Problem Solving in Chemistry Tutorial
Key Concepts
There are 5 steps to solving problems in chemistry^{(1)} which can be thought of as a set of traffic lights:
1: 
STOP! 
State problem. 
↓ 
STOP 
← 
5: 
STOP! 
State solution or Start again 
2: 
PAUSE! 
Prepare game plan. 
↓ 
PAUSE 
↑ 
4: 
PAUSE! 
Ponder plausability. 
3: 
GO! 
Go with game plan. 
→ 
GO 
↑ 


AUSeTUTE calls this the StoPGoPS approach to problem solving:
Step 1: 
Stop to state the problem and extract all the data from the question. 
Step 2: 
Pause to prepare your game plan, your approach to solving the problem. 
Step 3: 
Go do it! Follow the steps in your game plan. 
Step 4: 
Pause to ponder whether your solution to the problem is reasonable.
Check appropriateness of scientific principles you applied.
Check correctness of equations, calculations, units of measurement, etc.

Step 5: 
Stop. Satisified with your solution? State the solution!
Not satisfied with your solution? Start the problem solving process again with Step 1.

You will find a 1 page template (pdf) to use for problem solving here.
All AUSeTUTE's tutorials use this heuristic "stopgops" procedure to solve problems.
This tutorial is much longer than we'd like, but this is because we are going to concentrate on some areas of concern raised by examiners (exam markers) in their reports on external exams.
So, before you begin, you might like to go to the bathroom, get something to drink and/or eat, and get an extra cushion for your chair ....
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STOP! State the Problem
The aim of this first step is to deconstruct the question so that you can clearly see:
 what the question is asking you to do
 what scientific principles need to be applied
 what information has been given to you in the question
Step 1. Read the question carefully.
Step 2. Underline the words or phrases in the question that tell you what you are being asked to do.
Some Key Words and What They Mean
Key Word  Meaning 
account 
state the reasons for this, or, report on this 
analyse 
identify components in this and the relationship between these components 
apply 
use the information given in this particular situation 
appraise 
estimate the value of this 
appreciate 
make a judgement about the value of this 
assess 
make a judgement of this based on its value, quality, outcome, result, or size 
calculate 
determine a value for this based on the data given 
clarify 
make this clear or plain 
classify 
arrange the data into groups, categories or classes 
compare 
show how these things are the same or different 
construct 
make or build a thing or a set of arguments 
contrast 
show how things are different, or, how one thing is the opposite of another 
critically 
analyse and evaluate this for the degree of accuracy and depth of understanding, that is, identify the components and the relationship between them and then make a judgement. 
deduce 
draw conclusions about this 
define 
state the meaning of this and identify its essential components 
demonstrate 
show this by using an example 
describe 
give the characteristics and features of this 
discuss 
identify issues and give the key points for and against this 
distinguish 
note the differences between these things 
evaluate 
make a judgement about this based on some specified criteria, or, determine the value of this 
examine 
inquire into 
explain 
relate cause and effect, make the relationship between things clear, give the reasons why or how this is so 
explore 
look closely at the information given in order to discover something 
extract 
from the information given, select the relevant and/or the approriate details 
extrapolate 
infer something about this from what is known 
identify 
recognize and name this 
interpret 
draw meaning from this 
investigate 
plan, inquire into, and draw conclusions about this 
justify 
support an argument or conclusion by giving reasons 
organise 
use the different pieces of information provided to make a united whole 
outline 
give the main features of this, sketch this in general terms 
predict 
suggest what may happen based on the information provided 
propose 
put forward an example, point of view, idea, argument, suggestion etc for consideration 
recall 
