Gases

1
Gases
2
Kinetic Molecular Theory

• The kinetic molecular theory is used to explain
• the behavior of gases.
• All matter is made up of particles called atoms.
• The atoms are in constant motion.
• Collisions between the particles are elastic (no
  energy is gained or lost due to the collision).

3
Properties used to describe gases.

• The following four properties are used to
• describe gases
• Temperature (oC or K)-how fast the particles
  making up the gas are moving.
• Volume (L)-the amount of space the gas occupies
  (usually the size of the container)
• Amount of sample (moles)- of particles in the
  sample
• Pressure (atm, kPa, mm Hg, torrs)

4
How is temperature measured?

• Temperature is measured with a thermometer.
• Almost all substances expand with an increase in
  temperature (exception is water).
• Thermometers are designed so that the substances
  they contain (mercury, etc.) expand and contract
  more than the volume of the glass tube that
  contains them so that the column height of the
  substance changes.

5
Temperature Scales

• Several temperature scales have been devised
• - Fahrenheit (oF) weather is measured using
  this scale.
• - Celsius (oC) the scale used in the metric
  system.
• -Kelvin (K) based on absolute zero used in
  the International System (SI).

6
Comparison of Temperature Scales
7
Comparison of Temperature Scales

• Celsius degrees are larger in size than
  Fahrenheit degrees.
• Celsius degrees are the same size as kelvins.
• The Kelvin scale is the same as the Celsius scale
  (only 273o higher).
• The only temperature that is the same on the
  Celsius and Fahrenheit scale is -40o.

8
Converting Between Scales

• Celsius to Fahrenheit
• oF 9/5oC 32
• Fahrenheit to Celsius
• oC (oF 32)5/9
• Celsius to Kelvin
• K oC 273
• Kelvin to Celsius
• oC K - 273

9
Practice Problems

• 65o C _______K
• 25oC _______K
• -50oC ______K
• 300 K _______oC
• 273 K _______oC
• 150 K _______oC
• 338 K b) 298 K c) 223 K d) 27oC
• e) 0oC f) -123oC

10
Pressure

• Pressure is the force that is exerted on a
  surface.
• P F/A
• Units for pressure are N/m2
• One pascal (Pa) 1 N/m2
• Since the pascal is a very small unit, the kPa is
  more commonly used.
• 1 kPa 1000 Pa

11
Practice Problem

• A car tire makes contact with the ground on a
  rectangular area of .12 m x .18 m. If the cars
  mass is 9300 N, what pressure does it exert on
  ground as it rests on all four tires?

12
Gases and Pressure

• Gases exert pressure due to the collisions
  between the molecules and the walls of the
  container.
• The atmosphere exerts a pressure of
• 14.7 lbs/in2.
• Gravity acts as the atmospheres container.

13
The atmosphere exerts a pressure that can
support a column of mercury 760 mm tall.
1 atm of pressure 760 mm Hg 14.7 lbs/in2
101.3 kPa
14
Complete the following conversion problems

• Convert 2.2 atm to kPa.
• Convert 750 torrs to atm.
• Convert 202.5 kPa to mmHg.
• Convert 10.5 lbs/in2 to atm.

15
Measuring Pressure

• The device used to measure pressure is a
  manometer. A barometer is a specific type of
  manometer used to measure air pressure.

Open Manometer
Closed Manometer
16
Manometer Problems
17
The Components of the Atmosphere

• The atmosphere consists of the following gases
• Nitrogen (N2) 78
• Oxygen (O2) 21
• Argon (Ar) 0.93
• Carbon Dioxide (CO2) 0.038

18
The Structure of the Atmosphere

• The atmosphere consists of five principal layers
  (starting closest to the earth and moving
  outward)
• Troposphere (lt20 km) where weather occurs,
  planes fly, etc.
• Stratosphere (20-50 km) where ozone layer is
  located, weather balloons fly, etc.
• Mesosphere (50-85 km) where most meteors burn up
• Thermosphere (85-690 km) International Space
  Station located here, aurora borealis , etc.
• Exosphere (690-10,000 km) mostly consists of
  hydrogen and helium

19
Layers of the atmosphere
20
Gas Laws
21
Boyles Law

• At constant temperature, the pressure and volume
  of a gas are inversely related. (The number of
  gas particles remains constant).
• As pressure increases, volume decreases.

• Examples/Applications of Boyles Law
• Opening a soft drink bottle
• Ears popping when an airplane
• takes off
• A bicycle pump
• Scuba diving

22
Predicting Pressure and Volume Using Boyles Law

• P1 x V1 P2 x V2
• P1 Original/Starting Pressure
• V1 Original/Starting Volume
• P2 New/Resulting Pressure
• V2 New/Resulting Volume

23
The volume of a gas at 99.0 kPa is 300.0 mL. If
the pressure is increased to 188 kPa, what will
be the new volume?

• P1 99.0 kPa
• V1 300.0 mL
• P2 188 kPa
• V2 ?
• P1 x V1 P2 x V2
• (99.0) (300.0) (188) x
• X 158 mL
• (The pressure increased, so the volume
  decreased).

24
Charles Law

• At constant pressure, the Kelvin temperature and
  volume of a gas are directly related. (The number
  of gas particles remains constant).
• As temperature increases, volume increases.

• Examples/Applications of Charles Law
• Bread rising in the oven
• Car tires appearing to be flat in the morning
• A balloon pops if left in a hot car

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Predicting Temperature and Volume Using Charles
Law

• V1 V2
• T1 T2
• V1 Original/Starting Volume
• T1 Original/Starting Temperature (Kelvin)
• V2 New/Resulting Volume
• T2 New/Resulting Temperature (Kelvin)

26
A helium balloon in a closed car occupies a
volume of 2.32 L at 40.0oC. If the car is parked
on a hot day and the temperature inside rises to
75.0oC, what is the new volume of the balloon
(assuming the pressure remains constant)?

