Corrosion: Example Problems

Module One: Why Study Corrosion (skip title)

Example problem 1.1: Describe a corrosion problem encountered in your immediate surroundings and discuss its relative importance.

Answer: A picture is worth a thousand words. Look at some examples on the Corrosion Doctors web site.

Example problem 1.2: Explain what are the main differences between direct and indirect costs associated to corrosion damage. Provide some examples from your own experience.

Answer: Your example does not have to be sophisticated. The importance here is to be able to distinguish between direct and indirect costs. See Cost Study.

Module Two: Chemistry of Corrosion (skip title)

Example problem 2.1: Compare the energy required to produce one metric ton of magnesium from its oxide to the energy required to convert enough copper oxide to produce one ton of metallic copper.

Answer: The source of information to answer this question is on page describing why metals corrode.

Example problem 2.2: Discuss the energy values presented in the Table shown on the page describing why metals corrode in relation to the order in which metals and associated alloys appeared in the history of mankind.

Answer: You will very useful information in Wikipedia and on the Web. You can start your search here.

Example problem 2.3: A solution is made up to contain 0.01 M HCl. What is its pH?

Answer: The negative log of 10^-2 is 2.

Example problem 2.4: A solution is made up to contain 0.01 M NaOH. What is its pH?

Answer: If you have 10^-2 OH^- ions the water dissociation constant indicates that you also have 10^-2 x 10^-14 H⁺ ions or 10^-12. The pH is then 12.

Example problem 2.5: A solution contains a mixture of sodium bicarbonate (0.05 M) and sodium carbonate (0.2 M).What is its pH?

Answer: By considering Figure 2.7 you know that the carbonate ion is dominant to the right of pH 10.3 on the diagram. A good approximation of the pH can be calculated with equation 2.7 which indicates that the concentration of H⁺ ions equals 10^-10.3 x [bicarbonate] / [carbonate], or 10^-10.3 x 0.05 / 0.2, or 10^-10.9. The pH is therefore 10.9 which is indeed to the right of pH 10.3.

Module Three: Corrosion Electrochemistry (skip title)

Example problem 3.1: Why is a separator commonly used between the anodic and cathodic half cells of a Daniell cell?

Answer: To prevent dilution of the chemicals present differently on the cathode and anode sides.

Example problem 3.2: Elaborate on the effect the absence of a separator would have on the potential generated by a Daniell cell. Make reference to the Nernst equation described in Module 4 to support your arguments.

Answer: The dilution effect will indeed decreases the potential difference between the two electrodes and the voltage produced by this electrochemical power source.

Example problem 3.3: Write a short-hand description of the reactions involved in the corrosion of zinc or Figure 3.3 in the book.

Answer: (-) Zn / H⁺_(aq) /H_2(g) / Zn(+)

Example problem 3.4: 24 g of zinc metal are dissolved in a 1 M HCl solution. How many coulombs have been produced by the anodic process?

Answer: A direct use of Faraday equation (equation 3.13) in which F is 96,485 C/mole e^-, n is 2 mole e^-/ mole zinc, and n is 24 g / 65.38 g /mole zinc. Q is equal to 96,485 x 2 x 24 / 65.38 or 70,836 coulombs.

Example problem 3.5: A sheet of carbon steel one meter wide by three meter long has lost 40 g to corrosion over the past six months. Convert that mass loss to a penetration rate of the steel in mm units. What would be the total corrosion current associated with such a corrosion rate? (carbon steel density = 7.8 g/cm³)

Answer: This other example of Faraday relation can be solved simply by using to convert one unit of mass loss into a penetration rate. Since the surface area is 3 m² and the exposure duration is six months we have a corrosion rate of 40 g / (3 m² x 6 months x 30 days /month) or 0.074 g m^-2 day^-1. Converting into mm/y means x 0.0463 which gives 0.0034 mm/y.

In order to estimate the total corrosion current one should first convert the corrosion penetration rate into a current density unit. Converting into mA cm^-2 means x 0.00401 which gives 0.000297 mA cm^-2. To obtain the total current we need to multiply by the surface area which is 3 m² or 30 000 cm². The total corrosion current is therefore 9 mA.