present remembered ideas, facts, experiences 
recognise 
identify from knowledge, experience or character 
recommend 
provide reasons in favour of this 
recount 
retell a series of events 
select 
carefully choose something in preference to other things 
summarise 
concisely give the relevant details 
synthesize 
pull the various pieces of data together into a whole 
Step 3. Write down what the question is asking you to do, that is, state the problem.
Use the key word at the beginning of the statement.
Example: Calculate the moles of gas.
Example: Explain why the rate of the reaction increases.
Step 4. Highlight key words that indicate the scientific principles that you will need to apply.
Some Examples of Words or Phrases that Indicate Scientific Principles
Word/Phrase  Scientific Principle (type of problem) 
acid 
Definition (Arrhenius? BrønstedLowry? Lewis? Monoprotic? Diprotic? Triprotic? Polyprotic?)? Neutralisation? Titration? Calculation of pH/pOH/concentration? Equilibrium? Buffer? Reaction Rate? Acid Rain? 
activity 
Activity Series? Periodic Table Trend? 
ammonia 
Structure/Intramolecular Forces (bonding)? Intermolecular Forces? Gas (stoichiometry? Gas Laws?)? Haber Process (equilibrium? reaction rate? catalysts? equation? stoichiometry?)? 
base 
Definition (Arrhenius? BrønstedLowry?), Neutralisation? Titration? Calculation of pH/pOH/concentration? Equilibrium? Buffer? Reaction Rate? 
bond 
Intramolecular Forces (covalent? ionic? metallic?)? Intermolecular Forces (dispersion forces? dipoledipole interactions? hydrogen bond?)? 
buffer 
Equilibrium? AcidBase? BrønstedLowry Theory? Strength of Acids/Bases? 
catalyst 
Reaction Rate? Enthalpy Change? Energy Profile? Use of? Enzyme? 
chromatography 
Type of (paper? thin layer? gas? high performance liquid?)? Calculation (retardation factor? retention time? concentration?)? 
combustion 
Organic Chemistry (write equation? complete/incomplete?)? Enthalpy (Heat of Combustion Calculation? Energy Profile? Hess's Law?)? Calorimetry? Fuels (efficiency of combustion? factors effecting?) 
concentration 
Type of solution (aqueous solution? gas mixture? etc)? Stoichiometry (calculation)? Unit Conversion? Dilution? 
conjugate 
BrønstedLowry Theory? Strength of Acids/Bases? 
cycle 
Type of (carbon? nitrogen?)? Stoichiometry (calculation)? Chemical Equation? Equilibrium? Reaction Rate? 
detergent 
Structure (anionic, cationic, neutral)? Cleaning (micelles? intermolecular forces? surface tension?)? 
displacement 
Displacement Reaction Equation? Activity Series? Calculation of Electrode Potential (emf)? 
electrolysis/electrolytic 
Electrolytic Cell? Redox Reaction Equation? Calculation of Electrode Potential (emf)? Application (battery recharging? electroplating? metal extraction/refining?)? 
electrophoresis 
Technique? Separation of Amino Acids? DNA? 
enthalpy 
Stiochiometry Calculation? Hess' Law? Energy Profile? Heat of Reaction? Heat of Neutralisation? Heat of Solution? Heat of Combustion? Heat of Formation? Bond Energy? Latent Heat? Calorimetry? Equilibrium? Reaction Rate? 
equilibrium 
Le Chatelier's Principle? Calculation of/using Equilibrium Constant (K)? Calculation of/using Reaction Quotient (Q)? Acid (K_{a})? Base(K_{b})? Water(K_{aw})? Precipitate(K_{sp})? Application (blood? Haber Process? Contact Process? Solvay Process?)? 
formula 
Organic (molecular formula? 2dimensional structural formula? 3dimensional structural formula? condensed (semi) structural formula? skeletal formula?)? Salt? Transition Metal Complex? 
gas 
GayLussac's Law? Avogadro's Principle? Boyle's Law? Charles' Law? Combined Gas Equation? Ideal Gas Law? Kinetic Theory of Gases? Dalton's Law of Partial Pressures? Graham's Laws of Effusion and Diffusion? 
greenhouse 
Effect? Gases (type of? stoichiometry? equations?) 
halflife 
Nuclear Decay? Reaction Rate? 
isotope 
Atomic Theory? Nuclear decay? Relative Atomic Mass? Mass Spectroscopy? Halflife? Properties/Uses? Stability? 
mass 
Stoichiometry (calculation?)? Unit Conversion? Relative Atomic Mass? Molar Mass? Molecular Mass? Formula Mass? Isotopic Mass? Mass Spectroscopy? 
metal 
Periodic Table Trends? Reactions of? Stoichiometry? Metallic Bonding? Activity Series? Extraction of Metals From Ores? Properties/Uses? 
