Name: gas laws behind the ideal gas equation
Uploaded: 2020-03-26T07:22:24.000Z
Duration: 4 min 6 s
Channel: JoVE

K12 Standards

north-carolina-k-12-science-standard-course-of-study

NC K-12 Science Standard Course of Study

9-12

Chemistry

Energy

PS.Chm.7.3

Ideal Gas Law

A gas is simply a dispersed sample of matter that is fluid and expands freely to occupy available space. However, a certain number of gas molecules occupy a specific volume under a defined temperature and pressure. We can describe the behavior of a gas under these parameters using the ideal gas law, which uses the universal gas constant, R, to relate all of these variables.
The universal gas constant is equal to 8.314 joules per mole Kelvin. This equation enables us to understand state relationships in a gaseous system. For example, in a system of constant temperature and pressure, we know that the addition of more moles of gas results in an increase in volume. Similarly, we can look at a system of constant temperature and moles and see that a decrease in volume results in an increase in pressure.
One challenge is that the ideal gas law describes gases behaving ideally. So what do we mean by that? Ideal behavior assumes that first, the molecules themselves are infinitesimally small and essentially have no volume and that the distance between the molecules is significantly larger than the size of the individual molecule.
Second, we assume that the molecules are constantly in motion. Any collisions occurring between the molecules are elastic, and their motion is frictionless, meaning that the molecules do not lose energy. Finally, we assume that there are no intermolecular forces acting between the molecules and their surroundings.
Unfortunately, most gases do not behave ideally. At very low temperature or high pressure, molecules are very close together and slow-moving, so intermolecular interactions are significant. Similarly, gases with a high molecular weight experience increased interactions due to their large size and mass. However, the ideal gas relationship serves as a good approximation in general.
So how do we use the ideal gas law to study the behavior of a gas in the laboratory? Pressure, volume, and temperature are generally more easily measured, but how about moles, and by extension, mass?
One of the simplest ways to measure the mass of a gas is by the Dumas method. To perform this test, a small amount of a volatile compound in its liquid phase is placed inside a Dumas tube, and the tube is then placed in boiling water.
A volatile compound has a high vapor pressure at room temperature. The vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid phase. Thus, a volatile compound with high vapor pressure transitions from liquid to gas rapidly.
When this happens, the newly formed gas forces the air out of the Dumas tube so that it is solely filled with gas. Once the tube is removed from the water bath and left at room temperature, the gas condenses to form a liquid again. Since mass is conserved, we know that the mass of the condensed liquid is equal to the mass of the gas that filled the known volume of the Dumas tube.
In this lab, you&#39;ll explore the ideal gas law by using the Dumas Method to determine the molar mass of an unknown volatile substance. You&#39;ll then measure the temperature, pressure, and volume of the system and see how much this gas deviates from ideality.