  Example problem 3.6: Why are there always a minimum of two electrochemical reactions to explain even the simplest corrosion reaction?

Answer: Even the simplest corrosion reaction consists of one oxidation reaction (corrosion) and one cathodic reaction that consumes the electrons produced by the oxidation process.

Module Four: Corrosion Thermodynamics (skip title)

Example problem 4.1: What is the significance of a negative cell potential?

Answer: A negative cell potential means that the cell as described with a cathode and an anode cannot be a spontaneous generator of electrical power. Electrolysers typically have negative potentials when at rest and require the use of an external power supply to force the reaction.

Example problem 4.2: Is it possible to use the power coming out of a half cell? Explain your answer.

Answer: Not, the circuit is not complete and no current can flow.

Example problem 4.3: Rank the following ions in order of their thermodynamic ease of plating out of a solution: Cu²⁺, Co²⁺, Fe²⁺, Fe³⁺, Na⁺, Pb²⁺, Cu⁺

Answer: Cu⁺ (0.522 V vs. SHE), Cu²⁺ (0.340 V), Fe³⁺ (-0.036 V), Pb²⁺ (-0.126 V), Co²⁺ (-0.28 V), Fe²⁺ (-0.409 V), Na⁺ (-2.711 V)

Example problem 4.4: Rank the following elements in order of their thermodynamic ease of being oxidized in solution: Hg, Al, Fe, Au, Cr, Zn, Ag, Mg

Answer: Mg (-2.375 V vs. SHE), Al (-1.706 V), Zn (-0.763 V), Cr (-0.74 V), Fe (-0.409 V), Ag (0.7996 V), Hg (0.851 V), Au (1.68 V)

Example problem 4.5: Using standard potentials and molarity for ion concentrations calculate the open circuit potential of the following electrochemical reactions (balance the equations with water related chemical species when necessary, i.e. H⁺, OH^- and H₂O):

1. H₂O₂ + Ni → H₂O + Ni²⁺

2. H₂O + Mg²⁺ → H₂O₂ + Mg

3. Ni + PbO₂ → Pb²⁺ + Ni²⁺

4. Al³⁺ + OH^- → Al + O₂

Answers:

1. H₂O₂+ Ni → H₂O + Ni²⁺

H₂O₂ + 2H⁺ + 2e^- → 2H₂O    cathode: 1.776 V vs. SHE

Ni →  Ni²⁺ + 2e^-    anode: -0.23 V

cell total reaction: H₂O₂ + 2H⁺ + Ni → 2H₂O + Ni²⁺

cell potential: E_cathode - E_anode = 1.776 - (-0.23) = 2.01 V

2. H₂O + Mg²⁺→H₂O₂+ Mg

Mg²⁺ + 2e^- →  Mg   cathode: -2.375 V vs. SHE

2H₂O → H₂O₂ + 2H⁺ + 2e^-    anode: 1.776 V

cell total reaction: H₂O + Mg²⁺ → H₂O₂ + 2H⁺+ Mg

cell potential: E_cathode - E_anode =  -2.375 - 1.776 = -4.151 V

3. Ni + PbO₂ → Pb²⁺+ Ni²⁺

PbO₂ + 4H⁺ + 2e^- → Pb²⁺ + 2H₂O    cathode: 1.467 V vs. SHE

Ni →  Ni²⁺ + 2e^-    anode: -0.23 V

cell total reaction: PbO₂ + 4H⁺ + Ni → Pb²⁺ + 2H₂O + Ni²⁺

cell potential: E_cathode - E_anode =  1.467 - (-0.23) = 1.70 V

4. Al³⁺+ OH^- → Al + O₂

4 x (Al³⁺ + 3e^- →  Al)     cathode: -1.706 V vs. SHE

3 x (4OH^- →  O₂ + 2H₂O + 4e^-)   anode: 0.401 V

cell total reaction: 4Al³⁺ + 12OH^-  → 4Al + 3O₂ + 6H₂O

cell potential: E_cathode - E_anode =  -1.706 - 0.401 = -2.107 V

Example problem 4.6: What does a measured potential value of 0.8 V vs. SHEwould be if the potential had been measured with a saturated silver chloride electrode? ... with a saturated copper sulfate electrode?

