Lesson Video: Standard Molar Gas Volumes | Nagwa Lesson Video: Standard Molar Gas Volumes | Nagwa

# Lesson Video: Standard Molar Gas Volumes Chemistry

In this video, we will learn how to calculate the molar volume of a gas from the gas volume and number of moles under standard conditions.

18:31

### Video Transcript

This lesson is about standard molar gas volumes or, in simpler terms, under certain conditions, how much space does a gas take up? In this lesson, we will investigate the relationship between the volume, temperature, pressure, and amount in moles of a gas. We will learn how to calculate the molar volume of a gas as well as what constitutes standard conditions. We will also use molar volume and the ideal gas law to calculate the characteristics of a given gas.

Letโs imagine for a moment a big pink balloon. As a thought experiment, what are the ways that we could change the volume of the balloon? Well, the simplest way to change the volume is to change the amount in moles of gas in the balloon. Blow the balloon up and the volume will increase, or let some air out of the balloon and the volume will decrease. We can also change the volume by changing the temperature. If we put the balloon in the fridge, it will shrivel and shrink. Leave it in the sun and the balloon will swell in size.

Lastly, we can also change the air pressure of the room, which will cause the air pressure in the balloon to change and cause the volume to change. We could increase the pressure and reduce the volume by pulling the balloon under water. And we could decrease the pressure and increase the volume by climbing into the low-pressure air atop a mountain. In this video, we will see how these four characteristics of a gas, amount in moles, temperature, pressure, and volume, are related. We will also use some key equations to calculate their values. First, some key concepts.

The molar volume of a gas is the volume occupied by every mole of the gas. Itโs given by the formula ๐ m equals ๐ divided by ๐, where ๐ m is the molar volume, ๐ is the volume occupied by the gas as a whole, and ๐ is the amount in moles of that gas. For example, if one mole of a gas has a volume of 24 liters, the volume per mole is 24 liters divided by one mole equals 24 liters per mole. If we have a smaller 2.4-liter container of a gas with 0.1 moles of the gas in it, the molar volume of that gas is 2.4 liters divided by 0.1 moles equals also 24 liters per mole. This unit of liters per mole looks similar to some other units that we might recognize from other topics in chemistry. The molar volume is the volume per mole of a gas.

On the other hand, molar mass is the number of grams in a mole of a substance. We can apply molar mass to any state of matter, including gases. Molar concentration, often expressed as moles per liter or molarity, is a measurement of the amount of moles of a solute dissolved in a unit of volume of a solvent. We most frequently see grams for mass and liters for volume, but we may see other units as well. The molar volume gives us the ratio of liters to moles. If we know the molar volume and either the amount in moles or the volume, we can solve for the missing value by using a rearranged version of the original formula.

For example, if we have another container of 12 liters of the gas with a molar volume of 24 liters per mole, we can use the formula ๐ equals ๐ divided by ๐ m to calculate that 12 liters divided by 24 liters per mole equals 0.5 moles. This answer also makes sense intuitively. If every 24 liters of gas is one mole, then half that amount, 12 liters, should be half a mole of the gas.

As another example, if we put exactly 0.25 moles of a gas with a molar volume of 24 liters per mole into a balloon, that balloon would have a volume of 24 liters per mole times 0.25 moles equals six liters. Note that since the volume of a gas will change depending on the temperature and pressure, the molar volume will change as well. That means that thereโs no one consistent molar volume for a specific gas like oxygen. It will depend on the temperature and the pressure of the room the oxygen is in. In fact, the type of gas generally does not affect the molar volume.

As weโve discussed a bit already, the different characteristics of gases are dependent on one another. Over the years, chemists have noticed different simple relationships between the characteristics of gases and developed laws about them. In 1662, Robert Boyle discovered Boyleโs law, which states that all other things equal, the pressure and volume of a gas are inversely proportional. This means that if the pressure or volume goes up, the other will go down. For example, a balloon will shrink or decrease in volume under increased pressure, like when itโs pulled underwater.

