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Problem Solving in Chemistry

Key Concepts


There are 5 steps to solving problems in chemistry1 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    

AUS-e-TUTE 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.

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 ....

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.

AUS-e-TUTE Members should go to the Members Only Tutorial

for a list of key words and their meanings.

Step 3. Write down what the question is asking you to do, that is, state the problem.
        Use the key word at the beinning 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.

AUS-e-TUTE Members should go to the Members Only Tutorial

for a list of key words and the scientific principle each indicates.

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.

AUS-e-TUTE Members should go to the Members Only Tutorial

for a list of symbols and data types.

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

  • datum i

  • datum ii

  • etc

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

  • datum i

  • datum ii

  • etc

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 rounded-off 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 SO42-, sulfite is SO32-, sulfide is S2-
    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.


What would you like to do now?


1This 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; 2nd ed.; Princeton University Press: Princeton, NJ, 1985.

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