Graphs

One of the underlying themes of the Chem 124/125 sequence is graphical analysis. During the two quarters, you will be drawing and using graphs on many different types of problems. At the end of the two quarters you should be familiar with:

• Drawing graphs
• Labeling axes appropriately with units
• Scaling correctly
• Determing exactly what to graph (what is x? what is y?)
• Analyzing graphs
• Extracting information from graphs including information related to the slope and intercept
• Understanding molecular behavior based on the graphical results
• Compare and contrast different systems
• Know when estimating is appropriate and knowing when using the equation is correct

I have found in previous quarters that graphing is typically a source for major point deductions for most students. To aid in your understanding of what constitutes a "good graph" and what constitutes a "bad graph", I have created a "bad graph" and pointed out the errors. Then I have corrected the errors to generate a "good graph". Click below to jump to a section or tip or just scroll down.

 Sections Tips

Data to Analyze:

The data below is for the chemical reaction:

CO (g) + H2O (g)→ CO2 (g) + H2 (g)

 1/Temperature (1/K) ln Equilbrium Constant (ln Keq) 2.09 x 10-3 5.35 1.88 x 10-3 4.29 1.70 x 10-3 3.43 1.56 x 10-3 2.77

The data above is used to determine the relationship between equilibrium contstants and temperature or to find the change in enthalpy (ΔH) or change in entropy (ΔS) according to the van't Hoff equation below: Here is a "bad graph" drawn using the data above: What is wrong with this graph?

• Title - The title in this case is non-descriptive. The reader can get all of the information in the title by just reading the axes labels. A more descriptive title is needed.
• y-axis - The scale doesn't reflect the number of significant figures in the original data. According to this scale, the numbers are #.#, when in reality they are #.##.
• x-axis - The scale has too many significant figures here. Using the scientific notation (perfectly acceptable) makes this scale a little cramped. Notice how the exponent is listed below the number. It would be better to design a graph where the scale markers all fit on the same line (either using scientific notation or writing out the numbers).
• Units - The x-axis does have units, but those are not mentioned anywhere on the graph
• Legend - The legend does not give any new information and instead crowds the graph. Since there is only one set of data here, the legend is not needed.
• Equation - The equation of the line is positioned right on top of the line and makes it difficult to read. The equation is also missing the R2 value indicating how well the line fits the data. Finally, the equation of the line has too many significant figures compared to the number given in the original data.
• Background - The default in Excel is the grey background and it make the graph a little more difficult to read. A white background would be easier to read and it would save ink during the printing process.
• Type of graph - The graph here has two lines drawn. There is the trendline (in black) that was added to the original data. The graph here has the points connected by a line (blue) that is not doing anything but cluttering the graph.
• Layout - Notice that all of the data is on the right half of the graph. It would be better to spread the axis out so that the data are distributed throughout the graph as opposed to concentrated on the right side.

"Good" Graph:

Here is a "good graph" drawn using the same data from above: What makes this "good" graph better?

• Title - The title here is more descriptive. It tells the reader what the purpose of the graph was. When you draw a graph you should consider the question: "Why am I drawing this graph?" (Hint: The answer is never "Because the lab or instructor said so.") Is it to extract information? Find a linear relationship?, etc. Whatever the reason is, it should appear in your graph title. Note that the title may be a little longer than you think is acceptable. Anything that fits in three lines is acceptable (two is usually sufficient). Longer than three lines becomes a little too long and should be avoided. Also note that there are subscripts within the title.
• Tip: How to include subscripts in a title or axis label: After completing the graph, highlight the character to be a superscript or subscript. Then right click and select "Format Chart Title" or "Format Axis Title". A window will appear allowing you to change the font. Click the box for superscript or subscript down near the bottom of the window and select "OK".

• y-axis - In this case, the scale reflects the correct number of significant figures. The scale indicates the numbers are accurate to #.##. The tick marks indicate the numbers are accurate to the tenths place (#.#) and if a reader looks in between two tick marks to guess a location then that number would thus be accurate to the hundreths place (#.##) In this case, tick marks needed to be added to the graph. In the graph above, I added tick marks every 0.2. Ideally, every 0.1 would have been better but it clutters the graph more than every 0.2. Tip: How to add tick marks to an axis: Double click on the axis where tick marks will be added. In the "Patterns" tab, select which type of marker for the minor tick labels (I usually select inside). Then on the "Scale" tab, select the appropriate spacing for the tick marks. This is called the "minor unit". Then select "OK".

• x-axis - I decided to remove the scientific notation since it was making the numbers longer and thus making them spill over onto the second line. Also, note that here the numbers reflect the accuracy of the measurement and tick marks are not required. If a reader reads the number off the graph between two marks, then will get the correct accuracy 0.#####. Do you understand why tick marks were not required here but required on the y-axis? If not, please ask
• TIp: How to change the display format of a number: Double click on the axis to change. Select the "Number" tab. If you choose "Number" from the list on the left, you can specify the correct number of decimal places. If you choose "Scientific" from the list, you can also choose the number of digits to display in scientfic notation.

• Units - Notice that the temperature units (1/Kelvin) are added on the axis label. Tip: How to add more information to an axis label: If the axis label has already been generated, click once on the axis label to display the axis label in a box. Then click where in the box you would like to type or correct a spelling mistake and add your information. If you drew the graph but forgot to generate a label or a title, click on the graph so it is highlighted. Then select from the top menu "Chart -> Chart Options". Choose the "Title" option and add the missing information.

• Legend - Here there is only one set of data, so the legend was not needed and deleted. Only include the legend if two sets of data with two different symbols are plotted at the same time. Be sure to label the legend better than "Series 1" and "Series 2".
• Equation - The equation now includes the R2 value. The equation does not overlap the data and it is not centered over a gridline. This makes the equation and the R2 value easy to read. It is also acceptable to move both the equation and the R2 value to a spot just off the graph (for instace, just above or below the graph). The equation also displays a more reasonable number of significant figures.
• TIp: To change the number of sig figs in an equation: Double click on the equation. Select the "Number" tab, and choose the best method to display the correct the number of significant figures. Oftentimes, scientific notation is the easiest to control since typically the slope and intercept are not usually on the same scale (one is on on the order of 2 and the other 2000).

• Background - Here the background color is not the default grey given by Excel. Instead, it is the white background that saves ink and is easier to read. Tip: To change the background color of a graph: Click on the background (the mouse should say "Plot Area" if you are holding it over the correct area. Be sure to avoid clicking right on a gridline or that is what you will be editing instead). In the "Patterns" tab, choose "None" for the "Area".

• Type of graph - Here the graph is just a scatter plot. The original graph only had 4 square data points, unconnected. The trendline was added later to connect the dots. You should ALWAYS use a scatter plot with unconnected points unless told otherwise.
• Layout - Note that the 4 points are spread out over the entire graph area. The x-axis does not start at zero and it does NOT have to start there. I probably should have started the y-axis at 2.0 to spread the data out even more.

All of the above information was to assist you with the better way of drawing a scientific graph. If you have questions about graphing, please ask me or a TA. We will gladly help you so you don't lose points on your graphs in the future.