3+}}\text{(}aq{\text{)+H}}_{\text{2}}\text{O(}l\text{) }\left(\text{Unbalanced}\right)\end{array}$
a. Write balanced chemical equations for the tworeactions.
b. In one analysis, a $\text{40}{\text{.0-cm}}^{\text{2}}$ sample of a chromiumplatedcan was treated according to this procedure.After dissolution and removal of excess ${\text{S}}_{\text{2}}{\text{O}}_{\text{8}}{}^{\text{2–}}$ ,3.000 g of ${\text{Fe(NH}}_{\text{4}}{\text{)}}_{\text{2}}{{\text{(SO}}_{\text{4}}\text{)}}_{\text{2}}\cdot {\text{6H}}_{\text{2}}\text{O}$ was added. Ittook 8.58 mL of 0.0520 M ${\text{K}}_{\text{2}}{\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}$ solution tocompletely react with the excess ${\text{Fe}}^{\text{2+}}$ . Calculate thethickness of the chromium film on the can. (Thedensity of chromium is $\text{7}{\text{.19 g/cm}}^{\text{3}}$ .)