Graphical techniques

11.2 Graphical techniques (2 hours)

Pause for thought

During the past decades the IB has used the same graph several times as the basis of a question. The latest is in the specimen papers for the new programme. The graph used is:

It is an interesting graph because it shows how primary pollutants build up during the morning rush hour periods and then the secondary pollutants, PAN (peroxyacylnitrates), increase during sunlight hours as the nitrogen oxides undergo photochemical reactions with the hydrocarbons. Because this is very much the focus of the questions asked, attention is drawn away from the fact that if a student drew such a graph when they were expressing their data graphically they would probably be penalized. It might be worth showing this graph to students and ask them to comment critically on it.

Firstly, is it a 'drawn' graph or a 'sketch' graph? It does not seem to fit either of the IB definitions so would seem to lie somewhere between the two. One of the axes does have a scaled axis (drawn graph) but the other does not have a scaled axis (sketch graph). Other problems include the fact that no units are given for the concentration - is the same unit of concentration being used for all four pollutants? No units are actually given for the time of day either although you are presumably meant to deduce that these are in hours. The title says' 'for a 24 hour period' but the exact date is not given - neither is the location of the city/town where the measurements were made. It could be that this was for an atypical day at an unusual location etc. etc. It might also be worth considering why NO and hydrocarbons build up during the morning rush hour but not during the evening rush hour - maybe nobody travelled back home that day?.

Graphing is a powerful tool but it is also a tool that can be used to manipulate interpretation. You only have to look in the financial press to see how graphs are often misused. For example, the press reported that Facebook shares plummetted after an announcement by the Chief Financial Officer, David Wehner in October 2014. A superficial look at the graph might lead you to conclude that the value of the company had almost been wiped out but on closer inspection of the y axis it can be seen that the company only lost about 9% of its value - hardly a 'plummet'.

Nature of Science

Graphs can be used to find connections between different variables - the idea of correlation.

Learning outcomes

After studying this topic students should be able to:

Understand:

The effect of an independent variable on a dependent variable can be effectively communicated by graphing techniques, which can be used to determine physical quantities.
Graphs that have labelled but unscaled axes are known as sketched graphs and are used to show qualitative trends, such as variables that are proportional or inversely proportional to each other..
Graphs that have have labelled and scaled axes, are known as drawn graphs and are used in quantitative measurements.

Apply their knowledge to:

Draw graphs with the correct choice of axes and scale of experimental results.
Interpret graphs in terms of the relationships between dependent and independent variables.
Produce and interpret lines or curves of best-fit through data points, including assessing when it can and cannot be considered as a linear function.
Calculate quantities from graphs by measuring the gradient (slope) and/or intercept with the appropriate units.

Clarification notes

No clarification notes are given in the Guide for this sub-topic.

International-mindedness

Because they are visual, charts and graphs mainly transcend language barriers so can facilitate communication between scientists worldwide.

Teaching tips

You will need to decide whether to teach this topic as a separate sub-topic or whether to simply include its contents as you cover graphing techniques elsewhere. Personally I think it is better to incorporate it as and when it arises. For example, sketched graphs can be covered under the gas laws (e.g. the relationship between P and V for a fixed mass of gas at a constant temperature) and under rates of reaction showing how the change in concentration depends upon time for first and second order reactions etc. For quantitative coverage, experiments such as Enthalpy changes and Determining E_a for a reaction can be used to show extrapolation (to determine the Arrhenius constant, A), Analysis of Cu(II) ions in solution using a spectrometer can be used to show interpolation and Reaction rates and Determining E_a for a reaction (for determining the activation energy, E_a) for taking tangents.

You will need to ensure that students can both sketch and draw their own graphs. Graphs should have a title, properly labelled axes with the appropriate units and a suitable scale such that all or most of the space is utilised correctly. Students should also know that a minimum of five data points is required before a line or curve of best-fit can have real validity. Error bars and detailed statistical analysis of graphs, e.g. t-tests are not required for IB Chemistry.