"So when will I ever to use this stuff?"

It would be quite a challenge to find a teacher who has not heard that question at least once. Fundamentally, this is an important question to ask. When will you ever use ionic nomenclature, or Graham's Law, or the mole concept in everyday life? Statistically speaking, you never will. Only the fraction of students who ultimately pursue technical careers will even have a chance of using this stuff, and then most likely only if they pursue careers in chemistry or chemistry-related industries.

However, what you will use – to a greater extent than you will ever believe (coming from any teacher, anyway) – are the critical thinking and problem analysis abilities that come with mastery of chemistry content. You may never titrate another weak acid in your entire life, but you will have to approach complex (and sometimes multiple-step) problems. Chemistry courses make it comparatively easy - most of the information you need to solve a problem is right there on the paper in front of you, or at least as close as your notes. It is typically presented in a logical order (or, at least, is relatively organized). Since the course is chemistry, you can make certain metacognative assumptions about the direction the information provided is leading you. For the sake of getting a concept to sink in, many times the material is simplified from its real-life conditions. When you put all of these things into perspective, even the most complex chemistry problems can be solved with relative ease. And if you still have trouble, well, a little partial credit here, a few points for getting the right idea there, and suddenly you have a passing grade. The problem becomes, well, no problem.

Now consider a real-world problem, which will be complex and have multiple (generally, many) steps. The disciplines required for solving it will almost definitely not be restricted to chemistry, so most metacognative assumptions are irrelevant. Data or information that is provided (if there is any provided at all) may be incomplete, unnecessary, and is usually presented out of order. You will need to call on prior knowledge for almost anything that can be considered even remotely fundamental. Information is also found with arresting frequency to be inaccurate or completely false, or, in rare cases, falsified (and there are some people whose jobs are exclusively to determine when this has happened. There is no such thing is partial credit - if you build a bridge, and it collapses into the ravine just as the first hundred cars embark on it, you can safely bet that the families of the victims are not going to pat you on the back for giving it your best.

Solving problems is an everyday commitment – and as much as you hate to hear it over and over again, you only learn it by practicing. You solve a problem every time you figure your way around a traffic jam, select clothes for the day, or decide what to have to eat at the food court. You may hate chemistry, but the bottom line is that chemistry content simply provides a context for learning – you cannot solve a problem about nothing. The advantage of using science or math or psychology or whatever in context to solve problems is because, maybe, just maybe, you will find that you have some interest in one of those areas, and you will quickly find yourself heading down your life's path towards what you really love. And it's not always obvious – there are “professional” wrestlers who studied to be accountants, and funny car drivers who have advanced degrees in mathematics (true stories, both).

Learning to effectively solve word problems in chemistry requires you to polish three of the most important life skills you will ever acquire – mathematical competency, reading comprehension, and critical thinking. Mathematical competency speaks for itself – no amount of understanding of the problem will allow you to arrive at an answer without the ability to effortlessly perform the necessary computations. Reading comprehension skills are necessary to decipher the problem in the first place, to determine what is given, what it means, and what answer the question requires. Finally, critical thinking is necessary to bridge the gap between the other two skills – taking what you have been given, adding any prior knowledge that might be required, set up the steps of the problem, and follow each one to the final answer.

Once you have mastered these three general skills (and it not the intention of this paper to trivialize the time required and difficulty in doing just that), thinking your way through complex problems becomes far easier. Remember – practice is the key. Like a strong muscle, these skills do not mature overnight. This reference is intended only to serve as a framework for your thinking. Every problem is different, so no structured list of steps applies in every situation. You must practice solving problems, review the solutions, and learn to think in just the right way. Also like a muscle, these skills can atrophy with disuse, so stay current in your coursework and practice on your own. The reward will be well worth the effort.

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There is a substantial set of basic skills that you, the student, must have mastery of prior to approaching any chemistry word problem. For reinforcement of any of these, materials and inquiry activities are available in this series of resource papers.

The following skills are required for all chemistry students:

• A strong grasp of the metric system, including:
• The names of the seven base units and what they quantify
• All of the common-usage prefixes and their magnitudes
• How derived, or compound, units are determined and assembled
• Basic but confident algebra skills including the ability to rearrange a multivariable equation to represent a specific quantity
• Representing and manipulating exponents and logarithms will be required for more advanced chemistry topics
• Converting numbers from decimal to scientific notation, properly formatted, and back again
• The ability to determine the precision of a measurement or a reported value
• Knowledge of proper representation of significant figures
• The technique of dimensional analysis (also called the factor-label method) to convert units, which will also be important in stoichiometric and thermochemical calculations
• The concept of the mole in its various forms
• Know how to use your calculator to properly input exponents, scientific notation, and preserve the correct order of operations
• Fundamental physical science vocabulary – terms you should know before attempting any physical science course

