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Engineering Problem Solving ¶

Some problems are so complex that you have to be highly intelligent and well-informed just to be undecided about them. —Laurence J. Peter

Steps in solving ‘real world’ engineering problems ¶

The following are the steps as enumerated in your textbook:

Collaboratively define the problem

List possible solutions

Evaluate and rank the possible solutions

Develop a detailed plan for the most attractive solution(s)

Re-evaluate the plan to check desirability

Implement the plan

Check the results

A critical part of the analysis process is the ‘last’ step: checking and verifying the results.

Depending on the circumstances, errors in an analysis, procedure, or implementation can have significant, adverse consequences (NASA Mars orbiter crash, Bhopal chemical leak tragedy, Hubble telescope vision issue, Y2K fiasco, BP oil rig blowout, …).

In a practical sense, these checks must be part of a comprehensive risk management strategy.

My experience with problem solving in industry was pretty close to this, though encumbered by numerous business practices (e.g., ‘go/no-go’ tollgates, complex approval processes and procedures).

In addition, solving problems in the ‘real world’ requires a multidisciplinary effort, involving people with various expertise: engineering, manufacturing, supply chain, legal, marketing, product service and warranty, …

Exercise: Problem solving

Step 3 above refers to ranking of alternatives.

Think of an existing product of interest.

What do you think was ranked highest when the product was developed?

Consider what would have happened if a different ranking was used. What would have changed about the product?

Brainstorm ideas with the students around you.

Defining problems collaboratively ¶

Especially in light of global engineering , we need to consider different perspectives as we define our problem. Let’s break the procedure down into steps:

Identify each perspective that is involved in the decision you face. Remember that problems often mean different things in different perspectives. Relevant differences might include national expectations, organizational positions, disciplines, career trajectories, etc. Consider using the mnemonic device “Location, Knowledge, and Desire.”

Location : Who is defining the problem? Where are they located or how are they positioned? How do they get in their positions? Do you know anything about the history of their positions, and what led to the particular configuration of positions you have today on the job? Where are the key boundaries among different types of groups, and where are the alliances?

Knowledge : What forms of knowledge do the representatives of each perspective have? How do they understand the problem at hand? What are their assumptions? From what sources did they gain their knowledge? How did their knowledge evolve?

Desire : What do the proponents of each perspective want? What are their objectives? How do these desires develop? Where are they trying to go? Learn what you can about the history of the issue at hand. Who might have gained or lost ground in previous encounters? How does each perspective view itself at present in relation to those it envisions as relevant to its future?

As formal problem definitions emerge, ask “Whose definition is this?” Remember that “defining the problem clearly” may very well assert one perspective at the expense of others. Once we think about problem solving in relation to people, we can begin to see that the very act of drawing a boundary around a problem has non-technical, or political dimensions, depending on who controls the definition, because someone gains a little power and someone loses a little power.

Map what alternative problem definitions mean to different participants. More than likely you will best understand problem definitions that fit your perspective. But ask “Does it fit other perspectives as well?” Look at those who hold Perspective A. Does your definition fit their location, their knowledge, and their desires? Now turn to those who hold Perspective B. Does your definition fit their location, knowledge, and desires? Completing this step is difficult because it requires stepping outside of one’s own perspective and attempting to understand the problem in terms of different perspectives.

To the extent you encounter disagreement or conclude that the achievement of it is insufficient, begin asking yourself the following: How might I adapt my problem definition to take account of other perspectives out there? Is there some way of accommodating myself to other perspectives rather than just demanding that the others simply recognize the inherent value and rationality of mine? Is there room for compromise among contrasting perspectives?

How ‘good’ a solution do you need ¶

There is also an important aspect of real-world problem solving that is rarely articulated and that is the idea that the ‘quality’ of the analysis and the resources expended should be dependent on the context.

This is difficult to assess without some experience in the particular environment.

How ‘Good’ a Solution Do You Need?

