# Calculation questions on Boyle's law

### Worked Examples on Boyle's Law:

Boyle's law states that the volume of a given mass of gas is inversely proportional to its pressure, provided the temperature remains constant.

The English physicist, Robert Boyle (1627 - 1691) formulated this law in 1662.

• #### Question 1

10dm3 gas at 1.5 atmosphere is heated at constant temperature. If the volume of the gas increases to 20dm3, calculate its pressure at this new volume.

• Solution

Step 1: List the known quantities from the question

• Initial Volume (V1) =10dm3

• Initial Pressure (P1) = 1.5atm

• Final Volume (V2) = 20dm3

• Final Pressure (P2) = Unknown

Step 2: Apply the formula for Boyles law to find the final pressure (P2). Below is the formula:

• V1 x P1 = Vx P2

Step 3: Make P2 the subject of the formula.

• V1 x P1 = V2 x P2

• P2 = V1 x P/ V2

• P2 = (V1 x P1) ÷ V2

Step 4: Substitute values into the formula to find the final volume (V2).

• P2 = (10 x 1.5) ÷ 20

• P2 = 15 ÷ 20

• P2 = 0.75atm

• Notice that the final pressure (P2) decreases while the final volume (V2) increases. This shows that they are inversely proportional, and this is in accordance with Boyle's law.

• #### Question 2

A balloon is filled with helium gas to a volume 0.5L at 3atm. This balloon was placed in a pressure compartment of 1530mmHg. Determine the new volume occupied by the helium gas in the balloon.

• Solution

Step 1: List the known quantities from the question

• Initial Volume (V1) = 0.5L

• Initial Pressure (P1) = 3atm

• Final Volume (V2) = Unknown

• Final Pressure (P2) = 1530mmHg

Step 2: The value for both pressures should be in the same unit. Understand that 1 atmosphere equals 760 millimeters of mecury. Convert the final pressure (P2) from millimeters of mecury (mmHg) to atmosphere (atm) by dividing by 760.

• P2 = 1530 ÷ 760 = 2atm

• P2 = 2atm

Step 3: Apply the formula for Boyle's law to find the final volume (V2).

• Vx P1 = V2 x P2

Step 4: Make V2 the subject of the formula.

• V1 x P1 = V2 x P2

• V2 = V1 x P1 / P2

• V2 = (V1 x P1) ÷ P2

Step 5: Substitute values into the formula to find the final volume (V2).

• V2 = (0.5 x 3) ÷ 2

• V2 = 1.5 ÷ 2

• V2 = 0.75L

• Notice that the final volume (V2) increases while the final pressure (P2) decreases. This implies that they are inversely proportional, which is in accordance with Boyle's law.

• #### Question 3

Convert 2L of oxygen gas at 380mmHg to its new volume at standard pressure. (Oxygen=16)

• Solution

Step 1: List the known quantities from the question.

• Initial Volume (V1) = 2L

• Initial Pressure (P1) = 380mmHg

• Final Volume (V2) = Unknown

• Final Pressure (P2) = Standard Pressure

Step 2: Find the value for standard pressure.

The value for standard pressure is 1atm or 760mmHg. This value is a constant, and may not given in some questions.

• Final Pressure (P2) = 760mmHg

Step 3: Apply the formula for Boyles law to find the final volume (V2).

• Vx P1 = V2 x P2

Step 4: Make V2 the subject of the formula.

• V1 x P1 = V2 x P2

• V2 = V1 x P1 / P2

• V2 = (V1 x P1) ÷ P2

Step 5: Substitute values into the formula to find the final volume (V2).

• V2 = (2 x 380) ÷ 760

• V2 = 760 ÷ 760

• V2 = 1

• Notice that the final volume (V2) decreases while the final pressure (P2) increases. This implies that they are inversely proportional, which is in accordance with Boyle's law.

You can read on molecular and molar mass with worked examples here.

• #### Question 4

If the pressure on a gas is decreased to 1%, Will the volume of the gas increase or decrease?

What percentage will the increase or decrease be?

• Solution

Step 1: Recall the definition of Boyle's law.

• Always understand that Boyle's law involves the volume of a gas and its pressure at a constant temperature.

• This volume and pressure are always inversely proportional. Therefore, when one increases, the other decreases. For instance, when volume increases, pressure decreases; and when pressure increases, volume decreases.

• From the question, since the pressure of the gas was decreased, its volume will increase according to Boyle's law.

• If the pressure decreased by 1%, the increase in volume will be in the same proportion. Therefore, the volume increased by 1% also.

• Notice that the pressure decreases from the question, therefore volume must increase since they are always inversely proportional, according to Boyle's law.

Please read the explanation on real life examples of Boyle's law here.

• #### Question 5

Giving your answer in millimeters of mecury, to what pressure must a 5000mL gas be compressed in order to get into a 1000mL container whose gas was compressed at standard pressure?

• Solution

Step 1: List the known quantities from the question

• Initial Volume (V1) = 5000mL

• Initial Pressure (P1) = Unknown

• Final Volume (V2) = 1000mL

• Final Pressure (P2) = Standard Pressure

Step 2: Find the value for standard pressure.

• The value for standard pressure is 1atm or 760mmHg. This value is a constant (and may not given in some questions).

• Final Pressure (P2) = 760mmHg

Step 3: Apply the formula for Boyles law to find the final pressure (P2). Below is the formula:

• V1 x P1 = Vx P2

Step 3: Make P1 the subject of the formula.

• V1 x P1 = V2 x P2

• P1 = V2 x P/ V1

• P1 = (V2 x P2) ÷ V1

Step 4: Substitute values into the formula to find the initial pressure (P1).

• P1 = (1000 x 760) ÷ 5000

• P1 = 760,000 ÷ 5000

• P1 = 152mmHg

• Notice that the initial pressure (P1) decreases while the initial volume (V1) increases. This shows that they are inversely proportional, and this is in accordance with Boyles law. 