Answer: See Table 4.7 and Figure 4.3. With a saturated silver chloride electrode: 0.8 - 0.199 = 0.601 V and with a saturated copper sulfate electrode: 0.8 - 0.318 = 0.482 V

Example problem 4.7: What is the principle of a Luggin capillary and what are the main functions of such a device?

Answer: See description associated with Figures 4.7 and 4.8. Some important functions of a cappillary Luggin are:

• to provide potential measurement points in close proximity to electrochemically active metallic surface while influencing only slightly electrical field lines
•  to prevent or greatly reduce ionic leakage from a reference half cell solution
• to prevent or greatly reduce ionic contamination of the reference cell solution by ions present in a test cell

Example problem 4.8: Some fuel cells operate by oxidizing hydrogen gas on an anode while reducing oxygen from ambient air in contact with a cathode. What would be the maximum voltage produced by such a cell running on pure hydrogen and air in an acidic environment? Would it be different if pure oxygen was used instead of ambient air?

Answer: Pure hydrogen and pure oxygen means that these gases are at 1 atm pressure or the standard conditions. A fuel cell working with such gases would produce a maximum potential of 1.23 V at any pH. This 1.23 V is in fact the difference between lines aand bin E-pH diagrams. When air is used instead of pure oxygen, its partial pressure is approximately 0.2 atm or 20% of the total air molecules. The correction for this factor can be estimated using Nernst equation for the reduction of oxygen (equation 4.40). The change in potential due to this dilution is log₁₀(p_oxygen) x 0.059/4  or -0.0103 V. The maximum voltage in this case would therefore be 1.22 V.

Module Five: Corrosion Kinetics (skip title)  

Example problem 5.1: What is the relation between the overpotential and standard potential of an electrochemical reaction?

Answer: The overpotential is a complex function that essentially describes the departure from the rest potential due to the passage of current through the electrode interface. The standard potential is this rest potential in standard conditions of concentration, temperature, and pressure.

Example problem 5.2: What is the relation between polarization and overpotential?

Answer: The polarisation of a metallic sample is made by changing its potential or passing current through it and the response will include the complex overpotential function. 

Example problem 5.3: Propose an alloy modification that would possibly disfavor the production of hydrogen at an electrode. ... and one that would favor it.

Answer: Some elements in Table 5.1 obviously favor the production of hydrogen (Ni, Ag, Cu, Cd, Fe, Au, Mo, W, Co, Ta, Pd, Rh, and Pt) while others clearly disfavor this reaction (Pb, Hg, Zn, Sn, Al, and Be). Using one of these elements as an alloying addition to a base metal could possibly modify the response towards the production of hydrogen at an electrode.

Example problem 5.4: Describe a simple method to verify if an electrochemical reaction is limited by a concentration polarization effect.

Answer: The concentration polarization behavior may be greatly affected by a simple agitation of the environment. The agitation would provide a faster rate of transfer of the reactive species towards the electrode that is under limiting current conditions.

Example problem 5.5: How many grams of dissolved oxygen are present in one liter of aerated water at 5ºC? ... at at 30ºC?

Answer: From Table 5.2 one can read that at at 5ºC water can contain 12.72 ppm or 12.72 mg per liter of dissolved oxygen, Similarly it can contain 7.57 ppm or 7.57 mg per liter at at 30ºC.

Example problem 5.6: Describe a simple method to reduce the quantity of dissolved oxygen in a water container or vessel.

Answer: Boiling water has been used in a wide range of industrial applications to greatly reduce the danger of corrosion due to dissolved oxygen.

Example problem 5.7: Explain the main differences between the ohmic drop in an aqueous environment and the ohmic drop in an electrical conductor.

