Physical Characteristics of Gases

The Kinetic-Molecular Theory of Matter

Section 1

Elemental states at 25oC

He

Rn

XeI

KrBrSe

ArClS

NeFO

P

NC

H

Li

Na

Cs

Rb

K

TlHgAuHfLsBa

Fr

PtIrOsReWTa PoBiPb

Be

Mg

Sr

Ca

CdAgZrY PdRhRuTcMoNb

AcRa

ZnCuTiSc NiCoFeMnCrV

In SbSn

Ga Ge

Al

Gd

Cm

Tb

Bk

Sm

Pu

Eu

Am

Nd

U

Pm

Np

Ce

Th

Pr

Pa

Yb

No

Lu

Lr

Er

Fm

Tm

Md

Dy

Cf

Ho

Es

At

Te

As

Si

B

5 - 2

SolidLiquidGas

Behavior of Atoms

Kinetic-molecular theory based on the idea that particles of matter are always in motion

Can be used to explain the properties of solids, liquids, and gases in terms of the energy of the atoms and the forces that act between them

K-M Theory of Gases

Theory provides model of ideal gas Ideal gas imaginary gas that

perfectly fits all the assumptions of the kinetic-molecular theory

Based on 5 assumptions

Assumption #1

Gases consist of large numbers of tiny particles that are far apart relative to their size.

Typically occupy volume about 1000 times greater than volume of liquid or solid

Molecules of gas are much farther apart than liquid/solid

Accounts for lower densities, and compressibility

5 - 7

The gaseous state

In this state, the particles have sufficient energy to overcome all forces that attract them to each other.

Each particle is completelyseparated from the others.

This results in low densitiesand the fact that gases completely fill the container that holds them.

Assumption #2

Collisions between gas particles and between particles and container walls are elastic collisions.

Elastic collision there is no net loss of kinetic energy

Kinetic energy transferred but TOTAL kinetic energy remains the same as long as temperature is constant

Assumption #3

Gas particles are in continuous, rapid, random motion. They therefore possess kinetic energy, which is energy of motion.

Gas particles move in all directions Kinetic energy overcomes attractive

forces between atoms

Assumption #4

There are no forces of attraction or repulsion between gas particles.

Think of gas atoms like billiard balls

They hit each other and bounce off

Assumption #5

The average kinetic energy of gas particles depends on the temperature of the gas.

Kinetic energy of any moving object shown by

m = mass of particle v = velocity (speed)

K-M Theory and the Nature of Gases

K-M theory only applies to ideal gases They do not actually exist Many gases behave NEARLY ideally if

pressure not very high or temperature not very low

How does K-M theory account for the physical properties of gases?

Expansion

Gases do not have definite shape OR volume

Completely fill any container and take its shape

K-M theory: Assumption 3 gas particles move rapidly

in all directions Assumption 4 no significant attraction or

repulsion between them

Fluidity

Because attractive forces between gas particles are insignificant (assumption 4), the particles easily pass each other

This ability causes gases to behave similarly to liquids

Because liquids and gases flow, both are referred to as fluids

Low Density

Density of gases about 1/1000 density of same substance in liquid or solid state

This is because the particles are so much farther apart in the gaseous state (assumption 1)

Compressibility

During compression, the gas particles, which are initially very far apart (assumption 1), are crowded closer together

The volume of a given sample of a gas can be greatly decreased

Diffusion and Effusion

Gases spread out and mix with one another, even without being stirred

If the stopper is removed from a container of ammonia in a room, ammonia gas will mix uniformly with the air and spread throughout the room

The random and continuous motion of the ammonia molecules (assumption 3) carries them throughout the available space

Such spontaneous mixing of the particles of two substances caused by their random motion is called diffusion

Rate of diffusion of one gas through another depends on three properties of the gas particles