molarity 
Stoichiometry (calculation)? Type of Reaction (acidbase? redox? metal + acid? displacement? combustion? synthesis, etc?)? Write Chemical Equation? Dilution? 
moles 
Stoichiometry (calculation)? Gas? Solid? Liquid? Solution? Type of Reaction (acidbase? displacement? redox? synthesis? combustion? etc)? Limiting Reagent/Reactant in Excess? 
name 
Organic Nomenclature (IUPAC? Common?)?, Binary Inorganic Compound or Salt? Transition Metal Complex? 
neutralisation 
Arrhenius Theory? BrønstedLowry Theory? Proton Transfer? Titration? Salt (pH? concentration? identity?)? 
nuclear decay 
Write Equation? Calculation (halflife? mass? percent?) Isotopes? Radiation (alpha?, beta?, gamma?)? 
oxidation 
Organic Chemistry (write equation? oxidizing agents?)? Electrochemistry (oxidation state? write halfequation? oxidizing agent?) 
ozone 
Structure? Ozone Layer? Ozone Depletion? Stoichiometry (calculation)? Chemical Equation? 
polymer 
Name/Structure? Type of (addition/ condensation?)? Examples of? 
precipitate 
Equation (molecular? ionic? net ionic?)? Stoichiometry (calculation?)? Solubility Rules? Solubility Product (K_{sp})? Gravimetric Analysis? Intermolecular Forces? 
rate 
Collision Theory? Kinetic Energy Distribution? Rate Law? Equilibrium? Enthalpy/Energy? 
redox 
Oxidation State? Oxidation Reaction? Reduction Reaction? Halfequation? Redox Equation? Electrode Potentials (emf)? Galvanic Cell? Electrolytic Cell? Faraday's Laws of Electrolysis? Electroplating (electrodeposition)? Metal Extraction from Ore? Titration? 
reduction 
Organic Chemistry (write equation? reducing agent?)? Electrochemistry (oxidation state? halfequation? reducing agent?) 
salt 
Neutralisation Reaction? Binary Inorganic Nomenclature? Metal + Acid? Carbonate + Acid? Arrhenius Theory? BrønstedLowry Theory? Titration? 
soap 
Synthesis/structure (saponification)? Cleaning (micelles? intermolecular forces? surface tension?)? 
spectroscopy 
Type of (mass? atomic absorption? emission? infrared? uvvisible? ^{1}H? ^{13}C?)? Qualitative? Quantitative? 
sulfuric acid 
Stoichiometry? Acid Strength? Neutralisation? Dehydration reaction? Oxidising Acid? Contact Process (equilubrium? reaction rate? catalysts? stoichiometry?) 
surface 
Adhesion? Cohesion? Surface Tension? Wetting? Capillary Action? Intermolecular Forces? Detergent? Soap? Catalysis (reaction rate? enthalphy change?)? 
solution 
Stoichiometry calcuation (concentration, dilution)? Colligative Properties of Solutions (freezing point depression, boiling point elevation, vapour pressure lowering, osmotic pressure)? 
solubility 
Solubility Rules? Precipitation? Intermolecular Forces? Lattice Energy? Stoichiometry (calculation)? Solubility Product (K_{sp})? Equilibrium? Reaction Rate? Solvation? 
titration 
Type of (direct acidbase? back titration? redox? complexometric? conductometric?)? Technique? Stoichiometry (calculation)? Neutralisation? Indicator? Titration Curve? 
volume 
Solid? Liquid? Gas? Solution? Unit Conversion? Density? 
water 
Equilibrium (K_{w})? Aqueous Solutions (stoichiometry? equations? reactions?)? Analysis of? Purification of? Surface Tension? Wetting? Structure/Intramolecular Forces (bonding)? Intermolecular Forces? 
yield 
Stoichiometry calculation? Equilibrium vs Rate of Reaction? 
Under your statement of the problem, write a brief note which tells you which scientific principle (highlighted) you will apply.
Begin your note with a word like "Use ..." or "Apply ...."
Step 5. Extract all the information, the data, given in the question and write it down as a list under your note about which scientific principle applies.
Include the units of measurement where appropriate.
Step 6. Where appropriate, write the symbol for a piece of data next to it in the list.
Some Examples 
quantity  symbol 
quantity  symbol 
Avogadro's number 
N_{A} 
mole 
n 
change : macroscopic 
Δ 
pressure 
P 
change : infinitesimal 
δ 
reaction quotient 
Q 
concentration (molarity) 
c 
retardation factor 
R_{f} 
enthalpy 
H 
retention time 
R_{t} 
equilibrium constant 
K 
specific heat capacity 
C_{g} 
faraday constant 
F 
standard electrode potential 
E^{o} 
halflife 
t_{1/2} 
temperature 
T 
ideal gas constant 
R 
time 
t 
mass 
m 
volume 
V 
molar mass 
M 


