1.1 What is Chemistry?

14.2. Gas Laws http://www.ck12.org

Combined Gas Law

We can combine the relationships described in Boyle’s law, Charles’s law, and Gay-Lussac’s law to create a com-
bined gas law that relates pressure, volume, and temperature.
P 1 V 1
T 1 =

P 2 V 2

T 2

We can use this expression to predict changes to these variables for a given chemical system.

Example 14.6

A helium-filled balloon has a volume of 50.0 L at 25°C and 1.08 atm. What volume will it have at 0.855 atm and
10.°°C?

P 1 = 1 .08 atm,P 2 = 0 .855 atm

V 1 = 50 .0 L,V 2 =?

T 1 = 25 ◦C+ 273 =298 K,T 2 = 10 ◦C+ 273 =283 K

V 2 =

P 1 T 2 V 1

P 2 T 1

V 2 =

( 1 .08 atm)(283 K)( 50 .0 L)

( 0 .855 atm)(298 K)

= 60 .0 L

Avogadro’s Law

In 1811, shortly after the work of Charles and Gay-Lussac, Amadeo Avogadro (1776-1856) was also studying the
relationships between pressure, volume, and temperature. He postulated that if you compare two samples of an
ideal gas at the same temperature, pressure, and volume, they contain the same number of molecules. This became
known asAvogadro’s Law. This means that at a given pressure and temperature, the volume of a sample is directly
proportional to the number of molecules present.
V
n=k
Where:

V is the volume of the gas

n is the amount of gas particles (generally measured in moles)

k is a proportionality constant

Ideal Gas Law

If we add Avogadro’s Law into the combined gas law, we get the following equation:
PV
T n=constant

Unlike the constants for the other gas laws, this constant is given a special name. The ideal gas constant (R) has the
same value for any sample of any ideal gas. A more common way to write theideal gas lawis the following:

PV=nRT

Recall that 1 mol of an ideal gas at 1 atm of pressure and 0°C (standard temperature and pressure) occupies a volume
of 22.4 L. We can use this information to calculate the value of R: