Question

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 Cr³⁺ to$\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{7}}^{\mathbf{2}\mathbf{-}}$with the peroxydisulfate ion:${\mathit{S}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{8}}^{\mathbf{2}\mathbf{-}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)}\mathbf{+}\mathit{C}{\mathit{r}}^{\mathbf{3}\mathbf{+}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)}\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathbf{\left(}\mathbf{l}\mathbf{\right)}\mathbf{\to }\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{7}}^{\mathbf{2}\mathbf{-}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)}\mathbf{+}\mathit{S}{\mathit{O}}_{\mathbf{4}}^{\mathbf{2}\mathbf{-}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)}\mathbf{+}{\mathit{H}}^{\mathbf{+}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)}\mathbf{\left(}\mathbf{U}\mathbf{n}\mathbf{b}\mathbf{a}\mathbf{l}\mathbf{a}\mathbf{n}\mathbf{c}\mathbf{e}\mathbf{d}\mathbf{\right)}$

After removal ofunreacted $S_2{O}_8^{2-}$,an excess of ferrousammonium sulfate $[Fe{\left(N{H}_4\right)}_2{\left(S{O}_4\right)}_2\cdot 6H_{2}O]$isadded, reactingwith $C{r}_2{O}_7^{2-}$producedfrom the first reaction. Theunreacted$F{e}^{2+}$from the excess ferrous ammonium sulfate is titrated with a separate${\mathit{K}}_{\mathit{2}}\mathit{C}{\mathit{r}}_{\mathit{2}}{\mathit{O}}_{\mathit{7}}$solution. Thereaction is:

${\mathit{H}}^{\mathbf{+}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)}\mathbf{+}\mathit{F}{\mathit{e}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)}\mathbf{+}\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{7}}^{\mathbf{2}\mathbf{-}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)}\mathbf{\to }\mathit{F}{\mathit{e}}^{\mathbf{3}\mathbf{+}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)}\mathbf{+}\mathit{C}{\mathit{r}}^{\mathbf{3}\mathbf{+}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)}\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathbf{\left(}\mathbf{l}\mathbf{\right)}\mathbf{\left(}\mathbf{u}\mathbf{n}\mathbf{b}\mathbf{a}\mathbf{l}\mathbf{a}\mathbf{n}\mathbf{c}\mathbf{e}\mathbf{d}\mathbf{\right)}$

a. Write balanced chemical equations for the tworeactions.

b. In one analysis, a 40.0-cm² sample of a chromiumplated can was treated according to this procedure.After dissolution and removal ofexcess${\mathit{S}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{8}}^{\mathbf{2}\mathbf{-}}$,3.000 g of $\mathbf{[}\mathbf{F}\mathbf{e}{\mathbf{\left(}\mathbf{N}{\mathbf{H}}_{\mathbf{4}}\mathbf{\right)}}_{\mathbf{2}}{\mathbf{\left(}\mathbf{S}{\mathbf{O}}_{\mathbf{4}}\mathbf{\right)}}_{\mathbf{2}}\mathbf{\cdot }\mathbf{6}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{]}$was added. Ittook 8.58 mL of 0.0520M ${\mathit{K}}_{\mathbf{2}}\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{7}}$solutiontocompletely react with theexcess.$\mathit{F}{\mathit{e}}^{\mathbf{2}\mathbf{+}}$Calculate thethickness of the chromium film on the can. (Thedensity of chromium is 7.19 g/cm³.)

Short answer

(a)

Balanced chemical equation for the first reaction:

$7H_{2}O\left(l\right)+2C{r}^{3+}\left(aq\right)+3S_2{O}_8^{2-}\left(aq\right)\to C{r}_2{O}_7^{2-}\left(aq\right)+14H^{+}\left(aq\right)+6S{O}_4^{2-}\left(aq\right)$

Balanced chemical equation for the second reaction:

$14H^{+}\left(aq\right)+6F{e}^{2+}\left(aq\right)+C{r}_2{O}_7^{2-}\left(aq\right)\to 2C{r}^{3+}\left(aq\right)+6F{e}^{3+}\left(aq\right)+7H_{2}O\left(l\right)$

