Boyles Law

 BOYLE’S LAW

Boyles states that the volume of a given mass of gas is inversely proportional to the pressure provided the temperature remains constant.

 This means that:

• When pressure increases, volume decreases

• When pressure decreases, volume increases

Mathematically,

       V α 1/P

       V = k/P

       PV = k

Hence,         P₁V₁ = P₂V₂

Boyle’s law can be represented graphically as shown below.

1. Pressure vs Volume (inverse curve):

 


2. Pressure vs 1/Volume (straight line):

  

The graph shows that if the pressure is doubled, the volume is reduced to half its former value and if it is halved, the volume is doubled.

 

EXPLANATION OF BOYLE’S LAW USING THE KINETIC THEORY

If a gas is compressed into a smaller space (when the volume of fixed mass of gas is decreased) the molecules of the gas will collide with each other more rapidly ( i.e the gas particles hit the walls of the container more often). This gives rise to an increase in pressure. However, If the volume is increased, the particles have more space to move, so the pressure decreases. 

Examples of Boyle’s Law

• When you push the plunger of a syringe, the air inside is compressed and the pressure increases.

• A bicycle pump works because reducing the volume of air increases its pressure.

Conclusion

Boyle’s Law shows the relationship between the pressure and volume of a gas at constant temperature.

example of calculations on Boyles law 

1. 200cm3 of a gas has a pressure of 510mmHg. What will be its volume if pressure in increased to 780mmHg, assuming there is no change in temperature?

    Solution:

    V₁ = 200cm³, P₁ = 510mmHg,       P₂ = 780mmHg V₂ =?

    Using the expression for Boyle’s law:

       P₁V₁ = P₂V₂

   V₂ = P₁V₁  =  510mmHg x 200cm³ = 130.769 = 131 cm³
                P₂              780mmHg

EASYKEMISTRY

CHEMISTRY TEST – BOYLE’S LAW
Time: 30 minutes

Name: __________________________ Class: __________ Date: __________

Choose the correct option from A–D

1. Boyle’s law states that for a fixed mass of gas at constant temperature,
A. pressure is directly proportional to volume
B. pressure is inversely proportional to volume
C. pressure is equal to volume
D. pressure is proportional to temperature

2. Which of the following is kept constant in Boyle’s law?

A. Pressure
B. Volume
C. Temperature
D. Mass and volume

3. If the volume of a gas is reduced to half at constant temperature, the pressure will

A. remain the same
B. be doubled
C. be halved
D. become zero

4. The mathematical expression for Boyle’s law is

A. V = kP
B. PV = k
C. P + V = k
D. P = k 
    V

5. A gas has a volume of 20 cm³ at a pressure of 2 atm. What will be its volume at 4 atm?

A. 5 cm³
B. 10 cm³
C. 20 cm³
D. 40 cm³

6. According to Boyle’s law, when pressure decreases, the volume of a gas

A. decreases
B. increases
C. remains constant
D. becomes zero

7. Which of the following devices works based on Boyle’s law?

A. Thermometer
B. Barometer
C. Syringe
D. Voltmeter

8. A graph of pressure against volume for a fixed mass of gas at constant temperature is

A. a straight line
B. a curve
C. a horizontal line
D. a vertical line

9. A gas occupies 40 cm³ at 1 atm. What will be its pressure if the volume is reduced to 10 cm³?

A. 2 atm
B. 3 atm
C. 4 atm
D. 5 atm

10. Boyle’s law is valid only when the

A. pressure is constant
B. volume is constant
C. temperature is constant
D. gas is solid

11.   A gas occupies 100 cm³ at 2 atm. What will be its volume at 1 atm, temperature remaining constant?

A. 50 cm³
B. 100 cm³
C. 150 cm³
D. 200 cm³

12.   Which of the following graphs best represents Boyle’s law?

A. Pressure vs Temperature
B. Volume vs Temperature
C. Pressure vs Volume
D. Mass vs Volume

13.  If the pressure of a gas is increased four times, its volume will become
A. four times
B. half
C. one quarter
D. double

14.  A gas occupies 60 cm³ at 3 atm. What will be its volume at 6 atm?
A. 10 cm³
B. 20 cm³
C. 30 cm³
D. 40 cm³

15.  Boyle’s law is useful in explaining the operation of
A. a thermometer
B. a hot-air balloon
C. a bicycle pump
D. a barometer

16.  A gas has a pressure of 4 atm and a volume of 50 cm³. What is the value of PV?
A. 50
B. 100
C. 150
D. 200

17.  A gas occupies 80 cm³ at 5 atm. What will be its volume at 10 atm?
A. 40 cm³
B. 60 cm³
C. 80 cm³
D. 160 cm³

18.  Which of the following statements is correct?
A. Pressure decreases when volume decreases
B. Pressure increases when volume decreases
C. Pressure is constant when volume changes
D. Pressure does not depend on volume

19.  Boyle’s law does not apply when
A. temperature is constant
B. pressure is constant
C. temperature changes
D. volume changes

20.  A gas at 1 atm occupies 500 cm³. What pressure will it have if its volume becomes 250 cm³?
A. 0.5 atm
B. 1 atm
C. 2 atm
D. 4 atm

THEORY QUESTIONS

1. State Boyle’s law. Explain the conditions under which the law is valid.

2. Describe an experiment to verify Boyle’s law. Include a labeled diagram of the apparatus used.

3. Define pressure and volume as used in Boyle’s law and state their SI units.

4. A fixed mass of gas occupies a volume of 40 cm³ at a pressure of 100 kPa.
   Calculate the new volume when the pressure is increased to 200 kPa, assuming temperature remains constant.

5. Explain why Boyle’s law does not hold for real gases at very high pressure.

6. State the mathematical expression of Boyle’s law and explain the meaning of each symbol used.

7. Sketch and explain the graph of pressure against volume for a gas obeying Boyle’s law.

8. Sketch and explain the graph of pressure against the reciprocal of volume (1/V) for Boyle’s law.

9. A gas initially at pressure ( P1 ) and volume ( V1 ) changes to pressure ( P2 ) and volume ( V2 ).
   Derive the Boyle’s law equation relating these quantities.

10. Mention two practical applications of Boyle’s law and explain any one of them.

11.  Explain Boyle's law using the kinetic theory