Gas Laws

Mr. Claus

The Kinetic Molecular Theory of Matter

• http://preparatorychemistry.com/KMT_flash.htm

Kinetic Molecular Theory of Gases• Gases are composed of a large number of particles that behave like

hard, spherical objects in a state of constant, random motion.• These particles move in a straight line until they collide with another

particle or the walls of the container. • These particles are much smaller than the distance between particles.

Most of the volume of a gas is therefore empty space. • There is no force of attraction between gas particles or between the

particles and the walls of the container. • Collisions between gas particles or collisions with the walls of the

container are perfectly elastic. None of the energy of a gas particle is lost when it collides with another particle or with the walls of the container.

• The average kinetic energy of a collection of gas particles depends on the temperature of the gas and nothing else.

Properties of Gases

• Each state of matter has its own properties. • Gases have unique properties because the

distance between the particles of a gas is much greater than the distance between the particles of a liquid or a solid. • Although liquids and solids seem very different from

each other, both have small intermolecular distances.

• In some ways, gases behave like liquids; in other ways, they have unique properties.

Properties of Gases

• Gases are considered fluids.

• The word fluid means “any substance that can flow.”

• Gas particles can flow because they are relatively far apart and therefore are able to move past each other easily.

Properties of Gases

• Gases have much lower densities than liquids and solids do.

• Because of the relatively large distances between gas particles, most of the volume occupied by a gas is empty space.

• The distance between particles explains why a substance in the liquid or solid state always has a much greater density than the same substance in the gaseous state does.

• The low density of gases also means that gas particles travel relatively long distances before colliding with each other.

Properties of Gases

• Suppose you completely fill a syringe with liquid and try to push the plunger in when the opening is plugged.

• You cannot make the space the liquid takes up become smaller.

• The space occupied by the gas particles is very small compared with the total volume of the gas.

• Applying a small pressure will move the gas particles closer together and will decrease the volume. This increases collisions between particles, so pressure increases

Physical Characteristics of gases

*also, 1.015x105 N/m2

Robert Boyle• Robert Boyle, (25 January 1627

– 31 December 1691) was a 17th-century natural philosopher, chemist, physicist, and inventor. Born in Lismore County Waterford, Ireland. Although his research clearly has its roots in the alchemical tradition, Boyle is largely regarded today as the first modern chemist, and therefore one of the founders of modern chemistry, and one of the pioneers of modern experimental scientific method.

Boyle’s Law

• Boyle studied the compressibility of gases in 1660. In his experiments he observed "At a fixed temperature, the volume of a gas is inversely proportional to the pressure exerted by the gas."

Boyle’s Law

• Boyle’s Law is mathematically expressed as: PV = K (constant)As pressure goes up, volume goes down and as

pressure goes down, volume goes up. (at a fixed temperature)

P1V1 = K, P2V2 = K So,

P1V1 = P2V2 Or,

V2 = P1V1 , Etc.

P2

Boyle’s Law: P1V1 = P2V2

Boyle’s Law: P1V1 = P2V2

Charles Law

Charles' law (also known as the law of volumes) is an experimental gas law which describes how gases tend to expand when heated. A modern statement of Charles' law is:

The volume of a given mass of an ideal gas is directly proportional to its temperature on the absolute temperature scale (in Kelvin) if pressure and the amount of gas remain constant; that is, the volume of the gas increases or decreases by the same factor as its temperature

Jacques Alexandre César Charles, 1820

BornNovember 12, 1746 (1746-11-12)Beaugency, Orléanais

Died April 7, 1823 (1823-04-08) (aged 76)

Interests Physics, mathematics, hot air ballooning

Jacques Charles                        

French inventor, scientist, mathematician balloonist. Charles wrote almost nothing about mathematics, and most of what has been credited to him was due to mistaking him with another Jacques Charles, also a member of the Paris Academy of Sciences, entering on May 12, 1785. He was sometimes called Charles the Geometer. Charles and the Robert brothershydrogen balloon Nicolas-Louis Robert manned the balloon. Their pioneering use of hydrogen for lift led to this type of balloon being named a Charlière (as opposed to a Montgolfière which used hot air). Charles's law, describing how gases tend to expand when heated, was formulated by Joseph Louis Gay-Lussac in 1802, but he credited it to unpublished work by Jacques Charles.[1] Charles was elected to the Académie des Sciences, in 1795, and subsequently became professor of physics at the Conservatoire des Arts et Métiers.

Joseph Louis Gay-LussacJoseph Louis Gay-Lussac (French: Born December

6th, 1778 – Died May 1st, 1850) was a French chemist and physicist. He is known mostly for two laws related to gases, and for his work on alcohol-water mixtures.

1804 – He and Jean-Baptiste Biot made a hot-air balloon ascent to a height of 7,016 metres (23,018 ft) in an early investigation of the Earth's atmosphere.

Gay-Lussac’s Law of volume and temperature

The pressure of a gas of fixed mass and fixed volume is directly proportional to the gas' absolute temperature (Kelvin) .

_P1 = _P2

T1 T2

Gay-Lussac’s Law of Combining Volumes

• Gases react together in volumes (measured at the same temperature and pressure) that bear a simple ratio to each other and to the gaseous products – reactants and products in gaseous reactions are present in simple, whole number ratios.

2 molecules of Hydrogen + 1 molecule of Oxygen = 2 molecules of water.

H2(g) + O2(g) 2H2O(g)

The Combined Gas Law

• The three gas laws just discussed can be combined into a single equation:

P1 – first pressureV1 – first volumeT1 – first temperature

P2 – second pressureV2 – second volumeT2 – second temperature

The Ideal Gas Law• The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good

approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Emile Clapeyron in 1834 as a combination of Boyle's law and Charles' law. The ideal gas law is often introduced in its common form:

PV=nRTwhere P is the absolute pressure of the gas, V is the volume of the gas, n is the amount of

substance of gas (measured in moles), T is the absolute temperature of the gas and R is the ideal, or universal, gas constant.

Gas Constant Values Depend on the units of pressure:

• It can also be derived from kinetic theory, as was achieved independently by August Krönig in 1856 and Rudolf Clausius in 1857. Universal gas constant was discovered and first introduced into the ideal gas law instead of a large number of specific gas constants by Dmitri Mendeleev in 1874.

Pressure in atmospheres

0.0821𝐿∗𝑎𝑡𝑚𝑚𝑜𝑙∗𝐾

Pressure in kilopascals

8.314𝐿∗𝑘𝑃𝑎𝑚𝑜𝑙∗𝐾

Pressure in mmHg or Torr

62.3637 𝐿∗𝑚𝑚𝐻𝑔𝑚𝑜𝑙∗𝐾

Limitations of the Ideal Gas Law

Limitations of the Ideal Gas Law1. Works well at low pressures and high temperatures2. Most gases do not behave ideally above 1 atm pressure3. Does not work well near the condensation conditions of a gas

Demonstration of Gas Laws

Animation of the Kinetic-Molecular Theory and the Gas Laws