Some rough examples:

10 second answer (answering a question at a meeting in front of your manager or vice president)

10 minute answer (answering a quick question from a colleague)

10 hour answer (answering a request from an important customer)

10 day answer (assembling information as part of a trouble-shooting team)

10 month answer (putting together a comprehensive portfolio of information as part of the design for a new $200,000,000 chemical plant)

Steps in solving well-defined engineering process problems, including textbook problems ¶

Essential steps:

Carefully read the problem statement (perhaps repeatedly) until you understand exactly the scenario and what is being asked.

Translate elements of the word problem to symbols. Also, look for key words that may convey additional information, e.g., ‘steady state’, ‘constant density’, ‘isothermal’. Make note of this additional information on your work page.

Draw a diagram. This can generally be a simple block diagram showing all the input, output, and connecting streams.

Write all known quantities (flow rates, densities, etc.) from step 2 in the appropriate locations on, or near, the diagram. If symbols are used to designate known quantities, include those symbols.

Identify and assign symbols to all unknown quantities and write them in the appropriate locations on, or near, the diagram.

Construct the relevant equation(s). These could be material balances, energy balances, rate equations, etc.

Write down all equations in their general forms. Don’t simplify anything yet.

Discard terms that are equal to zero (or are assumed negligible) for your specific problem and write the simplified equations.

Replace remaining terms with more convenient forms (because of the given information or selected symbols).

Construct equations to express other known relationships between variables, e.g., relationships between stoichiometric coefficients, the sum of species mass fractions must be one.

Whenever possible, solve the equations for the unknown(s) algebraically .

Convert the units of your variables as needed to have a consistent set across your equations.

Substitute these values into the equation(s) from step 7 to get numerical results.

Check your answer.

Does it make sense?

Are the units of the answer correct?

Is the answer consistent with other information you have?

Exercise: Checking results

How do you know your answer is right and that your analysis is correct?

This may be relatively easy for a homework problem, but what about your analysis for an ill-defined ‘real-world’ problem?

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Problem Solving in the Chemical Industry

LCGC North America

Identifying unknown compounds continues to challenge analysts.

Mass spectrometry (MS) has been a cornerstone technology of the chemical industries including petroleum research and related commercial product manufacturing in polymers. The American Society for Mass Spectrometry (ASMS) will celebrate its 60th anniversary next year. Although christened under its current name in 1969, it began as "ASTM Committee E-14" in 1952. The work of John Fenn and others that brought us electrospray ionization (ESI) and heralded the modern era where biological use of MS predominates was not seen until the 1980s. Before the 1980s gas-phase interests predominated and techniques were commonly performed in vacuum as opposed to atmosphere today and often as a set experiment using a solids probe rather than a flowing or chromatographic serial sample introduction.

Where is the interest among practitioners today? What generates the most problem solving interest today in the chemical industry? What tools do they employ with good success and which ones do they look forward to — or wish they had? I had an opportunity to speak with Colin Moore, Fellow and Technology Leader in Mass Spectrometry at Chemtura Corporation (Middlebury, Connecticut) about the types of analytical problems his group has been asked to solve recently and what they have learned in the process of solving them; this discussion evolved into a short tutorial on chemical industry practice.

A UK native, Moore worked for Shell Research for seven years doing analytical work on agrochemicals and simultaneously became a graduate of the Royal Society of Chemistry. Postgraduate studies at the University of Southampton were followed by three years at Warwick University and a Ph.D. with Professor Keith Jennings. He joined Uniroyal (now Chemtura Corporation) in 1994 as a member of the MS group, becoming a manager in 1997 and a Research Fellow in 2002. He has 20 publications in peer-reviewed journals and 24 posters and presentations at conferences to his credit.

A Simplified Overview

Sample analysis in Moore's laboratory generally falls into one of the following areas:

  • Confirmation of the chemical structure of the main components and identification of impurities to help synthetic chemists improve the synthesis.
  • Identification of minor components in a product that shouldn't be there (for example, color bodies).
  • Identification of additives in a polymer or oil (for example, antioxidants in engine oil).

Figure 1: GC–MS response for an oil sample (upper is a methanolic extract; lower is the oil sample dissolved in methylene chloride). (Courtesy of Colin Moore, Chemtura Corporation.)