Answer: The ohmic drop in an electrical conductor can be measured with either an AC signal or a DC signal and the results would be identical. However, the possibility to force electrochemical reactions at an electrode or the possibility to accumulate charges at the interface (capacitive effects) when using a DC signal mean that the response of an electrode in an aqueous environment is much more complicated than in a metallic conductor.

Module Six: Recognizing Corrosion in its Forms (skip title)

Example problem 6.1: Corrosion problems can rarely be attributed to single forms of corrosion. Provide some examples to illustrate that statement.

Answer: Provide enough convincing details about the combined mechanisms to illustrate your points. A picture or two may help your case.

Example problem 6.2: The seriousness of a corrosion situation is often directly related to the hidden nature of the specific corrosion defect that is progressing. Provide some examples in support of that statement.

Answer: There are many corrosion related accidents that fit these conditions. You can find some of these on the Corrosion Doctors Web site if you look carefully.

Example problem 6.3: Where would general loss (uniform corrosion) be a concern. Provide examples and explanation.

Answer: Again, a creative search of the open literature or the World Wide Web may provide good illustrations of what is hinted at in this question.

Example problem 6.4: Why would pitting corrosion be much more prone to provoke a catastrophic failure than uniform corrosion generally does?

Answer: Pitting corrosion develops the same vicious chemistry that is often ascribed to crevice corrosion. Once corrosion pits are initiated, they can additionally camouflaged themselves in such a way that only the most sophisticated inspection methods may be able to detect them. If a component is stressed for one reason or another, sharp pits have often led to the generation of cracks that a serious turn to the severity of such corrosion problems. 

Example problem 6.5: Explain in your own words the role played by dissolved oxygen in the general mechanism proposed to explain the various steps in crevice corrosion.

Answer: Make sure that all the steps are covered in your explanations.

Example problem 6.6: Why would some metals, such as titanium for example, which are relatively easy to oxidize can still be found at the top of a galvanic series in seawater ?

Answer: Metals such as titanium and its alloys are protected by their tenacious oxides and other products of oxidation. The excellent coverage provided the initial corrosion of the metallic substrate basically serves as a protective coating with self healing properties. Instead of being very active as predicted by the laws of thermodynamics metals with such behavior are called passive.

Example problem 6.7: Discuss the various types of stresses that can lead to SCC and highlight their importance with practical examples.

Answer: Please provide some good descriptions and documented examples from case histories.

Example problem 6.8: Provide a few examples of events that may lead to the initiation of SCC.

Answer: Search the literature and the World Wide Web for accidents where SCC was suspected or found to have played a role during subsequent failure investigations.

Module Seven: Corrosion Factors and Cells(skip title)

Example problem 7.1: Propose some arguments to explain the high variance, visible in the previous Figure, between expert opinions on the factors causing pitting corrosion.

Answer: The importance of pitting corrosion and the factors causing such problems vary greatly between systems, industries, and environments. The variance observed in expert opinions is a true reflection of the imprecision with the definition of what pitting corrosion really is and can do.

Example problem 7.2: What is a corrosion cell and what are its main components?

Answer: There are basically three components in a corrosion cell: one anode or an anodic site, one cathode or a cathodic site, and the presence of an electrolyte (water plus ions).

Example problem 7.3: Can you imagine some corrosion cells that would be cancelling each other?

Answer: That is surely a possibility. Please use your imagination and look carefully at some examples presented in the book.

Example problem 7.4: Describe the effects of corrosion stress cells in terms of energy release.

Answer: All mechanical stresses can be quantified and often measured in energy units. How do you think these stresses may be released?

Example problem 7.5: Provide some examples where microbes have been found to be the root cause of corrosion problems.

Answer: You can probably find tons of these examples by doing a careful search of the World Wide Web. However, you should be critical when reporting your findings since there is still a great deal of confusion between experts in these matters.

Example problem 7.6: Can crevice corrosion degenerate in other forms of corrosion? Provide some examples.

Answer: Absolutely and it often does. You will find a few detailed examples in the textbook.

