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?)
- Titling your graphs
- 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.
Data
to Analyze:
The data below is for the chemical
reaction:
CO (g) + H_{2}O
(g)→ CO_{2} (g) + H_{2} (g)
1/Temperature
(1/K) |
ln
Equilbrium Constant (ln K_{eq}) |
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:
_{}
"Bad"
Graph:
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 R^{2}
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 R^{2} value. The equation does
not overlap the data and it is not centered over a gridline. This makes
the equation and the R^{2} value easy to read. It is also acceptable
to move both the equation and the R^{2} 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. |