Problem 2

Cathodic protection is widely used to prevent metal corrosion by attaching a more active sacrificial metal to the structure. (a) In an experiment on protecting steel in seawater, a 25.0 g zinc block was attached to a steel apparatus. After some time, the block was reweighed at 28.0 g; assume that the only oxidation product is

\ce{Zn(OH)2}

adhering to the block (

M(\ce{Zn}) = 65.38

M(\ce{Zn(OH)2}) = 99.40

g mol

^{-1}

). Calculate the percentage of zinc that has oxidised. (b) Find the maximum service time (in hours) of this 25.0 g zinc block if the average protective current generated is 25 mA. (c) A steel ship hull with an immersed area of 1000 m

^2

requires an average protective current density of 2.5 mA m

^{-2}

. If zinc sacrificial anodes are used and 10 % of the zinc is lost to secondary processes, calculate the mass of zinc required per year (365 days).

Step 1 of 3: Percentage of oxidised zinc

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\Delta m = n(\ce{Zn})_{\text{ox}} \times 2 M(\ce{OH}) = 34.02\,n \Rightarrow n = \frac{3.0\ \text{g}}{34.02\ \text{g mol}^{-1}} = 0.0882\ \text{mol};\quad \%\,\ce{Zn} = \frac{0.0882 \times 65.38}{25.0} \times 100\,\% = 23.06\,\%

Analysis

Each mole of $\ce{Zn}$ converted to $\ce{Zn(OH)2}$ gains $2 M(\ce{OH}) = 34.015$ g mol $^{-1}$ of hydroxide mass. A 3.0 g increase corresponds to 0.0882 mol of zinc consumed, i.e. 5.766 g out of 25.0 g = 23.06 % (matches the official key: 23.06 %).