For highly pure samples, analysis by nuclear magnetic resonance (NMR) spectroscopy is probably the best way to obtain detailed structural information and therefore most of the samples that mass spectrometrists are asked to analyze are mixtures. The analyst's first decision therefore is to determine which separation technique will be used: gas chromatography (GC), liquid chromatography (LC), gel permeation chromatography (GPC), solid-phase microextraction (SPME) or some type of liquid–liquid extraction. For example, if an engine oil sample in methylene chloride is shaken with methanol, then the phenolic and aminic antioxidants will be concentrated in the methanol. GC–MS analysis of the methanol extract makes it easy to identify the major antioxidants in the oils (Figures 1 and 2).

Figure 2: EI spectrum of peak at 13.82 min in the methanol extract shown in Figure 1. (Courtesy of Colin Moore, Chemtura Corporation.)

An interesting aspect of identifying unknowns, which Moore says he has not seen in the literature, stems from making use of both electron ionization (EI) and ESI spectra of an unknown since the fragmentation patterns can be "complementary" (see the EI and ESI spectra in Figure 3).

Figure 3: The complementary diagnostic nature of EI and ESI spectra of the same compound. (Courtesy of Colin Moore, Chemtura Corporation.)

In the EI spectrum the first major loss is a C 10 alkyl radical whereas in the ESI spectrum it is loss of the C 10 alcohol. For those interested in a quick overview on mass spectra a recent column was devoted to that topic (1) that also highlights James Little's insights from his experiences solving problems at Eastman Chemical in Tennessee.

A significant difference in analytical practice between the pharmaceutical and specialty chemical industries is the level of dependence of the latter on GC–MS. Today the pharmaceutical world favors LC–MS. For those interested in the aspects of how LC–MS became what we think of as open access in the pharmaceutical world, I chronicled the insights of a few practitioners on how LC–MS transitioned from a relatively obscure novelty to become the beneficial tool we know today (2). A recent article also examined the ongoing need for development in MS ionization and related technologies to support work in areas where "electrospray just isn't enough" to do the job (3). According to a survey among practitioners in various disciplines, those identified with the chemical materials industry arguably rely on GC three times more than LC. A quick look around Moore's laboratory supports the observation.

One issue that all laboratories need to address is productivity. Two of Moore's GC–MS systems, an Agilent 5970 (Agilent Technologies, Palo Alto, California) and a Waters GCT (Waters Corporation, Milford, Massachusetts), are fitted with two GC columns in the injection port using a two-hole ferrule. One column is connected to the mass spectrometer and the other to an ancillary detection system such as flame ionization detection (FID). As Moore explained, "As soon as you tell somebody what an unknown peak is in a GC–MS trace, the next question is usually, How much [of it] is there? Collecting the FID data in parallel with the GC–MS data allows us to give our customers semiquantitative data as well as MS identification in a single experiment." Such a practice is analogous to LC–MS data acquisition with an in-line UV detector.

Moore's future interests include installing a nitrogen–phosphorus detection (NPD) system as well as FID on one GC system because many of the antioxidants that Chemtura makes are amines. Amines as a class are often easily ionized by ESI. Yet in some cases the analytes are just not amenable to the technique. Insufficient polarity, the inability to capture a proton, or perhaps excessive volatility that precludes transport and separation by condensed phase means in an LC could all contribute to ESI failure. Certainly due to its popularity great strides have occurred in recent years to increase the sensitivity, resolution, and overall utility of LC–ESI-MS instruments. Today techniques such as atmospheric pressure gas chromatography (APGC) and atmospheric solids analysis probes (ASAP), analogous to the vacuum solids probes used for years in GC–MS, are viable without sacrificing performance, which was not the case years ago (3,4).

Data Handling

The ability of software-driven applications to amass increasingly refined data streams has unleashed a data handling problem that crosses into all practices and disciplines. So much so that handling complex data has become a recurring workshop topic at the Conference on Small Molecule Science (CoSMoS) in recent years ( www.cosmoscience.org ).

