Chapter 13.10, Problem 55AAP

A galvanized (zinc-coaled) steel sheet is found to uniformly corrode at the rate of 12.5 × 10^-3 mm/year. What is the average current density associated with the corrosion of this material?

To determine

The average current density associated with the corrosion of zinc coated steel (galvanized steel).

Answer to Problem 55AAP

The average current density associated with the corrosion of zinc coated steel (galvanized steel) is $8.34\times {10}^{-7}{\text{A/cm}}^2$.

Explanation of Solution

Write the expression for corrosion rate.

  $\frac{w}{t}=\frac{IM}{nF}$                                                                                                        (I)

Here, the corrosion rate is $w/t$, the current flow is $I$, atomic mass of the metal is $M$, number of electrons per atoms produced or consumed in the process is $n$, and the Faraday’s constant is $F$, $F=96500\text{C/mol}\text{or}96500\text{A}\cdot \text{s/mol}$.

The current density is expressed as,

  $\begin{array}{l}i=\frac{I}{A}\\ I=iA\end{array}$

Substitute $iA$ for $I$ in Equation (I) and rearrange it to obtain $i$.

  $\begin{array}{l}\frac{w}{t}=\frac{\left(iA\right)M}{nF}\\ i=\left(\frac{w}{At}\right)\frac{nF}{M}\end{array}$                                                                                                 (II)

Write the formula to calculate the corrosion rate per area.

  $\frac{w}{At}=\rho \times \text{corrsion depth rate}$                                                                       (III)

Here, the corrosion mass is $w$, the area is $A$, the time taken is $t$, and the density of metal is $\rho$. In other words the corrosion rate per area is $w/At$.

Conclusion:

It is given that the corrosion depth rate is $12.5\times {10}^{-3}\text{mm/year}$.

Convert the unit $\text{mm/year}$ to $\text{cm/s}$.

  $\begin{array}{c}\text{corrosion depth rate}=12.5\times {10}^{-3}\frac{\text{mm}}{\text{year}}\times \frac{1\text{cm}}{10\text{mm}}\times \frac{1\text{year}}{365\text{days}}\times \frac{1\text{day}}{24\text{hr}}\times \frac{1\text{hr}}{3600\text{s}}\\ =3.9637\times {10}^{-11}\text{cm/s}\end{array}$

The density of the zinc is $7.13{\text{g/cm}}^3$.

Substitute $7.13{\text{g/cm}}^3$ for $\rho$ and $3.9637\times {10}^{-11}\text{cm/s}$ for corrosion depth rate in

Equation (III).

  $\begin{array}{c}\frac{w}{At}=7.13{\text{g/cm}}^3\times 3.9637\times {10}^{-11}\text{cm/s}\\ =2.8261\times {10}^{-11}{\text{g/cm}}^2\cdot \text{s}\end{array}$

Refer Table 13.1, “Standard electrode potentials at 25 °C”.

The anodic reaction of iron is as follows:

  ${\text{Zn}}^{2+}+2e^{-}\to \text{Zn}$

Here, the number of electrons produced is, $n=2$.

Refer Figure 2.3, “Periodic Table of Elements”

The atomic mass of zinc is, $M_{\text{Zn}}=65.38\text{g/mol}$.

Substitute $2.8261\times {10}^{-11}{\text{g/cm}}^2\cdot \text{s}$ for $w/At$, $2$ for $n$, and $96500\text{A}\cdot \text{s/mol}$ for $F$, and $65.38\text{g/ mol}$ for $M$ in Equation (II).

  $\begin{array}{c}i=\left(2.8261\times {10}^{-11}{\text{g/cm}}^2\cdot \text{s}\right)\frac{\left(2\right)\left(96500\text{A}\cdot \text{s/mol}\right)}{65.38\text{g/ mol}}\\ =8.3427\times {10}^{-7}{\text{A/cm}}^2\\ \simeq 8.34\times {10}^{-7}{\text{A/cm}}^2\end{array}$

Thus, the average current density associated with the corrosion of zinc coated steel (galvanized steel) is $8.34\times {10}^{-7}{\text{A/cm}}^2$.