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Chapter 14 “The Behavior of Gases”. Compressibility. Gases can expand to fill its container, unlike solids or liquids The reverse is also true: They are easily compressed , or squeezed into a smaller volume

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compressibility
Compressibility
  • Gases can expand to fill its container, unlike solids or liquids
  • The reverse is also true:
    • They are easily compressed, or squeezed into a smaller volume
    • Compressibility is a measure of how much the volume of matter decreases under pressure
compressibility1
Compressibility
  • This is the idea behind placing “air bags” in automobiles
    • In an accident, the air compresses more than the steering wheel or dash when you strike it
    • The impact forces the gas particles closer together, because there is a lot of empty space between them
compressibility2
Compressibility
  • At room temperature, the distance between particles is about 10x the diameter of the particle
    • Fig. 14.2, page 414
  • This empty space makes gases good insulators(example: windows, coats)
  • How does the volume of the particles in a gas compare to the overall volume of the gas?
variables that describe a gas
Variables that describe a Gas
  • The four variables and their common units:

1. pressure (P) in kilopascals

2. volume (V) in Liters

3. temperature (T) in Kelvin

4. amount (n) in moles

  • The amount of gas, volume, andtemperature are factors that affect gas pressure.
1 amount of gas
1. Amount of Gas
  • When we inflate a balloon, we are adding gas molecules.
  • Increasing the number of gas particles increases the number of collisions
    • thus, the pressure increases
  • If temperature is constant, then doubling the number of particles doubles the pressure
pressure and the number of molecules are directly related
Pressure and the number of molecules are directly related
  • More molecules means more collisions, and…
  • Fewer molecules means fewer collisions.
  • Gases naturally move from areas of high pressure to low pressure, because there is empty space to move into – a spray can is example.
common use
Common use?
  • A practical application is Aerosol (spray) cans
    • gas moves from higher pressure to lower pressure
    • a propellant forces the product out
    • whipped cream, hair spray, paint
  • Is the can really ever “empty”?
2 volume of gas
2. Volume of Gas
  • In a smaller container, the molecules have less room to move.
  • The particles hit the sides of the container more often.
  • As volume decreases, pressure increases. (think of a syringe)
    • Thus, volume and pressure are inversely related to each other
3 temperature of gas
3. Temperature of Gas
  • Raising the temperature of a gas increases the pressure, if the volume is held constant. (Temp. and Pres. are directly related)
    • The molecules hit the walls harder, and more frequently!
  • Should you throw an aerosol can into a fire? What could happen?
  • When should your automobile tire pressure be checked?
the gas laws are mathematical
The Gas Laws are mathematical
  • The gas laws will describe HOW gases behave.
    • Gas behavior can be predicted by the theory.
  • The amount of change can be calculated with mathematical equations.
  • You need to know both of these: the theory, and the math
robert boyle 1627 1691
Robert Boyle(1627-1691)
  • Boyle was born into an aristocratic Irish family
  • Became interested in medicine and the new science of Galileo and studied chemistry. 
  • A founder and an influential fellow of the Royal Society of London
  • Wrote extensively on science, philosophy, and theology.
1 boyle s law 1662
#1. Boyle’s Law - 1662

Gas pressure is inversely proportional to the volume, when temperature is held constant.

  • Pressure x Volume = a constant
  • Equation: P1V1 = P2V2 (T = constant)
graph of boyle s law page 418
Graph of Boyle’s Law – page 418

Boyle’s Law says the pressure is inverse to the volume.

Note that when the volume goes up, the pressure goes down

jacques charles 1746 1823
Jacques Charles (1746-1823)
  • French Physicist
  • Part of a scientific balloon flight on Dec. 1, 1783 – was one of three passengers in the second balloon ascension that carried humans
  • This is how his interest in gases started
  • It was a hydrogen filled balloon – good thing they were careful!
2 charles s law 1787
#2. Charles’s Law - 1787
  • The volume of a fixed mass of gas is directly proportional to the Kelvin temperature, when pressure is held constant.
  • This extrapolates to zero volume at a temperature of zero Kelvin.
converting celsius to kelvin
Converting Celsius to Kelvin
  • Gas law problems involving temperature will always require that the temperature be in Kelvin. (Remember that no degree sign is shown with the kelvin scale.)
    • Reason? There will never be a zero volume, since we have never reached absolute zero.