Moore's laboratory uses MassLynx mass spectrometry software (Waters Corporation) to process its MS data. For GC–MS data, workers export the files using the NetCDF converter option in ChemStation software in the three Agilent systems (Agilent Technologies) and then convert the files to the MassLynx format using the Waters DBridge program. NetCDF does not produce a file for the FID system that can be read by MassLynx, and therefore processing the FID trace has to be done using ChemStation. On the GCT system the FID trace is recorded as analog data by MassLynx that can be processed with the MS data. The retention time differences between the two traces can be time-aligned in the chromatogram plots (the peaks come out earlier in the MS data because the vacuum system of the MS increases the helium flow rate in the column connected to the mass spectrometer).

Understanding the Problem and Designing the Experiment

As an analytical problem, identifying color bodies in polymers is neither trivial nor obvious. In a 2005 paper (5), Moore shows there is often more than one way to solve a problem using mass spectrometry. Analysis by LC–MS with an inline photodiode-array (PDA) detector is probably the best way to identify a new color body. Techniques like time-of-flight secondary ionization mass spectrometry (TOF SIMS) can be used to quickly confirm that the color body on fresh samples is the same as on previously determined samples.

Moore's 2005 work detailed the analysis of a yellow discoloration on the surface of a compounded ethylene–propylene–diene monomer (EPDM) rubber sample. Surface discoloration of a polymer can result from various phenomena, including contamination, component migration, oxidation, and other chemical reactions. Components rising to the surface can give rise to "bloom," a process in which one component of a polymer mixture (usually not a polymer) undergoes phase separation and migration to an external surface of the mixture, according to the IUPAC definition. Protective waxes can be beneficial, but thiazoles (mercaptobenzothiazole) leading to discoloration of the product are undesirable. For example, oxidation of antioxidants can form color bodies (that is, phenolic antioxidants can form quinone methides) (6). The first step in identifying a color body is to separate it from the polymer often by washing the surface with a suitable solvent.

The washings result in a complex mixture of the color bodies, additives, and other surface contaminants. Identification of the colored components requires further separation of the mixture, analysis of the separated components, and the ability to ascertain which of the components are colored. The combination of LC–MS-MS with an inline PDA detector is able to do the complete analysis in a single experiment. Moore recalls that when he joined Uniroyal Chemical in 1994, identifying a color body often involved pooling fractions from multiple LC runs to acquire enough material for the particle beam LC–MS system (an early 1990s rather short-lived technique that, although not very sensitive, produced EI spectra from typical LC-amenable analytes not volatile enough for GC–MS). The much greater sensitivity of ESI sources and TOF mass spectrometers has made the process much quicker and easier, illustrating a central point in mixture analysis: the importance of matching the separation technique with the sensitivity of the final analysis technique.

Matching aspects of the analytical technique is not as simple as it sounds. When light reflects off a colored substance, the reflected light has the complementary color to the wavelength or wavelengths absorbed. Yellow light covers the wavelength range 570–585 nm, but the complementary color to yellow is indigo over the range 420–430 nm. So when processing the LC–MS data, Moore looked for a component with strong absorption over that range of wavelengths. He found one component that yielded the UV and LC–MS spectra shown in Figure 4. Note that the color body is the neutral Cu(II) dibutyl dithiocarbamate, but for it to be detected by the LC–MS system it must be oxidized in the electrospray process to the positively charged Cu(III) compound. A quick review of spectral color properties can be found at www2.chemistry.msu.edu/faculty/reusch/VirtTxtJml/Spectrpy/UV-Vis/spectrum.htm .

Figure 4: Mass spectrum of the color body (inset) and its UV spectrum. (Courtesy of Colin Moore, Chemtura Corporation.)

Color bodies are often polar molecules, which means that they are easy to ionize in an ESI source. For some time now, following improvements in the instrument capabilities, accurate mass MS has been recognized as an efficient means of enhancing separation of closely related chemical species. As Moore points out, when "the electrospray spectrum contains few (if any) fragment ions identifying unknowns, [that] requires that either an LC–MS-MS spectrum is acquired and/or exact mass measurements [7] are performed to get the elemental formula of the pseudo-molecular ion." An inline UV detector is sometimes an overlooked adjunct as well in LC–MS. Here the color of the offending samples of course indicates distinct chromophoric benefits. Components separated by the high performance liquid chromatography (HPLC) column absorb at the appropriate wavelength to give the observed discoloration with the added advantage of well-characterized algorithms employed by PDA detectors to distinguish differences in homologous components on the samples that the unaided eye cannot.

