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# How do you graph Boyle's law?

Boyle’s Law examines the relationship between the volume of a gas and its pressure.

So you would do an experiment in which you measure the volume of a gas at various pressures.

Let’s assume you get the following data.

The best way to determine a relationship is to plot a graph that gives a straight line.

At this point we (theoretically) don’t know the relationship, so we plot V vs. P to see what the plot looks like.

We plot pressure as the independent variable (along the horizontal or x axis) and volume as the dependent variable (along the vertical or y axis).

You could do this by hand, but it is more convenient to use a computer to do the job for you.

Your graph, as in the figure, looks like a hyperbola.

The equation for a hyperbola is y = k/x. It looks as if we should try a plot of V vs. 1/P.

We calculate the values of 1/P and then plot V vs. 1/P. We get the straight line plot shown above.

If you plot the data manually, you extend the line backwards until it reaches V ≈ "0 cm"^3.

The graph of V against 1/P is a straight line through the origin.

This means that the measured volume is INVERSELY PROPORTIONAL to its pressure — .

If you use a computer or a calculator, you can tell it to calculate the equation for the line that best fits all the points (the regression line). My computer tells me that the equation is

V = 6185.8/P - 0.0827

This says that when 1/P = 0, V = "-0.08 cm"^3.

Since we measured the volumes only to the nearest cubic centimetre, "0.08 cm"^3 is negligible. Therefore, within experimental uncertainty,

V = 6185.8/P

This is Boyle’s Law, V = k/P.

If V = k/P, then PV = k.

The graph of PV against P should be a straight line parallel to the P axis. In other words, the product PV is a constant at a fixed temperature.

We can test this by plotting PV vs. P as shown below.

The graph looks like a horizontal straight line.

The computer gives the equation for the best fit line as

PV= -0.149P + 6192.8

That means that the line starts at PV = 6183.8 at the left hand end and finishes at 6163.0 at the right hand end.

However, since we are justified in using only two for the PV product, it starts and ends at 6200.

Therefore, within the limits of experimental uncertainty,

PV = "constant" → BOYLE'S LAW