In 1787, Jacques Charles developed Charlesโs law, which states that all other things equal, the temperature of a gas in kelvin and its volume are directly proportional. This means that temperature and volume will increase together and they will decrease together. For example, a balloon will swell and increase in volume if it is heated in the sun and increase in temperature. In 1808, Joseph Gay-Lussac discovered Gay-Lussacโs law, which states that all other things equal, the temperature in kelvin and the pressure of the gas will be directly proportional. As an example, in a container where the volume cannot change like a propane tank, if the temperature of the gas is increased, the pressure will increase as well because the heated particles will collide with the container with more energy.

And in 1811, Amedeo Avogadro proposed Avogadroโs law, which states that two different gases with the same volume, temperature, and pressure will have the same number of particles. Avogadroโs law allows us to draw conclusions about the amount in moles from the other characteristics. Amazingly, all of these individual relationships can be combined together in a single equation that incorporates pressure, volume, temperature, and amount in moles. That equation is called the ideal gas law, and it reads as such: ๐๐ equals ๐๐๐, where ๐ is the pressure, ๐ is the volume, ๐ is the amount in moles, ๐ is the gas constant, and ๐ is the temperature in kelvin.

The trickiest part of the equation, ๐, is a constant that acts as a unit conversion factor, often in liter bars per mole kelvin. Why do we need to include a constant with this bizarre unit? Well, from a purely unit-based perspective, in order for this equation to be truly equal, the left and right sides must have the same unit. When we look at how the units cancel out, we can see that the conversion factor makes that equivalence happen. As a deeper explanation, ๐ is the conversion factor that mathematically links all four of the individual characteristics weโre examining. ๐ tells us the precise, quantifiable, and natural relationship between the pressure and volume and the amount and temperature of an ideal gas so we can actually convert from one to another rather than just using the individual relationships from the gas laws.

Since ๐ is a constant, the value will not change. But it might appear as a different number if we change its units. Just as 100 centimeters and one meter are the same length represented by different units, 0.08315 liter bars per mole kelvin and 0.08206 liter atmospheres per mole kelvin, the two most commonly used numbers for ๐, are the same unit conversion factor with different units. The equation as a whole reveals the relationship between the different characteristics within. Mainly, there is a direct relationship between variables on opposite sides of the equation, such as pressure and temperature, and an indirect relationship between variables on the same side of the equation, such as pressure and volume.

We can think back to our balloon example to put this equation into context. Letโs imagine that we heat up the balloon, increasing its temperature. Well, as a result, in order for the equation to remain equal, the left side of the equation must increase as well, either by increasing in pressure, volume, or both. Letโs also imagine a situation where we squeeze in on the balloon. In this situation, weโre decreasing the volume available. One way for the gas to compensate for this would be an increase in pressure. The decrease on the left side of the equation can be balanced out by an increase on the same side.

Again, there is a direct relationship between variables on opposite sides of the equation and an indirect relationship between variables on the same side of the equation. Note that none of these variables represent anything about the type of gas involved. The volume of two different ideal gases with the same temperature, pressure, and amount in moles will be equal. This equation is called the ideal gas law. What makes a gas ideal? An ideal gas is a simplified theoretical version of a gas that lets us more easily carry out calculations. Gas particles in real life attract one another and take up a minuscule amount of space, whereas the simplified ideal gas particles are assumed to not interact with one another at all and take up no space.

While these assumptions are technically inaccurate, these traits have such a small effect on the gas that we can ignore them at low temperatures and pressures to simplify the math involved. The simple takeaway, an ideal gas is a simplified gas. One question that may arise when looking at gases is if traits including molar volume depend on the temperature and pressure which vary from place to place, wouldnโt it be difficult to make conclusions about gases? How do we overcome this variance? Well, thatโs why scientists developed some standards for temperature and pressure. These standards set baseline values for temperature and pressure so that we can more easily make calculations and more easily compare different gases.