(b) The thickness of the chromium film on the can is.$300\mu m$

Step-by-step solution

Step 1:Determinethe balanced chemical equations

Balanced chemical equation for the first reaction:

$\begin{array}{c}\frac{\begin{array}{c}7H_{2}O+2C{r}^{3+}\to C{r}_2{O}_7^{2-}+14H^{+}+6e^{-}\\ 6e^{-}+3S_2{O}_8^{2-}\to 6S{O}_4^{2-}\end{array}}{7H_{2}O\left(l\right)+2C{r}^{3+}\left(aq\right)+3S_2{O}_8^{2-}\left(aq\right)\to C{r}_2{O}_7^{2-}\left(aq\right)+14H^{+}\left(aq\right)+6S{O}_4^{2-}\left(aq\right)}\\ \end{array}$

Balanced chemical equation for the second reaction:

$\begin{array}{c}\frac{\begin{array}{c}6F{e}^{2+}\to 6F{e}^{3+}+6e^{-}\\ 6e^{-}+14H^{+}+C{r}_2{O}_7^{2-}\to 2C{r}^{3+}+7H_{2}O\end{array}}{14H^{+}\left(aq\right)+6F{e}^{2+}\left(aq\right)+C{r}_2{O}_7^{2-}\left(aq\right)\to 2C{r}^{3+}\left(aq\right)+6F{e}^{3+}\left(aq\right)+7H_{2}O\left(l\right)}\\ \end{array}$

Determine the thickness of the chromium film 

The amount of excess $F{e}^{2+}$will be

$\begin{array}{l}=8.58\times {10}^{-3}L\times \frac{0.0520molC{r}_2{O}_7^{2-}}{L}\times \frac{6molF{e}^{2+}}{molC{r}_2{O}_7^{2-}}\\ =2.68\times {10}^{-3}molofexcessF{e}^{2+}\end{array}$

Total amount of$F{e}^{2+}$will be

$\begin{array}{l}=3.000g[Fe{\left(N{H}_4\right)}_2{\left(S{O}_4\right)}_2\cdot 6H_{2}O]\times \frac{1mol}{392.17g}\\ =7.650\times {10}^{-3}molF{e}^{2+}\end{array}$

Therefore, the amount ofr$F{e}^{2+}$eacted will be

$\begin{array}{l}7.650\times {10}^{-3}molF{e}^{2+}-2.68\times {10}^{-3}molF{e}^{2+}\\ =4.97\times {10}^{-3}molF{e}^{2+}\end{array}$

Therefore, $4.97\times {10}^{-3}molF{e}^{2+}$reacted with $C{r}_2{O}_7^{2-}$generated from the Cr plating.

Numberof moles of Cr contained in the Cr plating

$\begin{array}{l}=4.97\times {10}^{-3}molF{e}^{2+}\times \frac{1molC{r}_2{O}_7^{2-}}{6molF{e}^{2+}}\times \frac{2molC{r}^{3+}}{molC{r}_2{O}_7^{2-}}\\ =1.66\times {10}^{-3}molC{r}^{3+}\\ =1.66\times {10}^{-3}molCr\end{array}$

Mass of Cr contained in the Cr plating

$\begin{array}{l}=1.66\times {10}^{-3}molCr\times \frac{52.00gCr}{molCr}\\ =8.63\times {10}^{-2}gCr\end{array}$

Volume of Cr plating

$\begin{array}{c}Volume=Mass\times Density\\ =8.63\times {10}^{-2}g\times \frac{1c{m}^3}{7.19g}\\ =1.20\times {10}^{-2}c{m}^3\end{array}$

Again, we can write

$\begin{array}{c}Volume=Area\times thickness\\ 1.20\times {10}^{-2}c{m}^3=40c{m}^2\times thickness\\ thickness=\frac{1.20\times {10}^{-2}c{m}^3}{40c{m}^2}\\ thickness=3.00\times {10}^{-4}cm\\ thickness=300\mu m\end{array}$