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1. Get Your Bearings

• Look the problem over
• Resist the urge to just start writing
• Use stand-outs to get a sense of where the problem will take you
• Be confident that you have the background to solve the problem

2. Read, Read, Read!

• Put your pencil down
• Read the problem several times to get strong familiarity
• Determine the exact question
• Take mental note of important information and key words

3. Organize the Given Information and Develop a Plan

• Identify a starting point
• Always head for the answer
• Follow your instincts
• Highlight important information
• Assign values to variables

4. Solve

• Use formulas that make sense
• Use references whenever available
• Be wary of significant figures and units
• Be confident in your abilities

5. Check Your Work

• Did you answer the question?
• Does the scale and sign of the answer make sense?
• Be confident in the work you have done

6. Metacognition

• What were you thinking?

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First, put down you pen or pencil. You will not need it just yet. If you think having it in front of you might be too tempting, then put it somewhere that makes it a little harder to get to.

All too often, a problem is presented to a student, and, out of sheer terror at the prospect of a poor grade, the student proceeds to start somewhere in the middle and ultimately ends up with an ever-enlarging snowball that becomes more overwhelming and inescapable than the problem ever was to begin with.

It is important to resist the feeling of intimidation when first confronted with a word problem, especially one that covers a full page (or sometimes more – New Jersey standardized tests include constructed response questions that include data and information spanning four pages!). Word problems are designed in such a way that, to the untrained solver, they are intimidating, and rightly so - they are the ultimate test of your logical thinking and reading comprehension.

Resist the urge to immediately dig for the question and start plugging numbers into equations. Resist the urge, even, to start reading the problem! The purpose of this step is to give you a sense of what you are up against, not to start solving.

As with any large body of text or information, it is necessary to skim the entire question. Take a look at any data tables, graphs, or diagrams provided, and ask yourself a few questions. Does anything pop out? Is there anything in italicized or boldfaced text? Is there something in color among black and white items? Do any large (or small) numbers catch your attention? Are there any chemical formulas or equations immediately obvious? Do the graphs make immediate sense, or are they going to require some additional context from the problem?

Without reading the question thoroughly (which, to reiterate, you should not be doing yet!), the idea is to get some sense of what solving the question will entail. If (to use a simple example) a question provides data tables on water quality tests and statistics on suspicious illnesses in the northeastern United States, you can estimate that the question will involve a link between the two. While this technique is not foolproof, it is at least a way to get a look at everything provided quickly and all at once.

Lastly, your confidence plays a major role in your success when solving a word problem. If you glance at the sheet, get immediately intimidated by all of the graphs and data and formulas and cry out “I can’t do this!” chances are – you guessed it – you will not be able to do it. Be confident that you have done your part – studying, focusing on the lessons in class, and completing relevant assignments – because if you have, you have nothing to fear.

This entire step may take only a few seconds, or as long as a few minutes, but the general sense of the problem obtained is worth much more than the time spent.

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Do not pick up that pencil yet!

Now, read the problem. Once. Twice. Eight times, if you have to. You need intimate familiarity with the language of the problem, so read and reread it with this in mind. A passing familiarity will not, unfortunately, result in a passing grade. The familiarity to which I refer is the kind to which you might have with a close friend or relative’s house – although you cannot necessarily describe every nook and cranny, you can explain the floor plan, the colors of the rooms, etc. So is it with word problems. You do not necessarily have to be able to recite that the mass of the polymer sample on the analytical balance was 21.3452 grams, but you should at least remember that there was a polymer sample.

When you read the problem, there are many things you must be aware of as you go. So many, in fact, that you generally will not pick everything up on the first pass (hence the command at the beginning of this section to read the problem more than once). At this point, the goal is to determine the question being asked (more on this below), given values or data (and their units!), provided equations or stated relationships, any implied relationships (more on this below, as well), and key words.

Key words can be hugely important – that is why they have their name. Most word problems contain key words intended to guide you in the direction of the correct procedure to solve the problem. For example, if a problem mentions that a particular compound “decomposes during the process,” then it follows that the reaction involved for this compound must be a decomposition reaction. The key words could be more subtle; they could offer hints to the scale of the answer (“A large quantity of salt is recovered from the water.”), the direction of heat flow (“The reaction vessel must be cooled...”), the quantity of reactants consumed or available (“Oxygen from the air is allowed to react...”), or perhaps some general condition or physical property (“…and the system is open to the air.”). Whatever the situation, it is up to you to determine what terms are key words, and what their significance is to the problem’s solution. This is a task that can be perfected only through experience, so the more practice you can do, the better at it you will become.

