### 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.