# Kinetic Molecular Theory and Gas Laws

## The kinetic molecular theory explains the macroscopic properties of gases and can be used to understand and explain the gas laws.

#### Key Points

• The kinetic molecular theory states that gas molecules are always in constant motion and tend to collide without loss of overall kinetic energy (Figure 1).

• The movement of gaseous particles can be used to explain both Charles' and Boyle's Laws.

• The average kinetic energy of gas molecules is directly proportional to absolute temperature, such that all molecular motion would cease at absolute temperature.

#### Terms

• referring to properties that can be visualized or measured by the naked eye; examples include pressure, temperature, and volume

• a hypothetical gas whose molecules exhibit no interaction and undergo elastic collision with each other and with the walls of the container

#### Figures

1. ##### Movement of Gaseous Molecules

Gaseous molecules are in a state of constant random motion.

2. ##### The Kinetic Molecular Theory of Gas (part 1)

Reviews kinetic energy and phases of matter, and explains the kinetic-molecular theory of gases.

3. ##### The Kinetic Molecular Theory of Gas (part 2)

Uses the kinetic theory of gases to explain properties of gases (expandability, compressibility, etc.)

The three basic states of matter we encounter every day are solid, liquid, and gas (or vapor). These three states of matter can be distinguished by the arrangement of their constituent atoms; gas particles are well separated with no regular arrangement, while particles of solids and liquids are closer together. Because of the differences in particle arrangement, each state of matter displays different properties.

By the late 19th century, scientists had begun to accept the atomic theory of matter and related it to individual molecules. The kinetic molecular theory of gases comes from observations that scientists made about gases to explain their macroscopic properties. The theory outlines the basic behavior of an ideal gas:

1. The volume occupied by the molecules of a gas is negligible compared to the volume of the gas itself.
2. The molecules of an ideal gas exert no attractive forces on each other or their surroundings.
3. The molecules are in a constant state of random motion and move in straight lines until they collide with another body.
4. The collisions exhibited by a molecule are elastic; when two molecules collide, they change directions and kinetic energy, but the total kinetic energy is conserved.
5. The average kinetic energy of the gas molecules is directly proportional to absolute temperature, which implies that all molecular motion would cease if the temperature were reduced to absolute zero.

Charles' Law states that at constant pressure, the volume of a gas increases or decreases by the same factor as its temperature. It can be written as:

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

According to kinetic molecular theory, an increase in temperature will increase the average kinetic energy of the molecules. As the particles move faster, they will likely hit the edge of the container more often. If the reaction is kept at constant pressure, they must stay farther apart, and the increase in particle collision with the surface of the container will be compensated for by an increase in volume.

Boyle's Law states that at constant temperature, the absolute pressure and volume of a given mass of confined gas are inversely proportional. This relationship is shown by the following equation:

$P_1V_1=P_2V_2$

At a given temperature, the pressure of a container is determined by the number of times gas molecules strike the container walls. If the gas is compressed to a smaller volume, then the same number of molecules will strike against a smaller surface area; therefore, the number of collisions against the container will increase, and therefore, the pressure will increase as well. Increasing the kinetic energy of the particles will increase the pressure of the gas.

Figure 2

Figure 3

#### Key Term Glossary

absolute zero
The coldest possible temperature, zero on the Kelvin scale, or approximately −273.15 °C, −459.67 °F; total absence of heat; temperature at which motion of all molecules would cease.
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Absolute zero
The theoretical lowest possible temperature. By international agreement, absolute zero is defined as 0K on the Kelvin scale and as −273.15° on the Celsius scale.
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atom
the smallest possible amount of matter that still retains its identity as a chemical element, now known to consist of a nucleus surrounded by electrons
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constant
Consistently recurring over time; persistent
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energy
a quantity that denotes the ability to do work and is measured in a unit dimensioned in mass × distance²/time² (ML²/T²) or the equivalent
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gas
Matter in a state intermediate between liquid and plasma that can be contained only if it is fully surrounded by a solid (or held together by gravitational pull); it can condense into a liquid, or can (rarely) become a solid directly.
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ideal gas
a hypothetical gas whose molecules exhibit no interaction and undergo elastic collision with each other and with the walls of the container
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Ideal gas
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles.
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kinetic
of or relating to motion
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kinetic energy
The energy possessed by an object because of its motion, equal to one half the mass of the body times the square of its velocity.
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kinetic molecular theory
a method of treating gases as a large number of small particles (atoms or molecules), all of which are in constant, random motion
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kinetics
The branch of chemistry that is concerned with the rates of chemical reactions.
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liquid
A substance that flows and keeps no definite shape, such as water. A substance whose molecules, while not tending to separate from one another like those of a gas, readily change their relative position, and which therefore retains no definite shape, except that determined by the containing receptacle; an inelastic fluid.
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macroscopic properties
referring to properties that can be visualized or measured by the naked eye; examples include pressure, temperature, and volume
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mass
The quantity of matter that a body contains, irrespective of its bulk or volume. It is one of four fundamental properties of matter. It is measured in kilograms in the SI system of measurement.
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matter
The basic structural component of the universe. Matter usually has mass and volume.
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molecule
the smallest particle of a specific element or compound that retains the chemical properties of that element or compound; two or more atoms held together by chemical bonds
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Pressure
the amount of force that is applied over a given area divided by the size of this area
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solid
A substance in the fundamental state of matter that retains its size and shape without need of a container (as opposed to a liquid or gas).
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state
The physical property of matter as solid, liquid, gas or plasma
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surroundings
All parts of the universe that are not within the thermodynamic system of interest.
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temperature
A measure of cold or heat, often measurable with a thermometer.
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volume
A unit of three-dimensional measure of space that comprises a length, a width, and a height. It is measured in units of cubic centimeters in metric, or cubic inches or cubic feet in English measurement.