# Boyle’s Law

Boyle’s Law says that gas volume is inversely proportional to gas pressure when we hold temperature constant. Inversely proportional means that, as you increase one, the other decreases, and vice versa. As you increase the pressure of a gas, its volume decreases. And as you decrease the volume of a gas its pressure increases. The reverse is also true.

The equation for Boyle’s Law is:

This equation says that the original pressure of a gas P_{1} times its original volume V_{1} is equal to the new pressure P2 times the new volume V_{2}.

This graph illustrates this inverse relationship. As volume decreases, pressure increases. At a volume of 12 L, the pressure of the gas is 1 atm. At the lower volume of 6 L, pressure as increased to 2 atm. When we reduced the volume to half its original value (from 12 L to 6 L), we doubled the amount of pressure (from 1 atm to 2 atm).

Let’s solve some sample problems.

**Sample Problem**

A sample of hydrogen at 1.5 atm had its pressure decreased to 0.50 atm, producing a new volume of 750 mL. What was its original volume?

First, we need to identify our variables. We’re given a sample of hydrogen at 1.5 atm, so let’s label this value P_{1}, the original pressure.

Then its pressure is decreased to 0.50 atm. We’ll label this new pressure P_{2}.

P_{1} = 1.5 atm

P_{2} = 0.50 atm

When the pressure is decreased to 0.50 atm, we have a new volume of 750 mL, which we’ll label V2. We’re asked to find the original volume, which we’ll label V1.

V_{1} = ?

V_{2} = 1.5 atm = 750 mL

Boyle’s Law is:

To solve for our unknown V_{1}, we isolate the variable by dividing each side of the equation by P_{1}.

Our equation now becomes:

Plugging in our values for P_{2}, V_{2} and P_{1}:

*The original volume was 250 mL.*

**Sample Problem**

A 175 mL sample of neon had its pressure changed from 75 kPa to 150 kPa. What is its new volume?

We are given a volume of 175 mL, which we’ll call V_{1}.

We are also told that the pressure changed from 75 kPa, which we’ll call P_{1}, to 150 kPa, which we’ll call P_{2}. We want to find its new volume, V_{2}.

P_{1} = 75 kPa

P_{2} = 150 kPa

V_{1} = 175 mL

V_{2} = ?

To solve for V_{2}, we isolate the variable by dividing each side of the equation by P_{2}:

Our equation now becomes:

Plugging in our values for P_{1}, V_{1} and P_{2}:

*The new volume V _{2} is 88 mL.*