Boyle’s Law

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:

boyles-law

This equation says that the original pressure of a gas P1 times its original volume V1 is equal to the new pressure P2 times the new volume V2.

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).

boyles-law-graph

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 P1, the original pressure.

Then its pressure is decreased to 0.50 atm. We’ll label this new pressure P2.

P1 = 1.5 atm

P2 = 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.

V1 = ?

V2 = 1.5 atm = 750 mL

Boyle’s Law is:

boyles-law

To solve for our unknown V1, we isolate the variable by dividing each side of the equation by P1.

v1-isolate

Our equation now becomes:

V1

Plugging in our values for P2, V2 and P1:

250mL

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 V1.

We are also told that the pressure changed from 75 kPa, which we’ll call P1, to 150 kPa, which we’ll call P2. We want to find its new volume, V2.

P1 = 75 kPa

P2 = 150 kPa

V1 = 175 mL

V2 = ?

boyles-law

To solve for V2, we isolate the variable by dividing each side of the equation by P2:

V2-isolate

Our equation now becomes:

V2

Plugging in our values for P1, V1 and P2:

88mL

The new volume V2 is 88 mL.