### Video Transcript

In this video, we will learn how to
use molar gas volume under standard conditions to calculate the volume and number of
moles of a gas. In 1811, Italian scientist Amedeo
Avogadro hypothesized that gases of equal volume at the same temperature and
pressure contain the same number of gas particles. This hypothesis is the basis for
what we call Avogadro’s law. This law states that at a constant
temperature and pressure, the volume and number of moles of a gas are directly
proportional. This means that as the number of
moles of a gas are increased, the volume occupied by the gas will also increase at a
constant rate. Likewise, if the number of moles of
a gas are decreased, the volume occupied by the gas will decrease at a constant
rate.

We can see Avogadro’s law in action
when we blow up a balloon. When the piston of the air pump is
depressed, more air or more moles of gas is added to the balloon, and the volume of
the balloon increases. Avogadro’s law can be expressed by
the proportionality statement which reads “Volume is directly proportional to the
number of moles.” If a graph is made of the number of
moles of gas versus its volume, the data points will exactly fit a linear trend line
which passes through the origin. It is important to recognize that
Avogadro’s law only holds true when the gas is maintained at a constant temperature
and pressure. If either of these variables are
changed when performing an experiment, the volume of a gas and the number of moles
of gas will no longer be directly proportional.

Let’s learn more about direct
proportions to expand our understanding of Avogadro’s law. Here is a graph of a generic
proportion. 𝑦 is directly proportional to
𝑥. The equation for the trend line of
a direct proportion has the same general formula as a linear equation: 𝑦 equals 𝑘
times 𝑥 or 𝑦 equals 𝑥 times 𝑘, where 𝑦 and 𝑥 are the variables in direct
proportion and 𝑘 is a proportionality constant, a value used to relate 𝑥 and
𝑦. Shown here is what we know thus far
about Avogadro’s law: volume is directly proportional to the number of moles of gas
and the corresponding graph.

In comparing a generic proportion
with Avogadro’s law, we can surmise that the trend line for the number of moles of
gas versus volume has the equation volume equals the number of moles times a
proportionality constant. The proportionality constant used
to relate volume and the number of moles of a gas is given the symbol capital 𝑉
subscript 𝑚 and is called the molar gas volume. Molar gas volume is a
proportionality constant that relates the volume and number of moles of a gas. It indicates the volume occupied by
one mole of gas at a specific temperature and pressure and typically has a unit of
liters per mole.

When looking at a graph of the
number of moles of a gas versus volume, the slope of the trend line is equal to the
molar gas volume. The volume a gas occupies is
dependent on the temperature and pressure. Therefore, the value of the molar
gas volume will change if temperature and/or pressure is changed. As changing the temperature and/or
pressure affects both volume and molar gas volume, it is useful to define a standard
temperature and pressure that can be used as reference conditions. Standard temperature is defined as
zero degrees Celsius and standard pressure is defined as one atmosphere. We often refer to standard
temperature and pressure by using the abbreviation STP.

Let’s consider one mole of oxygen
gas at STP. One mole of oxygen gas contains
6.022 times 10 to the 23rd molecules of oxygen gas and has a mass of 32 grams. At standard temperature and
pressure, one mole of oxygen gas will have a volume of 22.4 liters. Now let’s consider one mole of
methane gas. One mole of methane gas contains
6.022 times 10 to the 23rd molecules of methane and has a mass of 16 grams. Like one mole of oxygen gas at STP,
one mole of methane gas at STP also has a volume of 22.4 liters. As it turns out, one mole of any
gas at standard temperature and pressure will occupy a volume of 22.4 liters.

By using the equation volume equals
the number of moles times the molar gas volume, we can determine that the molar gas
volume of any gas at standard temperature and pressure is 22.4 liters per mole. When this molar gas volume value is
substituted back into the equation, we produce an equation that can be used to
determine the volume of a gas or the number of moles of a gas at standard
temperature and pressure. Once again, it’s important to
recognize that the molar gas volume of 22.4 liters per mole and the subsequent
equation are only valid when the temperature is zero degrees Celsius and the
pressure is one atmosphere. Now that we’ve learned about
Avogadro’s law, molar gas volume, and standard conditions, let’s take a look at a
few questions.

Under standard temperature and
pressure, STP, which of the following quantities of gas will occupy the largest
volume? (A) One mole of C2H4, (B) five
moles of H2, (C) 0.5 moles of N2, (D) two moles of Cl2, (E) three moles of O2.

Avogadro’s law states that at
constant temperature and pressure, the volume and number of moles of a gas are
directly proportional. This means that if the number of
moles of a gas are increased, the volume will also increase at the same rate. For example, one mole of gas will
occupy a certain volume. Two moles of gas will occupy twice
as much volume. The number of moles was doubled,
and the volume doubled. The amount of space a gas occupies
is dependent on the temperature and pressure. All of the gases in this question
are under standard temperature and pressure, or STP. Standard temperature and pressure
are zero degrees Celsius and one atmosphere, respectively.

