14.2. Gas Laws http://www.ck12.org
Step 3: Think about your result.
Both the increase in pressure and the decrease in temperature cause the volume of the gas sample to decrease. Since
both changes are relatively small, the volume does not decrease dramatically.
Practice Problem- A 400. mL sample of gas at 15°C and 113 kPa is heated to 227°C while expanding into a 900. mL container.
What is the new pressure of the gas in kPa?
It may seem challenging to remember all the different gas laws introduced so far. Fortunately, Boyle’s, Charles’s,
and Gay-Lussac’s Laws can all be easily derived from the combined gas law. For example, consider a situation
where a change occurs in the volume and pressure of a gas while the temperature is being held constant. In that
case, it can be said that T 1 = T 2. Look at the combined gas law and cancel the T variable out from both sides of the
equation. What is left over is Boyle’s Law: P 1 ×V 1 = P 2 ×V 2. Likewise, if the pressure is constant, then P 1 = P 2 ,
and canceling P out of the equation leaves Charles’s Law. If the volume is constant, then V 1 = V 2 , and canceling V
out of the equation leaves Gay-Lussac’s Law.
Avogadro’s Law
You have learned about Avogadro’s hypothesis: equal volumes of any gas at the same temperature and pressure
contain the same number of molecules. It follows that the volume of a gas is directly proportional to the number
of moles of gas present in the sample.Avogadro’s Lawstates that the volume of a gas is directly proportional to
the number of moles of gas when the temperature and pressure are held constant. The mathematical expression of
Avogadro’s Law is
V=k×n andV 1
27.14 N
=
V 2
n 2where n is the number of moles of gas, and k is a constant. Avogadro’s Law can be observed whenever you blow up
a balloon. The volume of the balloon increases as you add more gas particles to the balloon by blowing it up.
If the container holding the gas is rigid rather than flexible, pressure can be substituted for volume in Avogadro’s
Law. Adding gas to a rigid container makes the pressure increase.
Sample Problem 14.5: Avogadro’s Law
A balloon has been filled to a volume of 1.90 L with 0.0920 mol of helium gas. If an additional 0.0210 mol of helium
is added to the balloon while the temperature and pressure are held constant, what is the new volume of the balloon?
Step 1: List the known quantities and plan the problem.
Known
- V 1 = 1.90 L
- n 1 = 0.0920 mol
- n 2 = 0.0920 + 0.0210 = 0.1130 mol
Unknown
- V 2 =? L