1. Their speeds2. Their diameters3. The attractive forces between them

Effusion

Effusion process by which gas particles pass through a tiny opening

Rates of effusion directly proportional to the velocities of the particles

Deviation of Real Gases from Ideal Behavior

When their particles are far enough apart and have enough kinetic energy, most gases behave ideally

Real gas gas that does not behave completely according to the assumptions of the kinetic-molecular theory

1873 – Johannes van der Waals Accounted for movement away from ideal

behaviour by pointing out that particles of real gases occupy space and apply attractive forces on each other

At very high pressure and low temperatures, the deviation may be significant

Under such conditions, the particles will be closer together and their kinetic energy will be insufficient to completely overcome the attractive forces

(a) Gas molecules in a car engine cylinder expand to fill the cylinder. (b) As pressure is exerted on them, the gas molecules move closer together, reducing their volume. The closer they are together, the more the attractive forces act on the particles.

K-M theory more likely to hold true for gases whose particles have little attraction for each other

Ex. – noble gases They are monoatomic They are nonpolar

The more polar a gas’s molecules are, the greater the attractive forces between them and the more they will stray from ideal gas behavior

Suppose you have a one-liter bottle of air. How much air do you actually have? The expression a liter of air means little unless the conditions at which the volume is measured are known. A liter of air can be compressed to a few milliliters. It can also be allowed to expand to fill an auditorium.To describe a gas fully, you need to state four measurable quantities: volume, temperature, number of molecules, and pressure. You already know what is meant by volume, temperature, and number of molecules. We will examine the mathematical relationships between volume, temperature, number of gas molecules, and pressure.

Section 2 - Pressure

Pressure and Force

If you blow air into a rubber balloon, the balloon will increase in size

The volume increase is caused by the collisions of molecules of air with the inside walls of the balloon

The collisions cause an outward push, or force, against the inside walls

Pressure

Pressure (P) the force per unit area on a surface

SI unit for force = Newton (N) force that will increase the speed of a one kilogram mass by one meter per second each second it is applied

At Earth’s surface, each kilogram of mass exerts 9.8 N of force, due to gravity

5 - 27

Gas pressure

Gases exhibit pressure on any container they are in.

Pressure is defined as a force per unit of area. Pressure = Force / Area

Several common units 1.00 atm = 760 torr

760 mm Hg 29.9 in Hg 14.7 lb/in2

1.01 x 105 Pa

force

area

Gas molecules exert pressure on any surface with which they collide

The pressure exerted by a gas depends on volume, temperature, and the number of molecules present

Measuring Pressure

Barometer a device used to measure atmospheric pressure

Torricelli sealed a long glass tube at one end and filled it with mercury

Held open end with his thumb, he inverted the tube into a dish of mercury without allowing any air to enter the tube

When he removed his thumb, the mercury column in the tube dropped to a height of about 760 mm above the surface of the mercury in the dish

He repeated the experiment with tubes of different diameters and lengths longer than 760 mm

In every case, the mercury dropped to a height of about 760 mm

Units of Pressure

Many units used to measure pressure

mmHg millimeters of mercury

1 mmHg = 1 torr 1 atm

atmosphere of pressure = 760 mmHg

SI unit Pascal the pressure exerted by a force of one Newton (1N) acting on an area of one square meter

Standard Temperature and Pressure

To compare volumes of gases, it is necessary to know the temperature and pressure at which the volumes are measured

For purposes of comparison, scientists have agreed on standard conditions of exactly 1 atm pressure and 0°C

These conditions are called standard temperature and pressure and are commonly abbreviated STP

Practice Problems

1. The average atmospheric pressure in Denver, Colorado, is 0.830 atm. Express this pressure

(a) in mm Hg and (b) in kPa.631 mm Hg 84.1 kPa2. Convert a pressure of 1.75 atm to

kPa and to mm Hg.177 kPa, 1330 mm Hg3. Convert a pressure of 570. torr to

atmospheres and to kPa.0.750 atm, 76.0 kPa