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Now that you have finished reading, you can retrieve your writing implement. Write down the question that the problem is asking you to answer. If the answer will be numerical, make a note of the unit (or, if this is not yet evident, the type of unit [mass, molarity, etc.]) that the answer must be reported in. If the answer will be non-numerical, make a note as to the exact scope of the answer and any key words it must contain. Read through the problem again, underlining or otherwise highlighting important information and assigning values to variables wherever you can.

The two parts of this – determining what the question asks for and assigning values to variables – are particularly critical because they will help you determine which formulas and equations are required to solve the problem. Also, things that you already know (called prior knowledge) will help you fill in gaps in the information – constants or molar masses, for example. Be sure to filter out the superfluous information. This might be as simple as ignoring a block of background information, or as difficult as determining pieces of information intentionally included but unnecessary to solve the problem.

Once you’ve determined the given information and the question being asked, identify a starting point. Do you need to convert the given values to different units? Do you need to derive or rearrange the proper equation? Or can you just plug in known values and begin solving? Is there a useful diagram included, or can you create one? Is there any information not given that you already know that might come in handy? Write down whatever comes to mind, but don’t overdo it – info-dumping everything you can think of onto the page will just consume time and could confuse what’s already given.

No matter what plan you use, what approach you take, what route you follow, there is one immutable, consistent truth that must exist no matter what: whatever steps you take, equations you solve, or assumptions you make, they must take you one step closer to the solution. Even if the work you do seems lateral in nature (that is, you’re solving for something “on the side” that you need to be able to continue with your main plan), it should have some bearing on the solution. At no time should you be working on anything that has no relevance to your solution.

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Now that you have selected the formulas and equations that you think you will need, and you have decided on a sequence of steps (if the problem requires more than one step), grab your calculator and solve the problem.

Be aware of the requirements for significant figures, scientific notation, and unit conversions if any of these things are necessary. Be sure to transcribe properly the values that your calculator produces to the paper you are working on. Label everything with correct units, even values in simple formulas – this will help you keep track of your units as you go and help you check yourself if you make a mistake.

Write everything down – do not do any work just in your calculator or, worse, in your head. Students frequently do just this in an attempt to save time, or when they think the problem is too “easy.” You may need to refer back to your work or the calculated values later, or, if you find an error down the road, you may need to refer to the setup and calculations to try to determine where the error began.

Most importantly, be confident in your math proficiency. The answer is out there – just think carefully and logically and you can find it.

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When you finish solving, ask this simple question: Have you answered the exact question being asked? Solving equations, for example, and providing a numerical response, no matter how brilliant your work, does not answer the question “Will Jake have enough strong base to complete his titration?” This is a yes or no question, so answer it – yes, or no.

Do your units work out, based on the math you did? This is the simplest check to be sure you did not make a mechanical mistake when arriving at your answer.

Be confident that the work you’ve done supports the answers you get – even if they “seem wrong.” Do not be intimidated by big or small numbers; sometimes, numbers are big, and sometimes, numbers are small. The unit you are working with will also have a substantial effect on the apparent magnitude of your numbers. For example, 3000 grams and 3000 kilograms are vastly different quantities, even though the magnitudes of their numerical components are identical.

With that said, your answer should make sense. It should fit into a scale that matches the scale of the given information. If the question asks “How many atoms thick is the galvanized coating on the steel plate?” you answer must be some whole number, since you cannot have a fraction of an atom. Therefore, an answer like 3.45 x 10-9 does not make much sense, since a negative power of ten indicates a number less than one. Similarly, an answer of 10 million liters for a question such as “What is the volume of the solution that results from diluting 1.35 L a 3.4 M solution until it is 0.2 M ?” should simply not make sense – imagine about how many beakers you would need to see 10 million liters in one place!

Lastly, if there is an alternative way to complete the problem (or at least parts of the problem), and time permits, use these alternative methods to check your answers. The beauty of chemistry is that many roads frequently lead to the same destination!

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While this will prove to be difficult in real world problems with no immediate context, metacognition, or thinking about thinking, can aid in solving a word problem in chemistry. For one thing, the problem is a chemistry problem, which generally narrows the possible topic areas that the problem will cover. If the problem is on an assessment for a particular unit, then the topics from that unit can, obviously, be expected to show themselves in the problem.

Keep in mind that using the context of the problem to artificially determine a way to solve it will only go so far. The cumulative nature of chemistry as a discipline often leads to multi-step problems that span a broad range of topics, and so even an exam that focuses on intermolecular forces might include thermochemistry, or stoichiometry, or any combination of topics. Narrowing your thinking by considering only the current topics being discussed in class may lead to an incomplete solution to the problem, or the inability to solve the problem at all.