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Molar Volume: Using Avogadro's Law to Calculate the Quantity or Volume of a Gas

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  • 1:07 Pressure
  • 1:47 Volume
  • 2:25 Volume of a Mole
  • 4:13 Avogadro's Law Equation
  • 5:51 Practice Question 1
  • 7:05 Practice Question 2
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Lesson Transcript
Instructor: Kristin Born

Kristin has an M.S. in Chemistry and has taught many at many levels, including introductory and AP Chemistry.

Have you ever wondered why a balloon expands when you blow it up? How something as light as air is able to exert a force large enough to inflate a balloon? In this lesson, you will learn about the relationship between the volume of a container filled with a gas and the number of gas particles that container holds. This relationship is known as Avogadro's Law.

What Causes a Beach Ball to Expand?

Johnny Dalton and his family have been spending a relaxing day at the beach on Ideal Island. Johnny finishes up building his sandcastle, and he decides he would like to play with his beach ball. The only problem is that it's not inflated. He takes a few deep breaths and starts inflating it. As he's inflating the beach ball, he wonders, 'What is causing this ball to expand?' He decides to investigate further.

Each time he blows a breath into the ball, he sees it expand a little more. He sees that his breath is causing the ball to expand, but what specifically in his breath causes the expansion? Well, when we inhale, we breathe in a mixture of mostly nitrogen and oxygen, and when we exhale, we breathe out mostly nitrogen, oxygen, and carbon dioxide. So, the particles causing the expansion are nitrogen, oxygen, and carbon dioxide molecules.

Pressure

Recall that when the particles of a gas hit the insides of the container, it causes them to exert pressure on the inside of that container. Those little exhaled particles are essentially hitting the inside of the beach ball, causing it to inflate more and more with each little collision. The more particles that are colliding, the more pressure is being exerted, and the larger the beach ball gets. So, with each breath, Johnny is really just filling the ball with particles that will eventually contribute enough pressure to fill the ball to its maximum volume.

Volume

Just as Johnny is finishing up inflating his beach ball, he notices it has the words '1 mole' printed on the outside of it in large bold letters. What could this mean? Remember that very large number that chemists use to count very small things? That number is called a mole, and it represents 6.02 x 1023 . Johnny figures that in order to inflate his beach ball completely, it needs to have 6.02 x 1023 particles in it.

Volume of a Mole

So, just how big is the inflated beach ball? It turns out that it is 22.4 L (or about 6 gallons) in size. Now, as you may know, when it comes to gases, temperature and pressure are extremely important. They change the way the gas particles behave, so it's worth noting that the atmospheric pressure on this beach is 1 atmosphere or 760 mmHg or, as scientists might say, standard pressure. It is also important to mention that the temperature on this beach is 0 degrees Celsius (I know that seems kind of cold) or 273 Kelvin or what is known as standard temperature.

Johnny discovered that at standard temperature and standard pressure, 1 mole of ideal gas particles takes up 22.4 L of space. And, because we aren't dealing with super low temperatures and super high pressures, real gases will only deviate slightly from this 22.4 value. The difference is so small that when it comes to real gases, the 22.4 L value is almost always used.

So, when Johnny completely inflated his 1 mole beach ball, it must have contained 6.02 x 1023 particles! This relationship between the number of particles (n) and the volume (V) of a gas is called Avogadro's law. It simply relates what you probably already know: the more gas an expandable container has, the bigger it will be!

Avogadro's Law Equation

You have probably seen this relationship in action when you have blown up a balloon, inflated a bicycle tire, or even taken a deep breath. Each time you draw air into your lungs, they expand. Keep in mind this relationship is only between the number of particles of a gas (n) and the volume of a gas (V). The pressure and temperature are held constant. We can represent this relationship in a couple of different ways.

First, we can relate it graphically: as the number of moles of a gas increases, the volume of a gas also increases. This graph shows that if the temperature and pressure were held constant, the number of particles (n) and the volume (V) are directly related to each other.

The number of particles and the volume are directly related
n and V are directly related

Avogadro's law can also be represented as an equation: V1/n1 = V2/n2. Notice in this equation we have 1s and 2s. Often when discussing gas behaviors, we are interested in some sort of change that's taking place. The 1s will represent the 'before' measurements, and the 2s represent the 'after' measurements. So, the volume 'before' divided by the number of moles 'before' is equal to the volume 'after' divided by the number of moles 'after.'

The equation representing the relationship between the number of particles and pressure
Avogadros Law Equation Chalkboard

One final thing to mention about this equation is you can use any unit for your volume unit, as long as both volume units are the same. You can also use any unit for your number of particles unit - moles or atoms or molecules - as long as both number of particles units are the same.

Practice Question 1

Let's see this put into practice. Say you have a balloon that contains 0.5 moles of helium, and it has a volume of 10 L. Now you decide to double the volume to 20 L. How many more moles of gas would you need to add to the balloon?

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