If you have ever tried to force in the plunger of a syringe or a bicycle pump while sealing the opening with a finger, you will have seen Boyle's Law in action! This will now be demonstrated using a 10 ml syringe.
Aim:
To demonstrate Boyle's law.
Apparatus:
You will only need a syringe for this demonstration.
Method:
 Hold the syringe in one hand, and with the other pull the plunger out towards you so that the syringe is now full of air.
 Seal the opening of the syringe with your finger so that no air can escape the syringe.
 Slowly push the plunger in, and notice whether it becomes more or less difficult to push the plunger in.
Results:
What did you notice when you pushed the plunger in? What happens to the volume of air inside the syringe? Did it become more or less difficult to push the plunger in as the volume of the air in the syringe decreased? In other words, did you have to apply more or less force to the plunger as the volume of air in the syringe decreased?
As the volume of air in the syringe decreases, you have to apply more force to the plunger to keep pressing it down. The pressure of the gas inside the syringe pushing back on the plunger is greater. Another way of saying this is that as the volume of the gas in the syringe decreases, the pressure of that gas increases.
Conclusion:
If the volume of the gas decreases, the pressure of the gas increases. If the volume of the gas increases, the pressure decreases. These results support Boyle's law.
In the previous demonstration, the volume of the gas decreased when the pressure increased, and the volume increased when the pressure decreased. This is called an inverse relationship. The inverse relationship between pressure and volume is shown in Figure 2.
Can you use the kinetic theory of gases to explain this inverse relationship between the pressure and volume of a gas? Let's think about it. If you decrease the volume of a gas, this means that the same number of gas particles are now going to come into contact with each other and with the sides of the container much more often. You may remember from earlier that we said that pressure is a measure of the frequency of collisions of gas particles with each other and with the sides of the container they are in. So, if the volume decreases, the pressure will naturally increase. The opposite is true if the volume of the gas is increased. Now, the gas particles collide less frequently and the pressure will decrease.
It was an Englishman named Robert Boyle who was able to take very accurate measurements of gas pressures and volumes using highquality vacuum pumps. He discovered the startlingly simple fact that the pressure and volume of a gas are not just vaguely inversely related, but are exactlyinversely proportional. This can be seen when a graph of pressure against the inverse of volume is plotted. When the values are plotted, the graph is a straight line. This relationship is shown in Figure 3.
 Definition 3: Boyle's Law
The pressure of a fixed quantity of gas is inversely proportional to the volume it occupies so long as the temperature remains constant.
Proportionality
During this chapter, the terms directly proportional and inversely proportional will be used a lot, and it is important that you understand their meaning. Two quantities are said to be proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or if they have a constant ratio. We will look at two examples to show the difference between directly proportional and inversely proportional.
 Directly proportional
A car travels at a constant speed of 120 km/h. The time and the distance covered are shown in the table below.
Table 1Time (mins)  Distance (km) 
10  20 
20  40 
30  60 
40  80 
What you will notice is that the two quantities shown are constant multiples of each other. If you divide each distance value by the time the car has been driving, you will always get 2. This shows that the values are proportional to each other. They are directly proportional because both values are increasing. In other words, as the driving time increases, so does the distance covered. The same is true if the values decrease. The shorter the driving time, the smaller the distance covered. This relationship can be described mathematically as:
where y is distance, x is time and k is the proportionality constant, which in this case is 2. Note that this is the equation for a straight line graph! The symbol ∝∝ is also used to show a directly proportional relationship.
 Inversely proportional
Two variables are inversely proportional if one of the variables is directly proportional to the multiplicative inverse of the other. In other words,
or
This means that as one value gets bigger, the other value will get smaller. For example, the time taken for a journey is inversely proportional to the speed of travel. Look at the table below to check this for yourself. For this example, assume that the distance of the journey is 100 km.
Table 2Speed (km/h)  Time (mins) 
100  60 
80  75 
60  100 
40  150 
According to our definition, the two variables are inversely proportional if one variable is directly proportional to the inverse of the other. In other words, if we divide one of the variables by the inverse of the other, we should always get the same number. For example,
1001/60=60001001/60=6000
(4)
If you repeat this using the other values, you will find that the answer is always 6000. The variables are inversely proportional to each other.
We know now that the pressure of a gas is inversely proportional to the volume of the gas, provided the temperature stays the same. We can write this relationship symbolically as
This equation can also be written as follows:
where kk is a proportionality constant. If we rearrange this equation, we can say that:
This equation means that, assuming the temperature is constant, multiplying any pressure and volume values for a fixed amount of gas will always give the same value. So, for example, p11V11 = k and p22V22 = k, where the subscripts 1 and 2 refer to two pairs of pressure and volume readings for the same mass of gas at the same temperature.
From this, we can then say that:
p
1
V
1
=
p
2
V
2
p
1
V
1
=
p
2
V
2
(8)In the gas equations, kk is a "variable constant". This means that k is constant in a particular set of situations, but in two different sets of situations it has different constant values.
Remember that Boyle's Law requires two conditions. First, the amount of gas must stay constant. Clearly, if you let a little of the air escape from the container in which it is enclosed, the pressure of the gas will decrease along with the volume, and the inverse proportion relationship is broken. Second, the temperature must stay constant. Cooling or heating matter generally causes it to contract or expand, or the pressure to decrease or increase. In our original syringe demonstration, if you were to heat up the gas in the syringe, it would expand and require you to apply a greater force to keep the plunger at a given position. Again, the proportionality would be broken.
Shown below are some of Boyle's original data. Note that pressure would originally have been measured using a mercury manometer and the units for pressure would have been millimetres mercury or mm Hg. However, to make things a bit easier for you, the pressure data have been converted to a unit that is more familiar. Note that the volume is given in terms of arbitrary marks (evenly made).
Table 3
Volume

