Boyle’s Law
Pressure and Volume
Background
• The first careful experiments on gasses were
performed by Robert Boyle (1600s)
• Boyle studied the relationship between the
pressure of a trapped gas and its volume
• Boyle’s Observations:
– As the pressure increases, the volume of trapped
gas decreases
PV = k
P = Pressure
V = Volume
k = a constant at a specific temperature
for a given amount of gas
Boyle’s Law
• Boyle observed that as pressure increases,
volume decreases, and vice versa
• The relationship is proportional
• If we know the volume of a gas at a given
pressure, we can predict the change in volume
if the pressure is changed
P1V1 = k
we can say: P1V1 = k = P2V2
and
Or just: P1V1 = P2V2
P2V2 = k
Calculating Volume
A 1.5-L sample of gaseous CCl2F2 is contained at a
pressure of 56 torr. If the pressure is changed to 150
torr at a constant temperature,
a) Will the volume of the gas increase or decrease?
b) What will be the new volume of the gas?
Step 1: write down the information given:
P1 = 56 torr P2 = 150 torr
V1 = 1.5 L
V2 = ?
Step 2: use Boyle’s law to solve:
(56)(1.5)= (150)(V2)
V2 = (56)(1.5)
150
V2 = 0.56 L
Calculating Pressure
In a car engine the gaseous fuel-air mixture enters the
cylinder and is compressed by a moving piston before it is
ignited. In a certain engine the initial cylinder volume is
0.725-L. After the piston moves up, the volume is 0.075-L.
The mixture initially has a pressure of 1.00 atm. Calculate
the pressure of the compressed mixture.
Step 1: write down the information given:
P1 = 1.00 atm
P2 = ?
V1 = 0.725 L V2 = 0.075 L
Step 2: use Boyle’s law to solve:
(1.00)(0.725)= (P2 )(0.075)
P2 = (1.00)(0.725)
0.075
P2 = 9.7 atm
Boyle’s Law Practice Problems:
Calculate the missing quantity:
1.
2.
3.
4.
5.
6.
V = 249mL at 764 mm Hg; V = ? At 654 mm Hg
V = 1.04 L at 1.21 atm; V = ? At 0.671 atm
V = 525 mL at 1.09 atm; V = 122 mL at ? Atm
V = 2.79 mL at 20.2 atm; V = 209 mL at ? Atm
V = 52.1 L at 755 mm Hg; V = ? At 761 mm Hg
What pressure would be needed to compress 25.1 mL of
Hydrogen at 1.01 atm to 25% of its original volume?
7. If the pressure on a 1.04-L sample of gas is doubled, what will
be the new volume of the gas?
8. A 1.04-L sample of gas at 759 mm Hg pressure is expanded until
its volume is 2.24 L, what will the pressure be in the expanded
gas sample be?