Example problem 7.7: Why is it important to consider the electrical conductivity between various components when suspecting the presence of a galvanic corrosion problem?

Answer: Simply because the electrical continuity between dissimilar metals is an essential condition for having galvanic couples becoming a galvanic corrosion cell in the first place.

Module Eight: Corrosion by Water (skip title)

Example problem 8.1: Corrosion and the toxicity of potable water. Find and discuss various cases where corrosion processes have freed some toxic compounds in potable water.

Answer: If you look back in history you may find some interesting stories with dire consequences on the introduction of some toxic elements in potable water due to corrosion of the containing conduits or vessels. There are also some good examples of these problems in our societies today.

Example problem 8.2: Corrosion of waterworks is a major burden in many cities. Provide some examples from a search of the Internet.

Answer: Good luck!

Example problem 8.3: Summarize the main elements that make natural fresh waters more or less corrosive.

Answer: The answer to this question is pretty much textually in the textbook. Please use your own words.

Example problem 8.4: Propose an explanation for the maximum in corrosion rate reported in the corrosion rate vs % sodium chloride Figure.

Answer: The corrosive nature of chloride ions is due in great part to their high mobility since they are not bound easily in specific molecules. This makes the recipe for very soluble salts. Because of this, chloride ions tend to dissolved some of the oxy-hydroxide corrosion products on a metallic surface and accelerate further corrosion by exposing the metallic substrate. This effect increases as the concentration of chloride ions increases and reaches a maximum at around 3.5% salt sodium chloride, at which point the additional chloride ions becomes a hindrance to the chlorides mobility (a little bit like the moving in a crowd effect, the denser the crowd the less free you are to move around).

Example problem 8.5: What is the physical significance of a water that has a SL value smaller than 1.0? ... and one that has a SL value larger than 1.0?

Answer: A saturation level (SL) of one indicates that a given scaling species is at its precipitation equilibrium. Less than one means is has not reached this equilibrium and should therefore not precipitate while the contrary is true if it is higher than one.

Module Nine: Atmospheric corrosion (skip title)

Example problem 9.1: Are industrial sites near where you live more corrosive than adjacent locations? Provide some examples.

Answer: Industrial sites that produce inorganic pollutants tend to negatively alter the corrosivity of their surrounding environment. One questionable solution adopted by many industries is to increase the height of the discharging chimneys in order to push these pollutants higher in the atmosphere.

Example problem 9.2: Indoor corrosion has caused many unpleasant surprises. Find some examples close to your immediate surrounding.

Answer: Due to their relative high relative humidity, basements are typically a rich source of corrosion examples.

Example problem 9.3: The depression of the critical humidity levels on a metallic surface may seriously limit the use of some materials in various applications. Propose some design solutions to limit or avoid altogether such problems.

Answer: We are curious to see your creative answers to this question.

Example problem 9.4: Calculate the dew point temperature for a RH of 45% when the ambient temperature is 22^oC? ... when it is 26^oC? You may have to consult the Internet or the textbook to solve this problem.

Answer: 9.5^oC and 13.1^oC. See equation 9.3.

Example problem 9.5: The ISO 9223 standard indicates that there should be no corrosion at temperature below 0^oC. Independent researchers have however proposed to lower the minimum temperature stated in the standard to lower values in order to account for the actual corrosion observed in Nordic climates. Provide an explanation for the observed corrosion at temperature below the freezing point.

Answer: This is a relatively deep topic that could be the subject of a graduate thesis. For a simple example consider the serious corrosion impact of deicing salts.

Example problem 9.6: Find in your neighbourhood some structural elements made of copper and copper alloys and report on their state and condition.

Answer: Do not forget your camera!

Example problem 9.7: Find in your neighbourhood some structural elements made of galvanized steel and report on their state and condition.

Answer: Again, do not forget to take many pictures.

Example problem 9.8: Use one of the corrosivity maps to specify the thickness required of a galvanized coating to achieve a useful life of fifty years in the various environments described on that map.

Answer: This is a typical problem architects and manufacturers of outdoor equipment have to face on a daily basis.

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