Pressure

Volume

Pressure

(graduation 
(kPa) 
(graduation 
(kPa) 
mark) 

mark) 

12 
398 
28 
170 
14 
340 
30 
159 
16 
298 
32 
150 
18 
264 
34 
141 
20 
239 
36 
133 
22 
217 
38 
125 
24 
199 
40 
120 
26 
184 


 Plot a graph of pressure (p) against volume (V). Volume will be on the xaxis and pressure on the yaxis. Describe the relationship that you see.
 Plot a graph of pp against 1/V1/V. Describe the relationship that you see.
 Do your results support Boyle's Law? Explain your answer.
Did you know that the mechanisms involved in breathing also relate to Boyle's Law? Just below the lungs is a muscle called the diaphragm. When a person breathes in, the diaphragm moves down and becomes more 'flattened' so that the volume of the lungs can increase. When the lung volume increases, the pressure in the lungs decreases (Boyle's law). Since air always moves from areas of high pressure to areas of lower pressure, air will now be drawn into the lungs because the air pressure outside the body is higher than the pressure in the lungs. The opposite process happens when a person breathes out. Now, the diaphragm moves upwards and causes the volume of the lungs to decrease. The pressure in the lungs will increase, and the air that was in the lungs will be forced out towards the lower air pressure outside the body.
run demo
A sample of helium occupies a volume of 160 cm 3 cm 3 at 100 kPa and 25 ∘∘C. What volume will it occupy if the pressure is adjusted to 80 kPa and if the temperature remains unchanged?
 Step 1. Write down all the information that you know about the gas. :
V11 = 160 cm33 and V22 = ?
p11 = 100 kPa and p22 = 80 kPa
 Step 2. Use an appropriate gas law equation to calculate the unknown variable. :
Because the temperature of the gas stays the same, the following equation can be used:
p
1
V
1
=
p
2
V
2
p
1
V
1
=
p
2
V
2
(9)
If the equation is rearranged, then
V
2
=
p
1
V
1
p
2
V
2
=
p
1
V
1
p
2
(10)
 Step 3. Substitute the known values into the equation, making sure that the units for each variable are the same. Calculate the unknown variable. :
V
2
=
100
×
160
80
=
200
c
m
3
V
2
=
100
×
160
80
=
200
c
m
3
(11)
The volume occupied by the gas at a pressure of 80kPa, is 200 cm33
The pressure on a 2.5 l volume of gas is increased from 695 Pa to 755 Pa while a constant temperature is maintained. What is the volume of the gas under these pressure conditions?
 Step 1. Write down all the information that you know about the gas. :
V11 = 2.5 l and V22 = ?
p11 = 695 Pa and p22 = 755 Pa
 Step 2. Choose a relevant gas law equation to calculate the unknown variable. :
At constant temperature,
p
1
V
1
=
p
2
V
2
p
1
V
1
=
p
2
V
2
(12)
Therefore,
V
2
=
p
1
V
1
p
2
V
2
=
p
1
V
1
p
2
(13)
 Step 3. Substitute the known values into the equation, making sure that the units for each variable are the same. Calculate the unknown variable. :
V
2
=
695
×
2
.
5
755
=
2
.
3
l
V
2
=
695
×
2
.
5
755
=
2
.
3
l
(14)
It is not necessary to convert to Standard International (SI) units in the examples we have used above. Changing pressure and volume into different units involves multiplication. If you were to change the units in the above equation, this would involve multiplication on both sides of the equation, and so the conversions cancel each other out. However, although SI units don't have to be used, you must make sure that for each variable you use the same units throughout the equation. This is not true for some of the calculations we will do at a later stage, where SI units must be used.
 An unknown gas has an initial pressure of 150 kPa and a volume of 1 L. If the volume is increased to 1.5 L, what will the pressure now be?
 A bicycle pump contains 250 cm33 of air at a pressure of 90 kPa. If the air is compressed, the volume is reduced to 200 cm33. What is the pressure of the air inside the pump?
 The air inside a syringe occupies a volume of 10 cm33 and exerts a pressure of 100 kPa. If the end of the syringe is sealed and the plunger is pushed down, the pressure increases to 120 kPa. What is the volume of the air in the syringe?
 During an investigation to find the relationship between the pressure and volume of an enclosed gas at constant temperature, the following results were obtained.
Table 4Volume (cm33)  Pressure (kPa) 
40  125.0 
30  166.7 
25  200.0 
 For the results given in the above table, plot a graph of pressure (yaxis) against the inverse of volume (xaxis).
 From the graph, deduce the relationship between the pressure and volume of an enclosed gas at constant temperature.
 Use the graph to predict what the volume of the gas would be at a pressure of 40 kPa. Show on your graph how you arrived at your answer.
(IEB 2004 Paper 2)