At STP, one mole of any gas will
occupy a volume of 22.4 liters. Doubling the number of moles of gas
will double the volume. Thus, two moles of any gas at STP
will have a volume of 44.8 liters, and three moles of any gas at STP will have a
volume of 67.2 liters. The question asked us to determine
which quantity of gas will occupy the largest volume. As increasing the number of moles
increases the volume, we should choose the answer which has the greatest number of
moles of gas. This means that the correct answer
is answer choice (B). Five moles of hydrogen gas will
occupy the largest volume under standard temperature and pressure.

Under standard temperature and
pressure, STP, a gas occupies a volume of two liters. How many moles of gas molecules are
there? Give your answer to two decimal
places.

Avogadro’s law states that at
constant temperature and pressure, the volume and number of moles of a gas are
directly proportional. This proportion can be expressed by
the equation 𝑉 equals 𝑛𝑉 subscript 𝑚, where 𝑉 is the volume in liters, 𝑛 is
the number of moles, and 𝑉 subscript 𝑚 is the molar gas volume, a proportionality
constant that indicates the volume occupied by one mole of gas at a specific
temperature and pressure. Molar gas volume has the unit of
liters per mole. In this question, the gas is under
standard temperature and pressure, abbreviated STP. Standard temperature and pressure
are zero degrees Celsius and one atmosphere, respectively. At STP, one mole of any gas will
occupy a volume of 22.4 liters and have a molar gas volume of 22.4 liters per
mol.

Looking at the question, we see
that the gas occupies a volume of two liters, and we want to determine how many
moles of gas molecules there are. We also know that as the gas is
under standard temperature and pressure, we can use 22.4 liters per mol as the molar
gas volume. We can then substitute the volume
and molar gas volume into the equation and rearrange to solve for the number of
moles. We perform the calculation and
determine that the number of moles is equal to 0.08928 moles. But the question asked us to give
our answer to two decimal places. Rounding appropriately, we have
determined that there are 0.09 moles of gas molecules in two liters of gas under
standard temperature and pressure.

What volume would 8.5 grams of NH3
gas occupy at standard temperature and pressure, STP, taking the molar gas volume to
be 22.4 liters per mole? Give your answer in units of
liters. N equals 14 grams per mole. H equals one gram per mole.

Molar gas volume is a
proportionality constant that relates the volume and number of moles of a gas via
the equation 𝑉 equals 𝑛𝑉 subscript 𝑚, where 𝑉 is the volume in liters, 𝑛 is
the number of moles, and 𝑉 subscript 𝑚 is the molar gas volume. The molar gas volume indicates the
volume occupied by one mole of gas at a specific temperature and pressure. In this question, the NH3 gas is at
standard temperature and pressure, abbreviated as STP. Standard temperature and pressure
are zero degrees Celsius and one atmosphere, respectively. We are told that the molar gas
volume at STP is 22.4 liters per mole. This means that one mole of gas at
standard temperature and pressure will occupy a volume of 22.4 liters.

The question asked us to determine
a volume of gas given a mass and the molar gas volume. As the problem did not provide the
number of moles of gas, we will need to convert the mass of NH3 into moles of
NH3. This can be accomplished by using
the equation 𝑛 equals lowercase 𝑚 divided by capital 𝑀, where 𝑛 is the number of
moles, lowercase 𝑚 is the mass in grams, and capital 𝑀 is the molar mass in grams
per mole. The mass was provided in the
question, but we will need to determine the molar mass of ammonia, NH3.

The molar mass of ammonia can be
calculated by summing the average molar masses of the constituent atoms, which were
provided in the question. We need to multiply the average
molar mass of hydrogen by three as there are three atoms of hydrogen in each
molecule of ammonia. We perform the calculation and
determine the molar mass of ammonia to be 17 grams per mole. We can then substitute the mass
given in the question and the molar mass into the equation to determine the number
of moles of ammonia to be 0.5 moles.

Now that we know the number of
moles and the molar gas volume, we are ready to solve for the volume. We substitute the value we
determined for the number of moles and the molar gas volume given in the question
into the equation. We perform the calculation and
determine the volume to be 11.2 liters.

Now let’s summarize what we’ve
learned with the key points. Avogadro’s law states that at
constant temperature and pressure, volume is directly proportional to the number of
moles. This can be expressed by the
equation 𝑉 equals 𝑛 times 𝑉 subscript 𝑚, where 𝑉 is the volume, 𝑛 is the
number of moles, and 𝑉 subscript 𝑚 is the molar gas volume. Molar gas volume is a
proportionality constant that indicates the volume occupied by one mole of gas at a
specific temperature and pressure. It is often useful to use standard
conditions when measuring gases. Standard temperature and pressure,
abbreviated STP, are zero degrees Celsius and one atmosphere, respectively. All gases at standard temperature
and pressure will have a molar gas volume of 22.4 liters per mole.