PAUSE! Prepare a Game Plan
After completing the STOP step above you should have a page that looks like the diagram below:
The problem: ............
Apply .................
Data

The aim of this step is to prepare a game plan that you can follow in order to solve the problem.
The plan could be a set of numbered steps or it could be a flow chart, but it must be something that you can follow sequentially.
Step 1: Underneath the list of data you have already written down, write down a list of steps, say 10 steps, leaving plenty of space between each one:
The problem: ............
Apply .................
Data

Step 1
Step 2
Step 3
etc

You can always add more steps later if you need to, or ignore ones that you don't use.
Step 2: Think about how your unknown (the thing you need to find) is related to the information you have been given by the scientific principle(s) you have decided on.
How the unknown is related to the knowns given in the question will determine what you write next to each number in your list of steps.
 What do you need to do first?
Do you need to write a chemical equation? Make this Step 1.
Example: Step 1: write the balanced chemical equation for the reaction between X and Y to produce Z
 What do you need to do next?
Do you need to find the stoichiometric (mole) ratio? Make this Step 2.
Example: Step 2: find n(x):n(z) using balanced chemical equation
 What do you need to do next?
Do you need to calculate the moles of a reactant? Make this Step 3.
Example: Step 3: calculate n(X)
 What do you need to do next?
Do you need to use the mole ratio to calculate the moles of product formed? Make this Step 4.
Example: Step 4: use mole ratio to calculate n(Z)
 What do you need to do next?
Do you need to calculate the mass of product? Make this Step 5.
Example: Step 5: calculate m(Z) in grams
 Does this last step enable you to solve the problem? If it does, then you have the framework for your plan!
Step 3: Read through your steps and decide whether you need to use a formula (equation), and write that in as part of that step:
Step 1: 
write the balanced chemical equation for the reaction between X and Y to produce Z 
Step 2: 
find n(x):n(z) using balanced chemical equation 
Step 3: 
calculate n(X)
n(X) = c(X) x V(X)

Step 4: 
use mole ratio to calculate n(Z) 
Step 5: 
calculate m(Z) in grams
m(Z) = n(Z) x M(Z)

Step 4: Read through your steps again and place the information you have been given under the heading for the appropriate step.
Step 1: 
write the balanced chemical equation for the reaction between X and Y to produce Z 
Step 2: 
find n(x):n(z) using balanced chemical equation 
Step 3: 
calculate n(X)
n(X) = c(X) x V(X)
c(X) = 0.010 mol L^{1}
V(X) = 25.0 mL

Step 4: 
use mole ratio to calculate n(Z)

Step 5: 
calculate m(Z) in grams
m(Z) = n(Z) x M(Z)

Step 5: Read through your steps again. Do you need to make any assumptions in order to solve the problem? If so, write them into that step:
Step 1: 
write the balanced chemical equation for the reaction between X and Y to produce Z 
Step 2: 
find n(x):n(z) using balanced chemical equation 
Step 3: 
calculate n(X)
n(X) = c(X) x V(X)
c(X) = 0.010 mol L^{1}
V(X) = 25.0 mL

Step 4: 
use mole ratio to calculate n(Z)
assume reaction goes to completion

Step 5: 
calculate m(Z) in grams
m(Z) = n(Z) x M(Z)

Step 6: Do you need any additional information, for example, do you need to use the Periodic Table to find relative atomic masses? Or do you need to use a Data Sheet to look up a physical/chemical constant? If so, write this into the appropriate step:
Step 1: 
write the balanced chemical equation for the reaction between X and Y to produce Z 
Step 2: 
find n(x):n(z) using balanced chemical equation 
Step 3: 
calculate n(X)
n(X) = c(X) x V(X)
c(X) = 0.010 mol L^{1}
V(X) = 25.0 mL

Step 4: 
use mole ratio to calculate n(Z)
assume reaction goes to completion

Step 5: 
calculate m(Z) in grams
use Periodic Table to find relative atomic masses for elements making up compound Z
calculate M(Z) using relative atomic masses
m(Z) = n(Z) x M(Z)

Step 7: Do you need to convert units so that all the units you use will be consistent? For example, do you need to convert a volume in mL to a volume in L? If so, add this to the appropriate step:
Step 1: 
write the balanced chemical equation for the reaction between X and Y to produce Z 
Step 2: 
find n(x):n(z) using balanced chemical equation 
Step 3: 
calculate n(X)
n(X) = c(X) x V(X)
c(X) = 0.010 mol L^{1}
V(X) = 25.0 mL
convert V(X) in mL to V(X) in L (because concentration is in moles per L)

Step 4: 
use mole ratio to calculate n(Z)
assume reaction goes to completion

Step 5: 
calculate m(Z) in grams
use Periodic Table to find relative atomic masses for elements making up compound Z
calculate M(Z) using relative atomic masses
m(Z) = n(Z) x M(Z)