Moore noted another frequently overlooked element in the analytical chemist's trade that bears mentioning: Structure elucidation is made much easier if the analyst has a thorough knowledge of the sample chemistry and its history.

He also points out that "imaging mass spectrometry is a powerful technique for mapping the concentration of a compound on the surface of a matrix." The technique applies in many fields, including the analysis of inorganic materials, polymers, and biological materials. An early publication discusses TOF-SIMS analysis in which a TOF system measures secondary ions produced by bombarding a surface with high-energy particles (8). TOF-SIMS has been used to detect light stabilizers (9) and antioxidants (10) on the surface of a polymer as well as to characterize the bulk polymer (11).

In the few years since Moore published his work, a number of techniques operating by various mechanisms on or near the surface of a material (as opposed to techniques requiring analytes of interest be in solution — desorption electrospray ionization [DESI], direct analysis in real time [DART], ASAP, and a few others) have been examined in some detail in this column (4,12,13).

DESI can be used in combination with chemical reactions to improve the selectivity and sensitivity of the analysis. Moore's studies with Keith Jennings and attending presentations by Graham Cooks and John Beynon that emphasized the utility of chemical reactions in MS encouraged him to attempt using novel chemical ionization (CI) reagent gases to help solve problems. "Many antioxidants are alkylated aromatic amines and therefore a paper by Buchanan [14] was of great interest," he says. As shown by the spectra in Figure 5, the technique not only gives the number of aminic protons in the molecular ion, but it also helps identify fragment ions. The m / z 106 ion in the EI spectrum becomes m / z 108 in the CI data because of the NH 2 group.

Figure 5: Deuterated (ND3) CI and EI spectrum of 4,4'-methylenedianiline. (Courtesy of Colin Moore, Chemtura Corporation.)

Moore has also updated a method first reported by Morgan and colleagues (15) for analyzing zinc dialkyldithiophosphate (ZDDP) in engine oils. Engine oils are complex mixtures of base oils and performance enhancing multifunctional additives, like ZDDP. They are excellent antiwear agents and effective oxidation and corrosion inhibitors (Figure 6).

Figure 6: Potential alkyl group positions. (Courtesy of Colin Moore, Chemtura Corporation.)

The original work used negative ion CI to produce chloride ion adducts of the oil without any prior separation. Moore has used an atmospheric pressure chemical ionization (APCI) source and a mobile phase containing methylene chloride to give similar results.

Note that the mass spectrum in Figure 7 yields two complementary pieces of information about the ZDDP sample and gives the molecular weight of any phenolic antioxidants in the oil. The phenolic antioxidant present in the oil is evident by the response at m / z 389 (M–H ion) and at m / z 425 (M+Cl ion).

Figure 7: Chloride ion APCI spectrum of an engine oil sample dissolved in methylene chloride. (Courtesy of Colin Moore, Chemtura Corporation.)

The chloride adduct pseudomolecular ion [ZnL2Cl] – permits calculating the total number of carbon atoms in the four alkyl groups (R 1 + R 2 + R 3 + R 4 ). The ligand ions, L – , tell us whether the ZDDP was prepared by blending individual ZDDPs or was produced using a mixture of alcohols. Table I illustrates how we can deduce that a mixture of C 4 and C 6 alcohols were used to prepare the ZDDP.

Table I: Understanding the comparative diagnostic value of the ZDDP spectrum*

Though effective for determining the carbon chain length of the R groups, the chloride adduction technique does not show whether the chains are linear or branched. However, collision-induced dissociation (CID)–ion mobility spectrometry (IMS)–CID data may hold the key to solve that puzzle (16).

