Question

A gas bubble has a volume of 0.650 mL at the bottom of a lake, where the pressure is
3.46-atm. What is the volume of the bubble at the surface of the lake, where the pressure is
1.00-atm? Assume that the temperature is constant. Will the new volume be bigger or smaller?

Answer 1

Considering the Boyle's law, as the pressure decreases, volume increases and has a value of 2.246 mL.

Boyle's law

Boyle's law establishes the relationship between the pressure and the volume of a gas when the temperature is constant.

This law says that the volume occupied by a given mass of gas at constant temperature is inversely proportional to the pressure. This means that if the pressure increases, the volume decreases, while if the pressure decreases, the volume increases.

Boyle's law is expressed mathematically as:

P×V=k

If an initial state 1 and a final state 2 are analyzed, Boyle's law is expressed as:

P1×V1=P2×V2

Volume at the surface of the lake

In this case, you know:

• P1= 3.46 atm
• V1= 0.650 mL
• P2= 1 atm
• V2= ?

Replacing in Boyle's law:

3.46 atm× 0.650 mL= 1 atm×V2

Solving:

V2= (3.46 atm× 0.650 mL)÷ 1 atm

V2= 2.246 mL

Finally, as the pressure decreases, volume increases and has a value of 2.246 mL.

Learn more about Boyle's law:

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