ideal gas law

Derivation of the Ideal Gas Law
Gases are a fundamental state of matter. A gas is a collection of molecules that have a significant distance between their molecules. Due to this distance, colorless gases are invisible to the human eye and are studied using four measurable parameters: pressure (P), volume (V), number of moles (n), and temperature (T). The ideal gas law is a mathematical equation that relates all of these parameters. It is a combination of several different laws that describe the behavior of gases.
In 1662, Robert Boyle confirmed a prior discovery relating the pressure of a gas to its volume. Boyle&#8217;s law states that the pressure of a gas is inversely proportional to its volume if the temperature and number of moles of the gas are held constant.
<img src="/CDNSource/lm/labs/65/65_Concepts_1.jpg" alt="Boyle's law equation, P &#8733; 1/V, gas pressure-volume relationship, physics principle, formula representation." data-altupdatedat="1761830439000" />
Boyle&#8217;s law can be extended to calculate the new pressure or volume of a gas if the initial pressure and volume are known.
<img src="/CDNSource/lm/labs/65/65_Concepts_2.jpg" alt="Boyle's Law equation P&#8321;V&#8321;=P&#8322;V&#8322;, describing gas pressure-volume relationship, physics formula." data-altupdatedat="1761830439000" />
In the 1780s, the unpublished work of French scientist Jacques Charles was credited by French scientist Joseph Louis Gay-Lussac for describing the direct relationship between the volume and temperature of a gas.
<img src="/CDNSource/lm/labs/65/65_Concepts_3.jpg" alt="Charles's Law equation V&#8733;T, illustrating volume-temperature relationship, formula graphic." data-altupdatedat="1761830439000" />
Charles&#8217;s law allows us to calculate the new volume or temperature of a gas if the initial volume and temperature are known, and the pressure and number of moles are constant.
<img src="/CDNSource/lm/labs/65/65_Concepts_4.jpg" alt="Charles's Law formula V1/T1=V2/T2, diagram explaining gas behavior under temperature changes." data-altupdatedat="1761830439000" />
Joseph Louis Gay-Lussac provided an extension to Charles&#8217;s law by relating pressure and temperature. Gay-Lussac&#8217;s law establishes that the pressure of an enclosed gas is directly proportional to its temperature.
<img src="/CDNSource/lm/labs/65/65_Concepts_5.jpg" alt="Boyle's Law equation P&#8733;T, gas law, pressure-temperature relation, scientific concept" data-altupdatedat="1761830439000" />
Therefore, if a change is applied to a gas at a constant volume and number of moles, the new pressure or temperature can be calculated if the initial pressure and temperature are known.
<img src="/CDNSource/lm/labs/65/65_Concepts_6.jpg" alt="Gay-Lussac's law equation; gas pressure-temperature relation; equations; thermodynamics concept." data-altupdatedat="1761830439000" />
Finally, in 1811, Amedeo Avogadro proposed the direct proportionality between the volume of a gas and the number of moles present.
<img src="/CDNSource/lm/labs/65/65_Concepts_7.jpg" alt="Avogadro's law: V&#8733;n equation, describing gas volume and mole relationship, educational concept." data-altupdatedat="1761830439000" />
The law describes how equal volumes of two gases, with the same temperature and pressure, contain an equal number of molecules.
<img src="/CDNSource/lm/labs/65/65_Concepts8.jpg" alt="Gas law equation V1/n1=V2/n2; chemical process; formula illustration for educational use." data-altupdatedat="1761830439000" />
All of these relationships combine to form the ideal gas law, first proposed by Emile Clapeyron in 1834, as a way to combine these laws of physical chemistry. The ideal gas law accounts for pressure (P), volume (V), moles of gas (n), and temperature (T), with an added proportionality constant, the ideal gas constant (R). The universal gas constant, R, is equal to 8.314 J&#183;K-1 mol-1.
<img src="/CDNSource/lm/labs/65/65_Concepts9.jpg" alt="Ideal gas law equation PV=nRT." data-altupdatedat="1761830439000" />
<h4>Assumptions of the Ideal Gas Law</h4>
The ideal gas law assumes that gases behave ideally, meaning they adhere to the following characteristics: (1) the collisions occurring between molecules are elastic and their motion is frictionless, meaning that the molecules do not lose energy; (2) the total volume of the individual molecules is magnitudes smaller than the volume that the gas occupies; (3) there are no intermolecular forces acting between the molecules or their surroundings; (4) the molecules are constantly in motion, and the distance between two molecules is significantly larger than the size of an individual molecule. As a result of all these assumptions, an ideal gas would not form a liquid at room temperature.
However, as we know, many gases become liquids at room temperature and therefore deviate from ideal behavior. In 1873, Johannes D. Van der Waals modified the ideal gas law to account for the molecular size, intermolecular forces, and volume that define real gases.
<img src="/CDNSource/lm/labs/65/65_Concepts10v2.jpg" alt="Van der Waals equation; P+a(n&#178;/V&#178;)(V-nb)=nRT; ideal gas behavior; scientific formula." data-altupdatedat="1761830439000" />
In the Van der Waals equation, parameters a and b are constants that can be determined experimentally and differ from one gas to another. Parameter a will experience larger values for gases with strong intermolecular forces (i.e., water) and smaller values for gases that have weak intermolecular forces (i.e., inert gases). Parameter b represents the volume that 1 mole of gas molecules occupies; thus, when b decreases, the pressure increases as a result.
<h4>The Dumas Method</h4>
Invented by Jean Baptiste Andre Dumas, the Dumas method utilizes the ideal gas law to study gas samples. The ideal gas law includes Avogadro&#8217;s law, where the number of moles of two gas samples occupying the same volume is the same at a constant pressure and temperature. This relationship allows the Dumas method to calculate the molar mass of an unknown gas sample.
To accomplish this, a Dumas tube is used. A Dumas tube is an elongated glass bulb with a long capillary neck. Prior to the experiment, the volume and mass of the tube are measured. Then, a small amount of a volatile compound is placed in the Dumas tube. Volatile compounds have a high vapor pressure at room temperature and are vaporized at low temperatures. Thus, when the Dumas tube containing the volatile liquid is placed in boiling water, the liquid vaporizes and forces the air out of the tube, and the tube is solely filled with vapor. When the tube is removed from the water bath and left at room temperature, the vapor condenses back to a liquid. Since mass is conserved, the mass of the liquid in the tube is equal to the mass of the gas in the tube. Using the known mass and volume of the gas, along with the known water bath temperature and room pressure, the moles and therefore molecular weight of the gas can be calculated using the ideal gas law.
Here, three assumptions are made: (1) the vapor is acting ideally, (2) the volume of the tube does not vary between the room temperature and the working temperature, and (3) the gas and the water bath are at thermal equilibrium.
<h4>References</h4>
<ol>
	<li style="font-size:17px">Kotz, J.C., Treichel Jr, P.M., Townsend, J.R. (2012) Chemistry and Chemical Reactivity. Belmont, CA: Brooks/Cole, Cengage Learning.</li>
	<li style="font-size:17px">Gay-Lussac, J.L. (1809). Memoir on the Combination of Gaseous Substances with Each Other. M&#233;moires de la Soci&#233;t&#233; d'Arcueil, Vol. 2, 207.</li>
	<li style="font-size:17px">Van der Waals, J.D. (1967). The equation of state for gases and liquids. Nobel Lectures, Physics. Elsevier: Amsterdam, pp. 254-265.</li>
	<li style="font-size:17px">Silderberg, M.S. (2009). Chemistry: The Molecular Nature of Matter and Change. Boston, MA: McGraw Hill.</li>
</ol>

Derivation of the Ideal Gas Law
Gases are a fundamental state of matter. A gas is a collection of molecules that have a significant distance between their ...