We can easily reference a standard by name and then immediately know the resulting pressure, temperature, and molar volume of that standard. Letโs take a look at some of the values associated with these named standards. STP, or standard temperature and pressure, refers to a pressure of one bar, a temperature of zero degrees Celsius, and a molar volume of 22.7 liters per mole. However, in other sources, you may also see STP refer to a pressure of one atmosphere. This changes the molar volume to 22.4 liters per mole. Both of these sets of numbers are correct. Youโll simply see different conventions used in different places.

SATP, or standard ambient temperature and pressure, refers to a pressure of one bar, a temperature of 25 degrees C, and a molar volume of 24.8 liters per mole. RTP, or room temperature and pressure, refers to a pressure of one atmosphere, a temperature of 20 degrees C, and a molar volume of 24.0 liters per mole. An NTP, or normal temperature and pressure, refers to the same values as RTP. When we answer a question about gases, we will likely see one of these named standards in the wording of the question telling us the temperature, pressure, and molar volume we can use in any calculations. STP and RTP are the most commonly used standards. Note that as the temperature of the standard increases, so does the molar volume. This makes sense, as a hotter gas will take up more space.

The two units of pressure that we see here, bar and atmosphere, are very similar in value. One atmosphere equals 1.013 bars. One atmosphere, which isnโt much different from one bar, is the approximate air pressure at sea level on Earth. Itโs simply convention whether we choose to use atmosphere or bar, so pay attention to the wording of the question to know which one to use. And itโs worth noting again that different textbooks might use slightly different definitions for each standard. Now that weโve learned about molar volumes, the ideal gas law, and standards, letโs do some practice that ties them all together.

What is the molar volume of a gas at standard temperature and pressure, to two significant figures?

This value is commonly listed as a reference value. In this problem, weโre simply deriving that value so we know where it comes from. If you have the molar volume of a gas at standard temperature and pressure memorized, you can use that reference value without doing the math shown here. But for this problem, we will carry out the calculations. As a reminder, molar volume is the number of liters taken up by a mole of the gas. Standard temperature and pressure refers to a temperature of zero degrees C and a pressure of one bar. Since we want our temperature to be in kelvin instead of degrees C, we simply add 273 to our value in degrees C to find that temperature in kelvin.

The formula for molar volume is ๐ m equals ๐ divided by ๐, where ๐ m equals the molar volume, ๐ equals the volume, and ๐ equals the amount in moles. However, we donโt know the volume or the amount in moles, so we canโt carry out the calculation directly. However, we do know the pressure, the temperature, and the value of the gas constant. If we look at the ideal gas law, we can put ๐ over ๐ in terms of numbers that we already know to find a value for ๐ over ๐. If we use algebra and divide both sides of the equation by ๐ times ๐, we end up with the equation ๐ over ๐ equals ๐๐ over ๐. Weโve grouped all of the variables that we donโt know the value of on the left side of the equation and all the variables that we do know the value of on the right side of the equation.

We know that the molar volume equals ๐ over ๐. We donโt know directly the value of ๐ over ๐, but we do know that it equals ๐๐ over ๐, a value that we can calculate. We wanna use the value of ๐ that matches the units that weโre using, namely, liters and bars. So we wanna use the value ๐ equals 0.8315 liter bars per mole kelvin. If we plug our known values back into the equation, we get 0.8315 liter bar per mole kelvin times 273 kelvin divided by one bar. If we carry out the arithmetic, we arrive at our final answer.

Note that if we had used the alternate value of one atmosphere instead of one bar for the pressure at STP, we would use a value of ๐ with different units, which would change our final answer. In this case, weโve used a value of one bar for the pressure and calculated the molar volume of a gas at standard temperature and pressure to be 22.7 liters per mole.

Letโs review with some key points. Molar volume is the volume per one mole of a gas, often expressed in the unit liters per mole. We can calculate the molar volume by dividing the volume by the number of moles. The ideal gas law ๐๐ equals ๐๐๐ relates the pressure, volume, number of moles, and temperature of the gas. The two most common standards are STP, referring to a pressure of one bar, a temperature of zero degrees Celsius, and a molar volume of 22.7 liters per mole, and RTP, referring to a pressure of one atmosphere, a temperature of 20 degrees Celsius, and a molar volume of 24.0 liters per mole.

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