Kelvin = C + 273

°C = Kelvin - 273

and

joseph louis gay lussac 1778 1850
Joseph Louis Gay-Lussac (1778 – 1850)
  • French chemist and physicist
  • Known for his studies on the physical properties of gases.
  • In 1804 he made balloon ascensions to study magnetic forces and to observe the composition and temperature of the air at different altitudes.
3 gay lussac s law 1802
#3. Gay-Lussac’s Law - 1802
  • The pressure and Kelvin temperature of a gas are directly proportional, provided that the volume remains constant.
  • How does a pressure cooker affect the time needed to cook food?
4 the combined gas law
#4. The Combined Gas Law

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

slide22
The combined gas law contains all the other gas laws!
  • If the temperature remains constant...

P1

V1

P2

x

V2

x

=

T1

T2

Boyle’s Law

slide23
The combined gas law contains all the other gas laws!
  • If the pressure remains constant...

P1

V1

P2

x

V2

x

=

T1

T2

Charles’s Law

slide24

The combined gas law contains all the other gas laws!

  • If the volume remains constant...

P1

V1

P2

x

V2

x

=

T1

T2

Gay-Lussac’s Law

5 the ideal gas law 1
5. The Ideal Gas Law #1
  • Equation: PV = nRT
  • Pressure times Volume equals the number of moles (n) times the Ideal Gas Constant (R) times the Temperature in Kelvin.
  • R = 8.31 (L xkPa) / (mol x K)
  • The other units must match the value of the constant, in order to cancel out.
  • The value of R could change, if other units of measurement are used for the other values (namely pressure changes)
the ideal gas law
The Ideal Gas Law
  • We now have a new way to count moles (the amount of matter), by measuring T, P, and V. We aren’t restricted to only STP conditions:

P x V

R x T

n =

ideal gases
Ideal Gases
  • We are going to assume the gases behave “ideally”- in other words, they obey the Gas Laws under all conditions of temperature and pressure
  • An ideal gas does not really exist, but it makes the math easier and is a close approximation.
  • Particles have no volume? Wrong!
  • No attractive forces? Wrong!
ideal gases1
Ideal Gases
  • There are no gases for which this is true (acting “ideal”); however,
  • Real gases behave this way at a) high temperature, and b) low pressure.
    • Because at these conditions, a gas will stay a gas!
6 ideal gas law 2
#6. Ideal Gas Law 2
  • P x V = m x R x T M
  • Allows LOTS of calculations, and some new items are:
  • m = mass, in grams
  • M = molar mass, in g/mol
  • Molar mass = m R T P V
density
Density
  • Density is mass divided by volume

m

V

so,

m M P

V R T

D =

D =

=

slide31

Real Gases

and

Ideal Gases

ideal gases don t exist because
Ideal Gases don’t exist, because:
  • Molecules do take up space
  • There are attractive forces between particles

- otherwise there would be no liquids formed

real gases behave like ideal gases
Real Gases behave like Ideal Gases...
  • When the molecules are far apart.
  • The molecules do not take up as big a percentage of the space
    • We can ignore the particle volume.
  • This is at low pressure
real gases behave like ideal gases1
Real Gases behave like Ideal Gases…
  • When molecules are moving fast
    • This is at high temperature
  • Collisions are harder and faster.
  • Molecules are not next to each other very long.
  • Attractive forces can’t play a role.
7 dalton s law of partial pressures
#7 Dalton’s Law of Partial Pressures

For a mixture of gases in a container,

PTotal = P1 + P2 + P3 + . . .

  • P1 represents the “partial pressure”, or the contribution by that gas.
  • Dalton’s Law is particularly useful in calculating the pressure of gases collected over water.
slide36

Connected to gas generator

Collecting a gas over water – one of our experiments involves this.

slide37
If the first three containers are all put into the fourth, we can find the pressure in that container by adding up the pressure in the first 3:

2 atm

+ 1 atm

= 6 atm

+ 3 atm

4

3

2

1

diffusion is
Diffusion is:
  • Molecules moving from areas of high concentration to low concentration.
    • Example: perfume molecules spreading across the room.
  • Effusion: Gas escaping through a tiny hole in a container.
  • Both of these depend on the molar mass of the particle, which determines the speed.
slide39

Diffusion:describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

  • Molecules move from areas of high concentration to low concentration.
slide40
Effusion: a gas escapes through a tiny hole in its container

-Think of a nail in your car tire…

Diffusion and effusion are explained by the next gas law: Graham’s

8 graham s law
8. Graham’s Law

RateA MassB

RateB  MassA

  • The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules.
  • Derived from: Kinetic energy = 1/2 mv2
  • m = the molar mass, and v = the velocity.

=

graham s law
Graham’s Law
  • Sample: compare rates of effusion of Helium with Nitrogen
  • With effusion and diffusion, the type of particle is important:
    • Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass.
  • Helium effuses and diffuses faster than nitrogen – thus, helium escapes from a balloon quicker than many other gases!