Chapter 10 - Physical Characteristics of Gases

The Kinetic-Molecular Theory of Matter

used study of gases to determine the behavior of atoms/molecules

Kinetic-molecular theory is based on the idea that particles of matter are always in motion -- solids v liquids v gases

Animation of physical states of matter:

ttp://mutuslab.cs.uwindsor.ca/schurko/animations/phasesofmatter/phasesofmatter.html

Factors to remember are energy of particles and forces acting between particles

The Kinetic-Molecular Theory of Gases

applies to an “ideal” gas

ideal gas - definition

assumptions of the k-m theory

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

particles are usually atoms or molecules

generally a gas occupies 1000 x the volume the same number of particles would occupy if they were in the solid state

most of the volume occupied by a gas is empty space -- lower density of gas compared to corresponding solid -- also gases can be greatly compressed

--collisions between gas particles and between particles and the container walls are elastic collisions

elastic collisions - definition

depends on temperature remaining constant

--Gas particles are in constant, rapid, random motion

Have kinetic energy - definition

Kinetic energy can overcome attractive forces if the energy is large enough and the attractive forces are small enough.

Figure 10-1 page 304

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

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

KE = 1/2 m v2 where m is the mass of the particles, v is the velocity (speed) of the particle

Because all the particles of a particular gas have the same mass, the speed depends only on the temperature -- higher speed implies a higher temperature

All the particles of a gas at the same temperature have the same average kinetic energy. i.e. lighter particles travel at higher speeds and heavier particles travel at slower speeds.

The Kinetic-Molecular Theory and the Nature of Gases

applies only to ideal gases

Ideal gases do not exist

Can simulate ideal behavior at very low pressure and very high temperature

Expansion

Gases have no definite shape and no definite volume

Fill whatever volume is available

Ideal gas animation: http://mutuslab.cs.uwindsor.ca/schurko/animations/idealgas/idealGas.htm

ideal gas molecles move rapidly in all directions and have no attraction or repulsion between themselves and other molecules

Fluidity

Gas particles glide easily past one another since the attractive forces are minimal

True also in liquids but to a lesser extent

Fluid - definition

Low Density

A gas has a density about 1/1000 of its liquid or solid form; Due to distance between particles

Compressibility

Compression pushes the gas particles which start out far apart, closer together

Gases can be compressed to occupy 1/100 of its normal volume

Diffusion and Effusion

Gases spontaneously spread out and, if another gas is present, they mix on their own

Diffusion - definition

Rate of diffusion depends on a) speed of gas particles, b) diameter of the particles, c) attractive forces between particles

Figure 10-2 page 305

Effusion - definition

Rates of effusion of different gases is directly proportional to the velocities of their particles

Molecules of low mass (higher velocity) effuse faster than molecules of high mass (lower velocity)

Deviation of Real Gases from Ideal Behavior

Real gases can behave like ideal gases when the particles are far enough apart and are moving fast enough to overcome attractive forces - low pressure and high temperature

Real gas - definition

1873 - Johannes van der Waals - deviation from ideal behavior by indicating the particles of a real gas occupy space and do exert attraction for each other

Van der Waals forces are most noticeable at very high pressure or very low temperature or both

Figure 10-3 page 306

Kinetic molecular theory holds true for gases that have little or no attractive forces for each other viz. noble gases. These are nonpolar molecules. Diatomic molecules also show similar behavior

If a gas molecule is polar (dipole) the attractive forces between the molecules will be greater and the deviation from ideal behavior will be larger. e.g. ammonia and water vapor

Homework: 10.1

Pressure

volume of a gas must also be accompanied by temperature and pressure if it is to be meaningful

The four important variables about a gas are a) volume, b) temperature, c) number of molecules; d) pressure

Pressure and Force

Pressure - definition

Equation for pressure: P = f / A

SI unit of force is the newton (N)

Newton - definition

Figure 10-4 page 308

Gas molecules exert a pressure on any surface with which they collide. The pressure depends on a) volume, b) temperature; c) number of molecules.

