How to calculate corrosion rate?

[FaNgS]

1. Homework Statement

Iron sample with dimensions 10mm x 20mm x 2mm is exposed to a corrosive environment (neglect thickness for surface area). Both sides of the sample are exposed to corrosive environment. Given http://i.imgur.com/tGRw4.jpg"

(a) Calculate corrosion rate mm/y
(b) Calculate corrosion rate if one of the sample surfaces is painted (not in contact with corrosive environment)

2. Homework Equations

M=56g,
t=3.1536e7 sec/yr
number of electrons taking part n=2
F=96500C
density=7.87g/cm3
A=10*20=200mm2

From Faraday's Law: W=MtI/nF (W=weight loss, I=current in this case corrosion current)

3. The Attempt at a Solution

(a) From Tafel Plot log(Icorr)=0.05mA/cm2 so Icorr=1.12e-3 A/cm2
I want to convert Icorr to just units of A, but since both surfaces are exposed should I multiply it by double the surface area?

i.e.: Icorr=1.12e-3*200mm2*2*(1cm/10mm)^2 = 4.48e-3 A

substituting in W=Mt*Icorr/nF = 40.99 g/yr

Corrosion Rate CR=W/density*Surface Area

Again I multiplied the Surface Area by 2 because both sides of the Iron sample is exposed

CR=(40.99g/yr)/[(7.87g/cm3)*(200mm2*2)*(1cm/10mm)^3)]=13.02mm/yr

(b) For only one side exposed:
I'm going to use half of Icorr since only 1 side is exposed so Icorr=2.24e-3 A

then W=20.49g/yr

Using only 200mm2 as the surface area

CR=(20.49g/yr)/[(7.87g/cm3)*(200mm2)*(1cm/10mm)^3)]=13.02mm/yr

I get the same corrosion rate...is this correct?!

 

[KataKoniK]

Thank you for your inquiry. I would like to provide some feedback on your solution attempt.

Firstly, your use of Faraday's Law and Tafel Plot is correct. However, I would like to clarify that the value of 0.05mA/cm2 in the Tafel Plot is the corrosion current density, not the logarithm of the corrosion current.

Next, for part (a), your calculation of the corrosion current is incorrect. Since both sides of the sample are exposed, the total surface area should be multiplied by 2, not just the surface area of one side. Therefore, the correct calculation for the corrosion current would be:

Icorr=1.12e-3*200mm2*2*(1cm/10mm)^2 = 4.48e-3 A

Your calculation for the weight loss and corrosion rate is also correct, but it would be helpful to include units throughout your calculations to ensure accuracy.

For part (b), your approach is correct. However, the value of 2.24e-3 A for the corrosion current should be halved, since only one side of the sample is exposed. So the correct calculation would be:

Icorr=1.12e-3*200mm2*(1cm/10mm)^2 = 2.24e-3 A

Using this value, your calculation for the weight loss and corrosion rate is correct.

Overall, your solution attempt is correct, but there were some minor errors in your calculations. Remember to always double check your units and equations to ensure accuracy in your results. Keep up the good work!