# Boyle's Law Explained With Example Problem

## Volume's inversely proportional to pressure if temperature's constant

Boyle's gas law states that the volume of a gas is inversely proportional to the pressure of the gas when the temperature is held constant. Anglo-Irish chemist Robert Boyle (1627–1691) discovered the law and for it he is considered the first modern chemist. This example problem uses Boyle's law to find the volume of gas when pressure changes.

## Boyle's Law Example Problem

• A balloon with a volume of 2.0 L is filled with a gas at 3 atmospheres. If the pressure is reduced to 0.5 atmospheres without a change in temperature, what would be the volume of the balloon?

### Solution

Since the temperature doesn't change, Boyle's law can be used. Boyle's gas law can be expressed as:

• PiVi = PfVf

where

• Pi = initial pressure
• Vi = initial volume
• Pf = final pressure
• Vf = final volume

To find the final volume, solve the equation for Vf:

• Vf = PiVi/Pf
• Vi = 2.0 L
• Pi = 3 atm
• Pf = 0.5 atm
• Vf = (2.0 L) (3 atm) / (0.5 atm)
• Vf = 6 L / 0.5 atm
• Vf = 12 L

The volume of the balloon will expand to 12 L.

## More Examples of Boyle's Law

As long as the temperature and number of moles of gas remain constant, Boyle's law means doubling the pressure of a gas halves its volume. Here are more examples of Boyle's law in action:

• When the plunger on a sealed syringe is pushed, the pressure increases and the volume decreases. Since the boiling point is dependent on pressure, you can use Boyle's law and a syringe to make water boil at room temperature.
• Deep-sea fish die when they're brought from the depths to the surface. The pressure decreases dramatically as they are raised, increasing the volume of gases in their blood and swim bladder. Essentially, the fish pop.
• The same principle applies to divers when they get "the bends." If a diver returns to the surface too quickly, dissolved gases in the blood expand and form bubbles, which can get stuck in capillaries and organs.﻿﻿
• If you blow bubbles underwater, they expand as they rise to the surface. One theory about why ships disappear in the Bermuda Triangle relates to Boyle's law. Gases released from the seafloor rise and expand so much that they essentially become a gigantic bubble by the time they reach the surface. Small boats fall into the "holes" and are engulfed by the sea.
View Article Sources
1. Walsh C., E. Stride, U. Cheema, and N. Ovenden. "A combined three-dimensional in vitro–in silico approach to modelling bubble dynamics in decompression sickness." Journal of the Royal Society Interface, vol. 14, no. 137, 2017, pp. 20170653, doi:10.1098/rsif.2017.0653

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