Name: ideal gas law at stp and gas density
Uploaded: 2020-09-03T13:38:26.000Z
Duration: 3 min 43 s
Channel: JoVE

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Chemistry

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PS.Chm.7.3

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Applications of the Ideal Gas Law: Molar Mass, Density, and Volume

All ideal gases conform, in behavior, to a particular relationship between pressure, volume, moles, and temperature as dictated by the ideal gas law.

In this equation, R is the ideal gas constant. Rearranging the equation allows any one of the variables to be calculated as long as the other three are known. 

For example, what is the volume of one mole of an ideal gas under standard temperature and pressure conditions? Abbreviated as STP, these conditions are 0 &#176;C or 273 K and 1 atm. 

Rearranging the equation and substituting in the values for n (1 mole), temperature (273 K), pressure (1 atm), and the ideal gas constant (0.08206 L&#183;atm/mol&#183;K), one mole of an ideal gas occupies a volume of 22.4 liters. This is the molar volume at STP, which is also a good approximation for many common gases.

At higher temperatures and lower pressures, the gas expands and its molar volume is larger than it is at standard conditions. At lower temperatures and higher pressures, the molar volume is smaller.

Another useful quantity of a gas is its density. Recall that the number of moles, n, is equal to the mass of the gas divided by its molar mass. Substituting this relationship into the ideal gas equation,

applications of the ideal gas law: molar mass, density, and volume

The volume occupied by one mole of a substance is its molar volume. The ideal gas law, PV = nRT, suggests that the volume of a given quantity of gas and the number of moles in a given volume of gas vary with changes in pressure and temperature. At standard temperature and pressure, or STP (273.15 K and 1 atm), one mole of an ideal gas (regardless of its identity) has a volume of about 22.4 L &#8212; this is referred to as the standard molar volume.

For example, one mole each of hydrogen, oxygen, argon, or carbon dioxide occupies 22.4 liters at STP. This implies that 0.5 moles of any gas at STP occupies a volume of 11.2 L, and similarly, 2 moles of any gas at STP occupies a volume of 44.8 L.

The ideal gas law is universal, relating the pressure, volume, number of moles, and temperature of a gas regardless of the chemical identity of the gas:

<img alt="Ideal gas law equation PV=nRT, formula representation, chemistry and physics education." src="/files/core/CDNSource/lessons/1037/1037_Equations-01.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq1" />

The density d of a gas, on the other hand, is determined by its identity. Density is the ratio of mass over volume. Rearranging the ideal gas equation to isolate V and substituting into the density equation yields:

<img alt="Density formula \(d = \frac{m}{V}\) equation for mass-volume relationship, educational diagram." src="/files/core/CDNSource/lessons/1037/1037_Equations-02.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq2" />

The ratio m/n that is, mass over moles, is the definition of molar mass, M:

<img alt="Molarity formula, M = m/n, chemical concentration equation, static image, educational use." src="/files/core/CDNSource/lessons/1037/1037_Equations-03.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq3" />

The density equation can then be written as

<img alt="Ideal gas density formula \(d = \frac{MP}{RT}\), key concept in thermodynamics equation." src="/files/core/CDNSource/lessons/1037/1037_Equations-04.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq4" />

This equation tells us that gas density is directly proportional to the pressure and molar mass, and inversely proportional to the temperature. For example, CO2 (molar mass = 44 g/mol) is heavier than N2 (molar mass = 28 g/mol) or O2 (molar mass = 32 g/mol), and is therefore denser than air. For this reason, CO2 released from a CO2 fire extinguisher blankets a fire, preventing O2 from reaching the combustible material. The phenomenon of the lifting of hot air balloons depends on the relationship that gases of equal molar masses (such as air) have lower densities at higher temperatures, and therefore hot air balloons can float.

This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/9-3-stoichiometry-of-gaseous-substances-mixtures-and-reactions">Openstax, Chemistry 2e, Section 9.3: Stoichiometry of Gaseous Substances, Mixtures, and Reactions.</a>

The volume occupied by one mole of a substance is its molar volume. The ideal gas law, PV = nRT, &nbsp;suggests that the volume of a given quantity of gas ...

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ideal gas law at stp and gas density

The ideal gas law links pressure, volume, number of moles, and temperature. It helps explain how gas volume changes when pressure or temperature changes. At standard temperature and pressure, or STP, the values are 273.15 K and 1 atm.

At STP, one mole of an ideal gas occupies about 22.4 L. This is called the standard molar volume. The gas can be hydrogen, oxygen, argon, or carbon dioxide, and the volume is still about 22.4 liters. Half a mole occupies 11.2 L, and 2 moles occupy 44.8 L.

The ideal gas law applies to gases in a universal way. It relates pressure, volume, moles, and temperature without depending on the chemical identity of the gas. Gas density is different, because density depends on what the gas is made of. Density is mass divided by volume.

Rearranging the ideal gas law and using the density formula shows a useful gas density relationship. In this form, the ratio of mass to moles is the molar mass, M. The equation shows that gas density increases with pressure and molar mass, but decreases as temperature rises.

This helps explain real examples. Carbon dioxide has a molar mass of 44 g/mol, so it is heavier than nitrogen at 28 g/mol or oxygen at 32 g/mol. Because of this, CO2 is denser than air and can blanket a fire in a CO2 fire extinguisher. Hot air balloons work because air has lower density at higher temperature, so the warmed gas can rise.

Ideal Gas Law at STP and Gas Density

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The ideal gas law links pressure, volume, number of moles, and temperature. It helps explain how gas volume changes when pressure or temperature changes. At standard temperature and pressure, or STP, the values are 273.15 K and 1 atm. At STP, one mole of an ideal gas occupies about 22.4 L. This is called the standard molar volume. The gas can be hydrogen, oxygen, argon, or carbon dioxide, and the volume is still about 22.4 liters. Half a mole occupies 11.2 L, and 2 moles occupy 44.8 L. The...

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Real gases are gases that do not always follow the ideal gas law, PV = nRT, especially when pressure is high or temperature is low. The ideal gas model assumes gas particles have no attractive or repulsive forces and take up negligible space compared with the container. At room temperature and 1 atm or less, many gases behave close to ideally. When conditions change, the measured relationships between pressure, volume, and temperature can drift away from the ideal prediction. One way to see...

key terms and concepts

Explore how the ideal gas law predicts gas volume at STP and explains density, molar mass, CO2 fire extinguishers, and hot air balloons.

Ideal Gas Law at STP and Gas Density | JoVE K12

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Ideal Gas Law at STP and Gas Density

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