1. 7.3 Pressure and Volume (Boyle’s Law)
Chapter 7 Gases
7.3 Pressure and Volume (Boyle’s Law)

2. Boyle’s Law Boyle’s law states that
the pressure of a gas is inversely related to its volume when T and n are constant
if the pressure (P) increases, then the volume (V) decreases 2

3. PV Constant in Boyle’s Law
The product P x V is constant as long as T and n do not change.
P1V1 = atm x 2.0 L = 16 atm L
P2V2 = atm x 4.0 L = 16 atm L
P3V3 = atm x 8.0 L = 16 atm L
Boyle’s law can be stated as
P1V1 = P2V2 (T, n constant)

4. Solving for a Gas Law Factor
The equation for Boyle’s law can be rearranged to
solve for any factor.
P1V1 = P2V Boyle’s Law
To solve for V2 , divide both sides by P2.
P1V1 = P2V2
P P2
V1 x P1 = V2 P2

5. Boyle’s Law and Breathing: Inhalation
During inhalation,
the lungs expand
the pressure in the lungs decreases
air flows towards the lower pressure in the lungs

6. Boyle’s Law and Breathing: Exhalation
During exhalation,
lung volume decreases
pressure within the lungs increases
air flows from the higher pressure in the lungs to the outside

7. Guide to Calculations with Gas Laws

8. Calculation with Boyle’s Law
Freon-12, CCl2F2, is used in refrigeration systems. What is the new volume (L) of an 8.0 L sample of Freon gas after its pressure is changed from 550 mmHg to 2200 mmHg at constant T?
STEP 1 Set up a data table:
Conditions 1 Conditions Know Predict
P1 = 550 mmHg P2 = 2200 mmHg P increases
V1 = 8.0 L V2 = ? V decreases

9. Calculation with Boyle’s Law (continued)
STEP 2 Solve Boyle’s law for V2. When pressure
increases, volume decreases.
P1V1 = P2V2
V = V1 x P1 P2
STEP 3 Set up problem
V = L x 550 mmHg = L
2200 mmHg
pressure ratio
decreases volume

10. Learning Check
For a cylinder containing helium gas, indicate if cylinder A or cylinder B represents the new volume for the following changes (n and T are constant):
1) Pressure decreases
2) Pressure increases

11. Solution
For a cylinder containing helium gas, indicate if cylinder A or cylinder B represents the new volume for the following changes (n and T are constant):
1) Pressure decreases (cylinder B)
2) Pressure increases (cylinder A)

12. Learning Check
If a sample of helium gas has a volume of 120 mL and a pressure of 850 mmHg, what is the new volume if the pressure is changed to 425 mmHg?
1) 60 mL ) 120 mL 3) 240 mL

13. Solution Conditions 1 Conditions 2 Know Predict
3) 240 mL
Conditions 1 Conditions Know Predict
P1 = 850 mmHg P2 = 425 mmHg P decreases
V1 = 120 mL V2 = ? V increases
V2 = V1 x P1 = mL x mmHg = mL
P mmHg Pressure ratio
increases volume

14. Learning Check
A sample of helium gas in a balloon has a volume of 10. L at a pressure of atm. At 1.40 atm (T constant), is the new volume represented by A, B, or C?

15. Solution A sample of helium gas in a balloon has a volume of
10. L at a pressure of atm. At a higher pressure
(T constant), the new volume is represented by the
smaller balloon.

16. Learning Check A) 3.2 L B) 6.4 L C) 12.8 L
If the sample of helium gas has a volume of 6.4 L at a pressure of atm, what is the new volume when the pressure is increased to 1.40 atm (T constant)?
A) 3.2 L B) 6.4 L C) 12.8 L

17. Solution STEP 1 Set up data table (conditions)
A) 3.2 L
STEP 1 Set up data table (conditions)
Conditions 1 Conditions Know Predict
P1 = 0.70 atm P2 = 1.40 atm P increases
V1 = 6.4 L V2 = ? V decreases
STEP 2 Solve for Boyles law for V2
V2 = V1 x P1 P2
STEP 3 Set up problem
V2 = L x atm = L
1.40 atm
Volume decreases when there is an increase in the pressure (temperature is constant).

18. Learning Check (T and n constant) 1) 200 mmHg 2) 400 mmHg 3) 1200 mmHg
A sample of oxygen gas has a volume of 12.0 L at 600 mmHg. What is the new pressure when the volume changes to 36.0 L?
(T and n constant)
1) 200 mmHg
2) 400 mmHg
3) mmHg

19. Solution P2 = P1 x V1 V2 600 mmHg x 12.0 L = 200 mmHg 36.0 L
Conditions 1 Conditions 2 Know Predict
P1 = 600 mmHg P2 = ? P decreases
V1 = 12.0 L V2 = L V increases
P2 = P1 x V1 V2
600 mmHg x L = 200 mmHg L