Kinetic Molecular Theory Explains the behavior of gases

POSTULATES:Gases are composed of a many 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, therefore the volume of a gas is mostly empty space and the volume of the gas molecule themselves is negligible

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 elastic.  That is, none of the energy of the gas particle is lost in a collision. The average kinetic energy of a collection of gas particles is dependent only upon the temperature of the gas

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

Kinetic Energy The energy of motion Directly proportional to the mass of the object and

to the square of its velocity

KE = _1_ mv2

2where m = mass

v = velocity

GAS LAWS: Gases have various properties which we can

observe with our senses, including the gas pressure, temperature, mass, and the volume which contains the gas

Scientific observation has determined that these variables are related to one another, and the values of these properties determine the state of the gas

Pressure in a closed container changes if1.temperature changes

2.number of molecules increases or decreases

3.volume changes

Using the Kinetic Molecular Theory to explain the Gas Laws The Relationship Between P and n Boyle's Law Amonton's Law Charles' Law Avogadro's Hypothesis Dalton's Law of Partial Pressures

Relationship between P and n Pressure (P) is the force exerted on the

walls of the container during a collision

An increase in the number of particles (n) increases the frequency of collisions with the walls

Therefore, P increases as n increases.

Boyle’s Law By Robert Boyle (1600s) - observed that the

product of the pressure and volume are observed to be nearly constant

p (V) = CCompressing a gas makes the V smaller but

does not alter the average KE of the molecules since temperature is constant

Though the speed of the particles remains constant, the frequency of collisions increases because the container is smaller

Therefore, P increases as V decreases.

Key Points:•Temperature and moles of gas are constant

•Graph is hyperbolic and asymptotic to both axes

•Pressure and volume are inversely proportional to each other

Equation:P1V1 = P2V2

where P1 is the pressure of a quantity of gas with a volume of V1

P2 is the pressure of the same quantity of gas when it has a volume V2

Example:1. Given a container of air with an initial volume

of 28 L and pressure of 40 Pa, calculate the pressure if the volume is changed to 141 L.

2. Sulfur dioxide (SO2) gas is a component of car exhaust and power plant discharge, and it plays a major role in the formation of acid rain. Consider a 3.0 L sample of gaseous SO2at a pressure of 1.0 atm. If the pressure is changed to 1.5 atm at a constant temperature, what will be the new volume of the gas?

3. Find the pressure on 5.25 L of gas that was originally 3.12 L at 1.54 atm

CHARLE’S LAW By Jacques CharlesThe average KE of a gas particle is

proportional to T Since mass is constant, the average

velocity of the particles must increase (KE = 1/2mv2)

At higher velocity, the particles exert greater force which increases P

If the walls are flexible, they will expand to balance the atmospheric pressure outside

Therefore, V is directly proportional to T

Key Points:• Pressure and moles of gas are constant

• Graph is linear

• Volume and temperature are directly proportional to each other

Equation: _V1_ = V2_

T1 T2

Example:1. A 5.0 L vessel of gas is held at 25°C. What will be

the new volume if the temperature is doubled?

2. What change in volume results if 60.0 mL of gas is cooled from 33.0 °C to 5.00 °C?

3. Given a container of helium gas with an initial volume of 496 L and temperature of 6.4 °C,calculate the volume if the temperature is changed to -16.9 °C.

Gay-Lussac’s Law By Joseph Louis Gay-Lussac (1778-1850)

Key Points:-- Volume and moles of gas are

constant-- Graph is linear (see below)-- Pressure and temperature are

directly proportional to each other

Equation: _P1_ = P2_

T1 T2

Example:1) 25.0 L of a gas is held in a fixed container at 1.25

atm at 20°C. What will be the pressure of the gas if the temperature is increased to 35°C?

2) If a gas is cooled from 323.0 K to 273.15 K and the volume is kept constant what final pressure would result if the original pressure was 750.0 mm Hg?

AMONTON’S LAW The pressure of a gas is directly proportional to the

Temperature (Kelvin) at a constant V and n

Absolute Zero – The temperature (-273.15 degrees C or 0 Kelvin) at which the volume and pressure of an ideal gas extrapolated to zero.

-- Proposed by Joseph Lambert in 1779

Where: TK is measured in Kelvin T0C is measured in

Celsius

DALTON'S LAW OF PARTIAL PRESSURES

Assumptions: Gases must be unreactive and follow ideal

gas behavior

the total pressure of a gas mixture is equal to the sum of the pressures of each individual gas

By John Dalton

Example:1. The pressure of a mixture of nitrogen, 

carbon dioxide, and oxygen is 150 kPa. What is the partial pressure of oxygen if the partial pressures of the nitrogen and carbon dioxide are 100 kPA and 24 kPa, respectively?

2. A container holds three gases: oxygen, carbon dioxide, and helium. The partial pressures of the three gases are 2.00 atm, 3.00 atm, and 4.00 atm, respectively. What is the total pressure inside the container?

AVOGADRO’S HYPOTHESIS By Amadeo Avogadro

The volume of a gas is directly proportional to the moles of the gas, n at constant P and T

The hypothesis that equal volumes of different gases at the same temperature and pressure contain the same number of particles

Avogadro's law can be expressed by the formula:

_Vi_ = _Vf_ ni  nfWhere:

Vi = initial volumeni = initial number of molesVf = final volumenf = final number of moles

Example:1. A 6.0 L sample at 25 °C and 2.00 atm of pressure contains 0.5 moles of a gas. If an additional 0.25 moles of gas at the same pressure and temperature are added, what is the final total volume of the gas?