Plotting Points on a Graph Chemistry Tutorial

Key Concepts

A graph is a way of presenting lots of information in a very condensed form.

Features common to graphs based on experimental data:

 y axis label Title x axis label

To draw a graph on graph paper you will need the following equipment:(1)

• graph paper
• sharp pencil
• eraser (rubber)
• ruler

After you have plotted your points on the graph you will need to draw a line of best fit through your data points.(2)

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Labelled Axes on a Graph

The horizontal axis, the x axis, is used for the independent variable, that is, the variable which you control (set at several known intervals).
The independent variable is also sometimes referred to as the controlled variable.

The vertical axis, the y axis, is used for the dependent variable, the variable that you observe or measure when you change the independent variable.

Example, in an experiment a student places 50.00 mL of hydrochloric acid in a conical flask on an electronic balance and records the mass.
A marble chip with a mass of 5.03 g is added to the conical flask.
The mass of the experimental apparatus is recorded every 2.5 minutes for 10 minutes.
 Independent variable is time.(You control time by taking measurements very 2.5 minutes.) Dependent variable is mass.(You do not control the mass, the mass will have changed each time you take a measurement.)

Label the x axis and the y axis:

• x axis (horizontal axis) label is the independent variable
that is "time" is on the x axis
• y axis (vertical axis) label is the dependent variable
that is, "mass" is on the y axis
 mass time

You also need to indicate what the units of each measurement are.

• time has been measured in minutes, abbreviated as min
• mass has been measured in grams, symbol is g

Units of measurement are written after the name of the quantity in the labels of each axis.
This can be done in several different ways:

• units in round brackets after the name:

example: time (min) and mass (g)

• units separated from name with a comma:

example: time, min and mass, g

• units separated from name using a forward slash:

example: time / min and mass / g

This is now the most acceptable format.

 mass / g time / min

Each axis should be marked off in regular intervals, referred to as the scale.

• Horizontal axis:
If you measure time every minute during the experiment, mark off 1 minute intervals on the x axis and label each mark as 1 then 2 etc.
A suitable scale might be to let 1 cm on the graph paper be equal to 1 minute.
• Vertical axis: inspect the values of the dependent variable then
(a) round up the highest value to a convenient number (eg, 14.12 g might become 15 g or even 20 g)
(b) round down the lowest value to a convenient number (eg, 2.92 g might become 2 g or even 0 g)
(c) calculate the range of values you need to plot
(ie, highest value minus smallest value, eg, 20 - 0 = 20)
(d) decide on a suitable scale: metric graph paper might have lighter ruled divisions every 2 mm and darker divisions to mark every 1 cm.
For a range of 20 g, every 1 cm on the graph paper could represent 1 g
 mass / g time / min

You do not need to start either the x axis or the y axis at zero, unless zero has some special significance.

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Title of the Graph

The title of a graph is usually in the format of "y-axis label (without units) versus x-axis label (without units)".
The word "versus" is Latin for "against".

On the graph shown on the right we see that the:

• y-axis is labelled mass / g
• x-axis is labelled time / min

The first step in writing a title for the graph is to remove the units from the labels on the x and y axes:

• y-axis = mass
• x-axis = time

Then we construct the title of the graph in the format y-axis versus x-axis, that is, "mass versus time".
The word versus is often abbreviated to vs
Using this abbreviation, the title of the graph becomes "mass vs time"

 mass /g Mass versus timetime / min
If you are including more that one graph in your lab report, it is a good idea to number the graphs as well.
You can use the phrases Graph 1., Graph 2., etc
or you can use the more general phrases Figure 1., Figure 2., etc

When you refer to a graph in your lab report, you write, "Figure 1. Mass versus time".
When you are talking to someone about your graph, you might say, "Figure one, mass versus time", or you might say, "Figure one, mass against time".

 Figure 1. Mass versus time mass / g time / min

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Plotting Data Points on the Graph

The data obtained from an experiment is plotted on the graph using a suitable symbol.
The symbol used must be large enough to be seen, but small enough so that there is no uncertainty about where the centre of the point is.
For this reason, the first choice for plotting points on a graph is a cross, x (the point is located where the two lines forming the x crossover, but, the two lines themselves make the point easy to see on the graph).

Example:

time / min mass / g
0 5.21
2.5 4.69
5.0 4.14
7.5 3.78
10.0 3.57
Time is the independent variable (measured every 2.5 minutes) and mass is the dependent variable (changes with time).
Time is on x axis, mass is on y axis.
Plotting the first point: x = 0 and y = 5.21
Graph starts at x=0 so we only need to go up vertically to the location of 5.21 and mark an x on the graph.
 Figure 2. Mass versus time mass / g time / min
Plot the second point: go along the x axis to 2.5, move up vertically to 4.69 and make a x on the graph.

Plot the third point: go along the x axis to 5.0, move up vertically to 4.14 and make a x on the graph.

Plot the fourth point: go along the x axis to 7.5, move up vertically to 3.78 and make a x on the graph.

Plot the last point, go along the x axis to 10.0, move up vertically to 3.57 and make a x on the graph.

 Figure 3. Mass versus time mass / g time / min
If the points on the graph form the pattern of a straight line or a smooth curve, draw the line of best fit through the points.

The line will

• start at the x value of the first data point
• end at the x value of the last data point
 Figure 4. Mass versus time mass / g time / min

If you need to include more than one set of data points on the same graph, use two different symbols, that is, use one symbol (x) for the first set of data but use a circle (o) for the second set of data points.

Example:

time / min Jo's
mass / g
Chris's
mass / g
0 5.21 5.05
2.5 4.69 4.50
5.0 4.14 4.27
7.5 3.78 4.00
10.0 3.57 3.38
Jo's results are plotted as x on the graph

Chris's results are plotted as o on the graph

Note that a legend has now been included on the graph so that the reader can identify which sets of data points belong to Jo and which belong to Chris.

 Figure 5. Mass versus time mass / g time / min

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Footnotes:

(1) Are you wondering why chemistry teachers still insist that you learn to draw a graph properly when it is so much easier to use an app or excel to draw it for you?
It is because we believe that by drawing the graph yourself you will come to a greater understanding of what the graph means and what its limititations are.
For instance, you've probably already realised that there is quite a bit of uncertainty involved in the placement of each point on the graph, and hence in your ability to read the point once plotted.
We also want you to recognise patterns in the plotted points, is it a straight line? a curve? random distribution? clusters of points?
Once you have mastered the technique of drawing your own graphs you can use a computer program or ap to draw it for you, but you should be the one to make meaning of the graph, to think about what it is telling you.

(2) This assumes, ofcourse, that the plotted points can be described by a line (straight, curved or periodic).
If the plotted points resemble a random distribution then you should not draw a line through them.