JSS 3: BOYLE'S LAW

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BOYLE'S LAW states that the volume of a given mass of a gas is inversely proportional to the pressure provided the temperature remains constant

V ∝ 1/P (V is inversely proportional to P)
V = k/P
P V = k
where: P = Pressure
            V = Volume
            k = a constant value for a given      
                  sample of gas at a constant 
                   temperature.

P₁V₁ = k and P₂V₂ = k, we can set them equal to each other. This gives us the most practical form of Boyle's Law:
                          P₁V₁ = P₂V₂
Where:
         P₁ and V₁ are the initial pressure and 
         volume.
         P₂ and V₂ are the final pressure and 
         volume

              Graph of Boyle's law 

    Simple calculations on Boyle's law
1. The volume of a given mass of a gas at 10°C and 600mmHg is 140cm³. What will be the volume of the gas at 10°C, if the pressure is 1200mmHg.
Solution:
P₁V₁ = P₂V₂
600 x 140 = 1200 x V₂
84000 = 1200 x V₂
V₂ = 84000 / 1200
V₂ = 70cm³

2. A sample of oxygen gas has a volume of 220 mL when its pressure is 2.2 atm. What will the volume of the gas be at a pressure of 1.2 atm if the temperature remains constant?

Solution:
Initial Volume (V₁) = 220 mL
Initial Pressure (P₁) = 2.2 atm
Final Pressure (P₂) = 1.2 atm
To Find: Final Volume (V₂) = ?
We can calculate the final volume of the gas using Boyle’s law.

P₁V₁ = P₂V₂
2.2  ×  220 = 1.2 × V₂
484 = 1.2 × V₂
484 / 1.2 = V₂
V₂ = 403.33 mL ≈ 403mL

Class activities
1. When the pressure on a gas increases at constant temperature, the volume will:
(a) Increase (b) Decrease (c) Remain constant (d) First increase then decrease

2. Boyle's Law states that the pressure of a fixed mass of gas is inversely proportional to its:
(a) Temperature (b) Volume (c) Mass (d) Density

3. According to Boyle's Law, the temperature of the gas is kept:
(a) Increasing (b) Decreasing (c) Constant (d) Changing

4. If the volume of a gas is reduced at constant temperature, the pressure will:
(a) Increase (b) Decrease (c) Remain constant (d) Become zero

5. The mathematical expression for Boyle's Law is:
(a) V₁/T₁ = V₂/T₂ (b) P₁V₁ = P₂V₂ (c) PV = nRT (d) P₁/T₁ = P₂/T₂

6. Which of the following best illustrates Boyle's Law?
(a) Inflating a balloon (b) Compressing air in a syringe (c) Melting ice (d) Boiling water

7. If the pressure on a gas is doubled at constant temperature, its volume will:
(a) Double (b) Triple (c) Be halved (d) Remain unchanged

8. Boyle's Law applies only when the ________ remains constant.
(a) Pressure (b) Volume (c) Temperature (d) Density

9. A gas occupies 400 cm³ at a pressure of 100 kPa. If the pressure is increased to 200 kPa at constant temperature, the new volume will be:
(a) 100 cm³ (b) 200 cm³ (c) 400 cm³ (d) 800 cm³

10. Which of the following is an application of Boyle's Law?
(a) Hot air balloon (b) Bicycle pump (c) Expansion of railway tracks (d) Evaporation of water

Assignment 
A certain volume of a gas at 20°C has a pressure of 400mmHg. If at the same temperature, this pressure is decreased to 200mmHg, the gas has now occupying a volume of 100cm³. Calculate the initial volume of the gas.

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