The atmosphere exerts pressure on us -- called atmospheric pressure

Difference between atmospheric pressure at sea level and atmospheric pressure 30 000 feet above sea level. Why?

Figure 10-6a page 310

Figure 10-6b page 310

http://mutuslab.cs.uwindsor.ca/schurko/animations/collisions/collision_particle.htm
Pressure due to collisons with container sides.

Measuring Force

barometer - definition

Torricelli in early 1600's - why water pumps could only raise water to 34 feet; depends on weight of water compared to weight of air; mercury is 14 times more dense than water should only go up 1/14 the height of water or 1/14 x 34 feet; tested using apparatus in

figure 10-7 page 311

torricellian vacuum

at sea level, at 0oC, the average height of mercury is 760 mm

barometric (atmospheric) pressure varies depending a)elevation, b) weather conditions

manometer - used to measure pressure of an enclosed gas sample; shaped like a U

http://www.chm.davidson.edu/chemistryapplets/gaslaws/pressure.html

figure 10-8 page 311

Units of Pressure

a) millimeters of mercury (mm Hg); average atmospheric pressure at zero degrees Celsius and at sea level is 760 mm Hg -- also known as standard pressure

b) atmosphere of pressure (atm); one atmosphere - definition; equal to 760 mm Hg

c) Pascal (Pa); an SI unit; expressed in derived units
Pascal - definition
also have kilopascals (kPa); 1 ATM = 1.013 x 105 Pa or 101.325 kPa

 

Unit
Symbol
Conversion
pascal Pa see below
millimeters of mercury mm Hg

760 mm Hg = 1 atm

1 mm Hg = 1 torr

torr torr

1 torr = 1 mm Hg

760 torr = 1 atm

atmosphere atm

1 atm = 760 mm Hg

1 atm = 760 torr

1 atm = 1.013 x 105 Pa

1 atm = 101.3 kPa

table 10-1 page 311

Standard Temperature and Pressure

When comparing volumes of gases you need to know temperature and pressure

We use standard temperature and pressure (STP)

Standard temperature is defined as zero degrees Celsius.

Standard pressure is defined as one atmosphere pressure.

Sample problem 10-1 page 312

The average atmospheric pressure in Denver, Colorado is 0.830 atm. Express this pressure in a) mm Hg and b) in kPa.

sample problem 10-1

Homework: 10.2

The Gas Laws

the gas laws - definition

Boyle's Law: Pressure-Volume Relationship

Boyle found doubling the pressure on a gas caused its volume to decrease by 1/2; tripling the pressure caused its volume to decrease by 1/3.

Figure 10-9 page 313

pressure due to molecules colliding with walls of container

for a given amount of gas, smaller container means more collisions and, thus, greater pressure -- temperature must be the same since temperature is a measure of the average KE of the molecules

Table 10-2 page 314

Boyle's Law - statement

PV = k where the volume of k depends only on the mass of gas and the temperature.

P1 V1 = P2 V2

http://www.grc.nasa.gov/WWW/K-12/airplane/aboyle.html

In doing gas law problems, units must be consistent i.e. if pressure is in mm Hg for one then the other pressure must also be in mm Hg

Sample Problem 10-2 page 315

sample problem 10-2

 

Homework: 10.3

Charles' Law: Volume-Temperature Relationship

When pressure is held constant and you heat a gas, the volume increases. E.g. hot air balloon.

Jacques Charles in 1787

All gases expand to the same extent when heated through the same temperature interval.

If a substance is at zero degrees Celsius and heated to one degree Celsius, the volume increases by 1/273 of the original volume it had at zero degrees Celsius. The same type of thing happens when cooling a gas except the volume decreases.

At -273 degrees Celsius (zero Kelvin), the volume theoretically would be zero -- hence the term absolute zero. Generally gases condense to liquids before reaching absolute zero.