• V1 2.32 L
• T1 40.0o 273 313 K
• T2 75.0o 273 348 K
• V2 ?
• V1 V2
• T1 T2
• 2.32 x
• 313 348
• x 2.58 L
• (The temperature increased, so the volume
  increased also)

27
Gay-Lussacs Law

• At constant volume, the Kelvin temperature and
  pressure of a gas are directly related. (The
  number of gas particles remains constant).
• As temperature increases, pressure increases.

• Everyday Examples/Applications of Gay-Lussacs
  Law
• An aerosol can explodes if left in a fire.
• A pressure cooker

• http//preparatorychemistry.com/Bishop_Gay_Lussac_
  frames.htm

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Predicting Temperature and Pressure Using
Gay-Lussacs Law

• P1 P2
• T1 T2
• P1 Original/Starting Pressure
• T1 Original /Starting Temperature (in Kelvin)
• P2 New/Resulting Pressure
• T2 New/Resulting Temperature

29
A cylinder contain a gas which has a pressure of
125kPa at a temperature of 200 K. Find the
temperature of the gas which has a pressure of
100 kPa.

• P1 125 kPa
• T1 200 K
• P2 100 kPa
• T2 ?
• P1 P2
• T1 T2
• 125 100
• 200 x
• X

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Avogadros Principle

• Equal volumes of gases at the same temperature
  and pressure contain equal numbers of molecules.
• 1 mole of any gas at standard temperature (0oC)
  and pressure (1 atm) occupies 22.4 L of space.
  (STP)

22. 4 L is known as the molar volume.
31
What is the volume of 2 moles of H2 at STP?
44.8 L
32
Predicting Volume and Moles of Gases Using
Avogadros Principle.

• V1 V2
• n1 n2
• V1 Original/Starting Volume
• n1 Original/Starting Number of Moles
• V2 New/Resulting Volume
• n2 New/Resulting Number of Moles
• 
  

33
What size container do you need to hold 0.05
moles of N2 gas at STP?

• V1 ?
• n1 0.05 moles
• V2 22.4 L
• n2 1 mole
• V1 V2
• n1 n2
• x 22.4
• .05 1
• X 1.12 L

34
Combined Gas Law

• The combined gas law states the relationship
  among pressure, temperature, and volume of a
  fixed amount of gas.
• All three variables have the same relationship to
  each other as they have in the other gas laws.
• This law can be represented by the following
  equation
• V1P1 V2P2
• T1 T2

35
Practice Problem

• A sample of air in a syringe exerts a pressure of
  1.02 atm at 22.0oC. The syringe is placed in a
  boiling water bath at 100.0oC. The pressure is
  increased to 1.23 atm by pushing the plunger in,
  which reduces the volume to 0.224 mL. What was
  the initial volume?
• P1 1.02 atm P1V1 P2V2
• T1 22.0oC 273 295 K
  T1 T2
• V1?
• P2 1.23 atm
  (1.02)(x) (1.23)(0.224)
• T2 100.0oC 273 373.0 K
  295 373
• V2 0.224 mL
  x 0.214 mL

36
Grahams Law

• Diffusion is the term used to describe the
  movement of one material through another.
• Effusion is a term used to describe the escape of
  a gas through an opening.
• Example Helium will effuse through a hole in a
  balloon.
• Grahams law states that the rate of effusion for
  a gas is inversely proportional to the square
  root of its molar mass.
• In other words the heavier the gas, the slower
  its rate of effusion.

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Predicting Rates of Effusion Using Grahams Law

• Rate of gas A
• Rate of gas B

Molar Mass of B Molar Mass of A
38
Which will deflate faster a balloon filled with
carbon dioxide or a balloon filled with helium?

• Rate of gas A
• Rate of gas B
• Gas A is Helium (He)
• Gas B is Carbon Dioxide (CO2)
• Molar mass of CO2 44 g
• Molar mass of He 4 g
• 44/4
• Helium diffuses 3.31 times faster

Molar Mass of B Molar Mass of A
39
Daltons Law of Partial Pressures

• The total pressure of a mixture of gases is equal
  to the sum of the pressures of all of the gases
  in the mixture.
• Ptotal P1 P2 P3
• A mixture of oxygen, nitrogen and hydrogen gases
  have a total pressure of 0.97 atm. What is the
  partial pressure of oxygen if the partial
  pressure of nitrogen is 0.70 atm and the partial
  pressure of hydrogen is 0.12 atm?
• 0.97 x 0.70 0.12
• 0.15 atm

40
Ideal Gas Law

• The ideal gas law is a mathematical equation that
  describes the relationship among all 4
  properties.
• The formula works best when gases obey the
  assumptions of the kinetic molecular theory.
• PV nRT
• P is pressure V is volume in liters T is
  temperature in Kelvin n is the number of moles
  and R is the gas constant
• R 8.314 if pressure is in kPA R 0.0821 if
  pressure is in atm R 62.4 if pressure is in mm
  Hg or torrs.

41
Calculate the number of moles of ammonia gas
contained in a 3.0 L container at 300. K with a
pressure of 1.50 atm.

• V 3.0 L
• P 1.50 atm
• T 300. K
• R 0.0821
• n ?
• PV nRT
• (1.50)(3.0) x (0.0821)(300)
• X 0.18 mol