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gas laws behind the ideal gas equation

The ideal gas equation brings together the main gas laws used in chemistry. Gases have molecules that are far apart, so their behavior is described with four measurable variables: pressure, volume, number of moles, and temperature. The ideal gas law links these variables with the gas constant, R, which equals 8.314 J·K−1 mol−1.

Boyle’s law describes the link between pressure and volume. When temperature and the number of moles stay constant, pressure and volume change in opposite directions. Charles’s law shows the direct relationship between a gas’s volume and temperature when pressure and moles are constant. Gay-Lussac’s law connects pressure and temperature in an enclosed gas at constant volume and constant moles.

Avogadro’s law adds the relationship between volume and the number of moles. It states that equal volumes of two gases contain equal numbers of molecules when temperature and pressure are the same. These ideas were combined into the ideal gas law, first proposed by Emile Clapeyron in 1834, to create one equation for gas behavior.

The ideal gas law uses a simple model of gas particles. It assumes elastic collisions, frictionless motion, very small molecular volume, no intermolecular forces, and constant motion with large spaces between molecules. Because of these assumptions, an ideal gas would not form a liquid at room temperature, but many real gases do. Those gases can deviate from ideal behavior.

Johannes D. Van der Waals changed the ideal gas law in 1873 to better fit real gases. His equation includes constants a and b, which account for molecular size and intermolecular forces. The value of a is larger for gases with strong intermolecular forces, such as water, and smaller for gases with weak intermolecular forces, such as inert gases. The value of b represents the volume occupied by 1 mole of gas molecules, and lower b values raise the pressure.

The ideal gas law also helps explain the Dumas method, which was developed by Jean Baptiste Andre Dumas to find the molar mass of an unknown gas sample. A Dumas tube is a long glass bulb with a capillary neck. A volatile compound is placed in the tube, then heated in boiling water so it vaporizes and pushes air out. When the tube cools, the vapor condenses, and the mass of the liquid equals the mass of the gas that filled the tube.

Using the known mass, volume, room pressure, and water bath temperature, the moles and molecular weight of the gas can be calculated with the ideal gas law. The method assumes that the vapor behaves ideally, that the tube volume does not change between room temperature and working temperature, and that the gas and water bath reach thermal equilibrium.

Gas Laws Behind the Ideal Gas Equation

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The internal energy of a substance&#8212;the total kinetic energy of all its molecules and the potential energy of their associated forces&#8212;depends ...

Phase Transitions

Whether solid, liquid, or gas, a substance&#39;s state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the ...

phase-transitions-vaporization-and-condensation

Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize ...

Vapor Pressure

When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules move randomly about, they will occasionally ...

Clausius-Clapeyron Equation

The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor ...

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy ...

phase-transitions-sublimation-and-deposition

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and ...

Heating and Cooling Curves

When a substance&#8212;isolated from its environment&#8212;is subjected to heat changes, corresponding changes in temperature and phase of the substance ...

Phase Diagrams

A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. ...

Use models to explain how changes in energy affect the arrangement and movement of the particles in solids, liquids, and gases, as well as the relative strengths of their intermolecular forces.

PS.Chm.7.1

Energy Basics

Chemical reactions, such as those that occur when you light a match, involve changes in energy as well as matter.

Chemical changes and their accompanying ...

First Law of Thermodynamics

Energy Conservation

Energy can be converted from one form into another, but all of the energy present before a change occurs always exists in some form ...

Internal Energy

The total of all possible kinds of energy present in a substance is called the internal energy (U), sometimes symbolized as E. Suppose a system with ...

Quantifying Heat

Thermal Energy&#160;

Microscopically, thermal energy is the kinetic energy associated with the random motion of atoms and molecules. Temperature is a ...

Quantifying Work

As a system undergoes a change, its internal energy can change, and energy can be transferred from the system to the surroundings, or from the ...

Enthalpy

Chemists ordinarily use a property known as enthalpy (H) to describe the thermodynamics of chemical and physical processes. Enthalpy is defined as the sum ...

Thermochemical Equations

For a chemical reaction (the system) carried out at constant pressure &ndash; with the only work done caused by expansion or contraction &ndash; the ...

Constant Pressure Calorimetry

Calorimetry is a technique used to measure the amount of heat involved in a chemical or physical process or to measure the heat transferred to or from a ...

Use mathematics and computational thinking to execute simple calorimetric calculations based on the Law of Conservation of Energy.

PS.Chm.7.2

Understand the relationship among pressure, temperature, volume, and phase.

Gas Laws Behind the Ideal Gas Equation

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