Table 10-3 page 317

Celsius ---> Kelvin - use degrees Celsius + 273.15

Charles' Law - statement

V / T = k ---- direct proportion

V1 / T1 = V2 / T2

http://www.grc.nasa.gov/WWW/K-12/airplane/aglussac.html

http://www.accad.ohio-state.edu/~midori/GasLaw.html

Table 10-4 page 318

Figure 10-12 page 318

Sample Problem 10-3 page 318

sample problem 10-3

Homework: 10.4

Gay-Lussac's Law: Pressure Temperature Relationship

Pressure is the result of the collisions of molecules with the walls of the container. More collisions, more pressure; hit the wall harder, more pressure.

Gay-Lussac's law - statement

P / T = k --- direct proportion

Figure 10-13 page 319

P1 / T1 = P2 / T2

Example Problem 10-4 page 320

The gas in an aerosol can is at a pressure of 3.00 atm at 25oC. Directions on the can warn the user not to keep the can in a place where the temperature exceeds 52oC. What would the gas pressure in the can be at 52oC?

sample problem 10-4

Homework: 10.5

The Combined Gas Law

Combined gas law - statement

P V / T = k

P1 V1 / T1 = P2 V2 / T2

Sample Problem 10-5 page 321

sample problem 10-5

Homework: 10.6

Dalton's Law of Partial Pressures

Found if you have two gases that do not react with each other, you place them in the same container, the total pressure would be equal to the pressure each would exert if it occupied the same container by itself.

Figure 10-14 page 323

Partial pressure - definition

Dalton's Law of Partial Pressure - statement

PT = P1 + P2 + P3 + P4 + .......

http://www.chm.davidson.edu/chemistryapplets/gaslaws/daltonslaw.html

Gas Collected by Water Displacement

one application of Dalton's Law of partial pressure

Figure 10-15 page 324

As the gas moves through the water some of the water, as vapor, will mix with the gas collected above the liquid water.

This creates a situation in which you have two gases mixed in the same space.

The total pressure will be equal to the atmospheric pressure and that pressure will be the same as the partial pressure of the gas collected and the water vapor pressure.

We can look up the water vapor pressure if we know the temperature of the mixture of gases.

Patm = PH2O + Pgas

Sample Problem 10-6 page 324

sample problem 10-6

Homework: 10.7

End of notes

 

Dalton's Law of Partial Pressure states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases.

Partial pressure is the pressure of each gas in a mixture.

The combined gas law expresses the relationship between pressure, volume, and temperature of a fixed amount of gas.

The pressure of a fixed mass of gas at constant volume varies directly with the Kelvin temperature.

Charles' law states that the volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature.

Absolute zero is -273.15 degrees Celsius and is the given value of zero in the Kelvin scale.

Boyle's Law states that the volume of a fixed mass of gas varies inversely with the pressure at constant temperature.

The gas laws are simple mathematical relationships between the volume, temperature, pressure, and quantity of a gas.

One pascal is defined as the pressure exerted by a force of one Newton (1 N) acting on an area of one square meter.

One atmosphere of pressure is defined as being exactly equal to 760 mm Hg.

A barometer is a device used to measure atmospheric pressure.

A Newton is the force that will increase the speed of one kilogram mass by one meter per second each second it is applied.

Pressure is the force per unit area on a surface.

A real gas is a gas that does not behave completely according to the assumptions of the kinetic molecular theory.

Effusion is the process by which gas particles under pressure pass through a tiny opening.

Diffusion is the spontaneous mixing of the particles of two substances caused by their random motion.

A fluid is anything that flows. Includes both liquids and gases.

An ideal gas is an imaginary gas that perfectly fits all the assumptions of the kinetic-molecular theory.

Elastic collisions are collisions in which there is no net loss of kinetic energy.

Kinetic energy is energy of motion.