If the chromatographic conditions are not ideal for interfacing with MS or if other analytical techniques are going to be used to assist in the identification then LC fraction collection may be the best methodology. Polyalkylmethacrylates (PAMAs) are used as viscosity modifiers in oils (Figure 8)

Figure 8: Generic structure for PAMAs. (Courtesy of Colin Moore, Chemtura Corporation.). Moore has used fraction collection from a GPC system (Figure 9),

Figure 9: GPC trace for oil sample. 99.5% of the sample yields an Mp of 564 and 0.5% having an Mp of 8630 (Mp, molecular weight). (Courtesy of Colin Moore and John Mannello, Chemtura Corporation.) then pyrolysis GC–MS (Figure 10) and IR analysis to identify PAMAs. If R 1 and R 2 are likely to be either H or methyl and R 3 is one of a mixture of alkanes, pyrolysis of this type of polymer gives two series of fragment ions: alkenes and alkyl methacrylates. Thus if R 3 is C 12 then one gets dodec-1-ene and dodecyl methacrylate (Figure 11).

Figure 10: Pyrolysis GC–MS at 550 °C of a PAMA standard (top) and the high mass component from the oil. (Courtesy of Colin Moore, Chemtura Corporation.)

Future Developments

Moore visited Graham Cooks at Purdue to try using a DESI source to detect the color body (17). Simply spraying the yellow polymer with acetonitrile indeed gave a small signal for the Cu dibutyl dithiocarbamate. Nevertheless, the signal was enhanced when the oxidizing agent I 2 was added to the DESI spray solvent.

Figure 11: Acquired EI spectrum(top) and best library match for the peak at 11.79 min found in the oil extract (Figure 10). (Courtesy of Colin Moore, Chemtura Corporation.)

An extension of the thermal investigations coming back into favor may in the not-too-distant future provide yet another chapter for these studies by combining thermal MS capabilities with the surface information derived by atomic force microscopy (AFM) (Figure 12).

Figure 12: Nanoscale physical and chemical imaging of plant growth regulators using proximal probe thermal desorption MS. (Courtesy of Olga Ovchinnikova and Gary Van Berkel, Organic and Biological Mass Spectrometry Group, Chemical Sciences Division, Oak Ridge National Laboratory.)

AFM uses a sharp-tipped probe, often only 2 µm long and less than 100 å in diameter, located on the free end of a cantilever, which is brought close to a sample surface. Forces between the tip and the sample surface cause the cantilever to deflect. The deflection of the tip is measured as it is scanned or changes position relative to the sample, generating a surface topographic map. Most commonly tip deflection is a result of interatomic (van der Waals) forces. A good reference for those interested in the topic can be found at http://invsee.asu.edu/nmodules/spmmod .

Coupling AFM with MS has given rise to an interest termed "molecular cartography" by Gary Van Berkel (Oak Ridge National Laboratory, Oak Ridge, Tennessee). His team's work was presented at the 2010 Conference on Small Molecule Science (Portland, Oregon) by Olga Ovchinnikova and can be downloaded at www.cosmoscience.org (18).

Ovchinnikova points out currently available techniques usually "face a trade-off between spatial resolution and chemical information." Combining spatial resolution, using a heated scanning AFM probe to thermally desorb material from a surface, they then draw the sample into either an ESI or APCI source adding chemical information from the sample surface. The authors refer to the technique as atmospheric-pressure hybrid proximal probe topography chemical imaging. The AFM tip plays a dual role, being used for the thermal desorption creating ions for MS analysis while obtaining topographic images of that same surface. Initial results demonstrate the viability of this technique for automated chemical interrogation of caffeine thin films with ~250-nm spatial resolution in the thermal desorption process. Lower resolution proximal probe thermal desorption chemical imaging results of different classes of compounds amenable to this technique including explosives, herbicides, pharmaceuticals, and dyes. The authors anticipate this analytical tool "will have broad application for determining the nanoscale spatial distribution of target molecules in plant and animal tissue and material junctions" (19).


The wisdom readers benefit from in this column often is a distillation from many years of endeavor by people like Colin Moore. "At the end of the day, it's people that solve problems and I'm very fortunate to work with a very talented group of people in the Analytical Services department at Chemtura," he says.

Michael P. Balogh Michael P. Balogh

"MS — The PracticalArt" Editor MichaelP. Balogh is principal scientist, MS technology development, at Waters Corp. (Milford, Massachusetts); a former adjunct professor and visiting scientist at Roger Williams University (Bristol, Rhode Island); cofounder and current president of the Society for Small Molecule Science (CoSMoS) and a member of LCGC 's editorial advisory board.

