Boyle's gas law states the volume of a gas is inversely proportional to the pressure of the gas when the temperature is held constant. This example problem uses Boyle's law to find the volume of a 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 does not change, Boyle's law can be used. Boyle's gas law can be expressed as:

P_{i}V_{i} = P_{f}V_{f}

where

P_{i} = initial pressure

V_{i} = initial volume

P_{f} = final pressure

V_{f} = final volume

To find the final volume, solve the equation for V_{f}:

V_{f} = P_{i}V_{i}/P_{f}

V_{i} = 2.0 L

P_{i} = 3 atm

P_{f} = 0.5 atm

V_{f} = (2.0 L)(3 atm)/(0.5 atm)

V_{f} = 6 L/0.5

V_{f} = 12 L**Answer:**

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 a 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 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 are brought from the depths up 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 sea floor 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.