Step 8: Read through your steps again. Does step 1 flow logically into step 2, then to step 3 etc?
If it all seems to make sense, then it's time to implement the game plan!
GO! with the Game Plan
If you have prepared a good game plan above, all you should have to do is follow each step you have written.
If you find there are gaps in your game plan, things you find you still need but haven't included, it's time to Pause! and read each step in your game plan carefully, making any additions as required, BEFORE you continue implementing the game plan.
Substitute values into equations as you go, step by step, and calculate each value as it appears.
When you complete the last step in your game plan, you should be looking at the solution to the problem.
It is important at this point to PAUSE! and ponder!
PAUSE! Ponder the Plausability of your Solution
Before you call this problem "finished" and move onto the next problem, take some time to think about your solution in relation to the question that was asked.
Step 1: Have you actually answered the question that was asked?
Before you laugh, I must tell you that one of the many complaints markers have about student exam papers is that the students have NOT answered the question that was asked ... so let's proceed ...
Read the question again.
Read your solution.
Does your solution provide an answer to the question that was asked?
Check this by asking yourself this question, "If I gave my solution to the problem to someone who had not read the problem, could they guess what question had been asked?"
If your solution does answer the question ... well done!
But if it doesn't ... STOP right here! Go back to the start of the problem solving process!
Step 2: Is your solution reasonable?
One of the most common mistakes students make on exam papers is that they incorrectly, or neglect to, convert units resulting in an answer that is out by orders of magnitude (factors of 10).
You can check whether your solution seems reasonable in lots of ways, here are a few:
 Get a ball park figure and see how this compares to your answer.
That is, round all the numbers you use up or down to the nearest 5 or 10, for example, 0.89 because 1, 22.76 becomes 20, etc, then use these roundedoff numbers to do quick calculations in your head just to check that you aren't off by orders of magnitude.
If you end up with a ball park figure of 50 and the solution you carefully calculated was 64.71, you're looking good, but if your carefully calculated solution was 0.6471 this indicates there is something terribly wrong somewhere, so it's time to STOP and go back to the beginning of the problem solving process.
 Should the number be higher or lower than one given?
If the question involves diluting a solution for example, then the concentration of the solution after dilution will be less than the concentration of the solution before it was diluted.
If your answer gives a concentration for the diluted solution that is greater than the original solution, STOP and go back to the beginning of the problem solving process.
If a reaction gives off energy (exothermic), the temperature of the reaction mixture should increase, if your answer shows a fall in temperature, you need to STOP and go back to the beginning of the problem solving process.
Similarly, if the temperature of the reaction mixture increased as the reaction gave off heat, but your answer gives a positive (rather than a negative) value for the enthalpy change, you need to STOP and go back to the beginning of the problem solving process.
 Work backwards by using your answer to calculate one of the known quantities given in the question (or use all the knowns and your value for the unknown to calculate the value of a constant in an equation) etc
Step 3: Check that all the data you used were correct.
Yes, this is another common error on exam papers.
Check formula of ions, for example; sulfate is SO_{4}^{2}, sulfite is SO_{3}^{2}, sulfide is S^{2}
Check that chemical equations are correctly balanced.
Check that you have used the correct stoichiometric (mole) ratio
Check that you used the correct formula (equation) in each calculation.
If you rearranged a formula, check that you did this correctly, for example, if c=n/V then V=n/c
Check that you have used the correct units and that the units used are all consistent.
Check that you have the appropriate number of significant figures, for example, if you have been given pH = 1.32, the concentration of hydrogen ions is NOT going to be 0.047863!
Step 4: Check your spelling!
There are some spelling mistakes examiners probably won't care about, for example there/their/they're, where/wear etc
But some spelling mistakes are guaranteed to lose you marks, for example, alkane/alkene/alkyne (huge difference in reactivity for one thing!).
Step 5: Check that the scientific principles you applied are valid for this problem.
This also means checking any assumptions that you may have made.
If you have checked all of the above, then it is time to ....
STOP!
If everything looked good after completion of the PAUSE to Ponder step above, then you have solved the problem.
State your solution to the problem by writing it down.
STOP working on this problem.
If, however, there is some doubt about the value, or quality, of your response after going through the checks above, you should STOP here and start the problem solving process again, from the beginning, with step 1.
Footnotes:
(1) This approach is based on Polya's approach to problem solving in maths, which I always think of as a 'Weapon of Maths Deconstruction', but is a good general approach to problem solving.
Polya, G. How to Solve It; 2^{nd} ed.; Princeton University Press: Princeton, NJ, 1985.