(1) M.P. Balogh, LCGC North America 2 8( 2), 122 (2010).

(2) M.P. Balogh, LCGC North America 27 (6), 480 (2009).

(3) M.P. Balogh, LCGC North America 28 (6), 440 (2010).

(4) M.P. Balogh, LCGC North America 25 (4), 368 (2007).

(5) C. Moore and P. McKeown, J. Am. Soc. Mass Spectrom. 16, 295–301 (2005).

(6) J. Pospíšil, W.-D. Habicher, J. Pilar, S. Nešpurek, J. Kuthan, G.-O. Piringer, and H. Zweifel, J. Polym. Degrad. Stab. 77, 531 (2002).

(7) M. Maizels and W.L. Budde, Anal. Chem. 73, 5436 (2001).

(8) M.L. Pacholski, and N. Winograd, Chem. Rev. 99, 2977 (1999).

(9) F. Andrawes, T. Valcarcel, G. Haacke, and J. Brinen, Anal. Chem. 70, 3762 (1998).

(10) M.J. Walzak, N.S. McIntyre, T. Prater, S. Kaberline, and B.A. Graham, Anal. Chem. 71, 1428 (1999).

(11) D. Briggs, I.W. Fletcher, S. Reichlmaier, L.J. Agulo-Sanchez, and R.D. Short, Surf. Interface Anal. 24, 419 (1996).

(12) M.P. Balogh, LCGC North America 24 (1), 46 (2006).

(13) M.P. Balogh, LCGC North America 25 (12), 1184 (2007).

(14) M.V. Buchanan, Anal. Chem. 54 (3), 570–574 (1982).

(15) R.P. Morgan, C.A. Gilchrist, K.R. Jennings, and I.K. Gregor., Int. J. Mass Spectrom. Ion Phys. 46, 309 (1983).

(16) C. Moore and A. Alexander, "The Identification of Engine Oil Additives Using Chloride Ion Addition IMS-LCMS/MS," presented at the 58th ASMS Conference on Mass Spectrometry and Allied Topics, Salt Lake City, Utah, 2010.

(17) M. Nefliu, R.G. Cooks, and C. Moore, J. Am. Soc. Mass Spectrom . 17, 1091–1095 (2006).

(18) O.S. Ovchinnikova and G.J. Van Berkel, "Molecular Cartography: Moving Towards Combined Topographical and Chemical Imaging using AFM and Mass Spectrometry," presented at CoSMoS 2010, Portland, Oregon, September 25, 2010.

(19) O.S. Ovchinnikova and G.J. Van Berkel, "Molecular Surface Sampling and Chemical Imaging Using Proximal Probe Thermal Desorption/Secondary Ionization Mass Spectrometry," https://external-portal.ornl.gov/doi/abs/10.1021/ac102766w . Publication Date (Web): December 15, 2010 (Article) DOI: 10.1021/ac102766w.


  • Research Matters — to the Science Teacher

Problem Solving in Chemistry

One of the major difficulties in teaching introductory chemistry courses is helping students become efficient problem solvers. Most beginning chemistry students find this one of the most difficulty aspects of the introductory chemistry course. What does research tell us about problem solving in chemistry? Just why do students have such difficulty in solving chemistry problems? Are some ways of teaching students to solve problems more effective than others? Problem solving in any area is a very complex process. It involves an understanding of the language in which the problem is stated, the interpretation of what is given in the problem and what is sought, an understanding of the science concepts involved in the solution, and the ability to perform mathematical operations if these are involved in the problem. The first requirement for successful problem solving is that the problem solver understand the meaning of the problem. In order to do so there must be an understanding of the vocabulary and its usage in the problem. There are two types of words that occur in problems, ordinary words that science teachers generally assume that students know and more technical terms that require understanding of concepts specific to the discipline. Researchers have found that many students do not know the meaning of common words such as contrast, displace, diversity, factor, fundamental, incident, negligible, relevant, relative, spontaneous and valid. Slight changes in the way a problem is worded may make a difference in whether a students is able to solve it correctly. For example, when "least" is changed to "most" in a problem, the percentage getting the question correct may increase by 25%. Similar improvements occur for changing negative to positive forms, for rewording long and complex questions, and for changing from the passive to the active voice. Although teachers would like students to solve problems in whatever way they are framed they must be cognizant of the fact that these subtle changes will make a difference in students' success in solving problems. From several research studies on problem solving in chemistry, it is clear that the major reason why students are unable to solve problems is that they do not understand the concepts on which the problems are based. Studies that compare the procedures used by students who are inexperienced in solving problems with experts show that experts were able to retrieve relevant concepts more readily from their long term memory. Studies have also shown that experts concepts are linked to one another in a network. Experts spend a considerable period of time planning the strategy that will be used to solve the problem whereas novices jump right in using a formula or trying to apply an algorithm. In the past few years, science educators have been trying to determine which science concepts students understand and which they do not. Because chemistry is concerned with the nature of matter, and matter is defined as anything that has mass and volume, students must understand these concepts to be successful problem solvers in chemistry. Research studies have shown that a surprising number of high school students do not understand the meaning of mass, volume, heat, temperature and changes of state. One reason why students do not understand these concepts is because when they have been taught in the classroom, they have not been presented in a variety of contexts. Often the instruction has been verbal and formal. This will be minimally effective if students have not had the concrete experiences. Hence, misconceptions arise. Although the very word "misconception" has a negative connotation, this information is important for chemistry teachers. They are frameworks by which the students view the world around them. If a teacher understands these frameworks, then instruction can be formulated that builds on student's existing knowledge. It appears that students build conceptual frameworks as they try to make sense out of their surroundings. In addition to the fundamental properties of matter mentioned above, there are other concepts that are critical to chemical calculations. One of these is the mole concept and another is the particulate nature of matter. There is mounting evidence that many students do not understand either of these concepts sufficiently well to use them in problem solving. It appears that if chemistry problem solving skills of students are to improve, chemistry teachers will need to spend a much greater period of time on concept acquisition. One way to do this will be to present concepts in a variety of contexts, using hands-on activities.

What does this research imply about procedures that are useful for helping students become more successful at problem solving?

Chemistry problems can be solved using a variety of techniques. Many chemistry teachers and most introductory chemistry texts illustrate problem solutions using the factor-label method. It has been shown that this is not the best technique for high school students of high mathematics anxiety and low proportional reasoning ability. The use of analogies and schematic diagrams results in higher achievement on problems involving moles, stoichiometry, and molarity. The use of analogs is not profitable for certain types of problems. When problems became complex (such as in dilution problems) students are unable to solve even the analog problems. For these types of problems, using analogs in instruction would be useless unless teachers are willing to spend additional time teaching students how to solve problems using the analog. Many students are unable to match analogs with the chemistry problems even after practice in using analogs. Students need considerable practice if analogs are used in instruction. When teaching chemistry by the lecture method, concept development needed for problem solving may be enhanced by pausing for a two minute interval at about 8 to 12 minute intervals during the lecture. This provides students time to review what has been presented, fill in the gaps, and interpret the information for others, and thus learn it themselves. The use of concept maps may also help students understand concepts and to relate them to one another. Requiring students to use a worksheet with each problem may help them solve them in a more effective way. The worksheet might include a place for them to plan a problem, that is list what is given and what is sought; to describe the problem situation by writing down other concepts they retrieve from memory (the use of a picture may integrate these); to find the mathematical solution; and to appraise their results. Although the research findings are not definitive, the above approaches offer some promise that students' problem solving skills can be improved and that they can learn to solve problems in a meaningful way.

For further information about this research area, please contact:

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Chemical Education: Towards Research-based Practice pp 235–266 Cite as

Problem-Solving in Chemistry

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Bodner, G.M., Herron, J.D. (2002). Problem-Solving in Chemistry. In: Gilbert, J.K., De Jong, O., Justi, R., Treagust, D.F., Van Driel, J.H. (eds) Chemical Education: Towards Research-based Practice. Science & Technology Education Library, vol 17. Springer, Dordrecht. https://doi.org/10.1007/0-306-47977-X_11

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