Behavior of Gases

Chapter 10 & 12

Pressure• What is pressure?

A Force Exerted by a Gas over a Given Area

• What causes pressure?Collisions of the Gas Particles with each

other &the Walls of the Container

Gas Particle

That’s Pressure! Walls of

theContaine

r

Which shoes create the most pressure?

Smaller the area of contact, larger the amount of pressure exerted by an object.

Units of Pressure

atmospheres = atmmillimeters of mercury =

mmHgkilopascals = kPa

pounds per square inch = psi

1 atm = 760mmHg = 101.3kPa = 14.7psi

Conversion Between Units of Pressure

1 atm = 760mmHg = 101.3kPa = 14.7psi

Sample Problem #1

How many kilopascals are equivalent to 880mmHg?

880 mmHg 101.3

760

= 120 kPa

Sample Problem #2

Calculate the number of psi that are in 2.60atm.

38.2 psi

14.7

1

2.60 atm

Temperature

ºF

ºC

K

-459 32 212

-273 0 100

0 273 373

K = ºC + 273

ALWAYS use absolute temperature (Kelvin) whenworking with gases.

Practice problemsK = °C + 273Ex) 32°C = ______ K K = 32 + 273 = 305 K

Try one:How much is 75°C in Kelvin?

K = 75 + 273 = 348 K

Behavior of Gases and the Kinetic Theory

Kinetic refers to motion.

The energy of an object has because of its motion is called kinetic energy.

The Kinetic theory states that the tiny particles in all forms of matter are in constant motion.

Watch the video segment (Kinetic Molecular Theory – Standard Deviants School Chemistry:

Molecular Geometry) and fill in the missing information in your

workbook.http://app.discoveryeducation.com/search?Ntt=standard+deviants+gas

Postulates of the Kinetic Molecular Theory of Gases

A gas is composed of particles, usually molecules or atoms that are far apart from one another in comparison with their own dimensions. Particles are relatively far apart from one another and between them is empty space. Gas molecules are in constant random motion. They travel in straight paths (unless they collide with a wall of a container) and move independently of each other.

Postulates of the Kinetic Molecular Theory of Gases

The molecules exert no force on each other or on the container until they collide with each other or with the walls of the container. The average kinetic energy of the molecules of a gas is proportional to the temperature.

Every time a molecule collides with the wall, it exerts a force on it which we call pressure.

Applying this knowledge we know…• Gases fill their containers regardless of the

shape and volume of the containers.

• Because there is so much space between particles, gases are easily compressible. Because gases are compressible, they are used in automobile airbags and other safety devices designed to absorb the energy of an impact

All collisions are perfectly elastic. This means that during collisions kinetic energy is transferred without loss from one particle to another, and total kinetic energy remains constant.

The average speed of oxygen molecules in air at 20oC is 1700 km/h. At these high speeds, the odor molecules from a hot pizza in Washington, D.C., should reach Mexico City in about 106 minutes. Why doesn’t this actually happen?

Answer

Molecules are constantly striking molecules of air and rebounding in other directions. Their path of uninterrupted travel in a straight line is short.

Questions: Pressure increases with the additional gas particles. Pressure exerted is caused by collisions of gas particles with the walls. If the number of gas particles is changed by any factor, the pressure changes by that same factor; until the container ruptures.

What happens when a closed container is inflated?

A gas inside a bicycle tire exerts a pressure of

35 pounds per square inch (psi). How much air must be pumped into the tire to produce a pressure of 70 psi?

Double the amount of air.Increased by a factor of 2!

Note!!!

The relationship between the amount of gas and pressure is proportional, assuming the volume & temperature stay the same.

This means more gas = higher pressure and less gas = lower pressure.

C. What happens to pressure when a closed container is deflated?

*Pressure of the gas is decreased because there are fewer gas particles and less collisions. *If the number of gas particles decreases by half, the pressure decreases by half.

(Note: Gas particles move from region of higher pressure to lower pressure until equilibrium is reached.)

Homework

• Complete pg. 4 in your booklet.• Bring an empty soda can to class

tomorrow.

Bell ringer – 2/5/141. Each of these flasks contains the same number

of gas molecules. In which would the pressure be lowest? Explain your answer choice.

2. Which temperature is colder: 36°C or 278 K?

Combined Gas LawThe Combined Gas Law helps us explain what happens to gases as the pressure, temperature, and volume changes in respect to moles of a substance.

Combined Gas Law

P1 V1 P2V2

n1 T1 n2T2

Boyle's Law

P1 V1 = P2V2

Charles's Law

V1 V2

T1 T2 Avogadro's Law

V1 V2

n1 n2

V1V

=

=

=

Letter or Number

Variable

Name

Unit

Conversions

P Pressure

atm mmHg

torr kPa psi

1 atm = 760 mmHg =760 torr = 101.3 kPa = 14.7 psi

V VolumeL

mL cm3 m3

1 L = 1000 mL1 mL = 1 cm3

Letter or

Number

Variable Name

Unit

Conversions

n* Moles Moles 6.02 x 1023 molecules

T Temperature K (Kelvin) K = oC + 2731 Initial

variable

2 Final variable

*NOTE: If “n” is not given in a problem, assume it to be 1 mole.

Temperature must be in Kelvin .

Remember: STP = 1.0 atm and 273 K or 0.0°C

Guided Practice1. A hot air balloon has a volume of 7500L at 270K and a pressure of 1.2atm. What will be the volume of the balloon if the pressure changed to 0.90atm and the temperature decreases to 230K?

Givens and Unknowns: P1 = 1.2 atm P2 = 0.90 atmV1 = 7500 L V2 = unknown n1 = 1 mole n2 = 1 mole T1 = 270 K T2 = 230 K

Substitute & Solve (Cross Multiply): (1.2 atm) (7500 L) = (0.90 atm) (V2) (1 mol) (270 K) (1 mol) (230 K)

(1.2 atm)(7500 L)(1 mol)(230 K) = (0.90 atm)(V2)(1 mol)(270 K)

2070000 atm*L*mol*K = (V2)(243 atm*mol*K)

2070000 atm*L*mol*K = (V2) 243 atm*mol*K

8518.5 L = V2

Use 2 sig figs 8500 L = V2

Guided Practice2. The volume of a gas at STP is 22.4L. At 12oC, the volume of the balloon changes to 55.0L. What is the new pressure?

Givens and Unknowns: P1 = 1.0 atm P2 = unknownV1 = 22.4 L V2 = 55.0 L n1 = 1 mole n2 = 1 mole T1 = 273 K T2 = 12oC + 273 =

285 K

Substitute & Solve (Cross Multiply): (1.0 atm) (22.4 L) = (P2) (55.0 L) (1 mol) (273 K) (1 mol) (285 K)

(1.0 atm)(22.4 L)(1 mol)(273 K) = (P2)(55.0L)(1 mol)(285 K)

6384 atm*L*mol*K = (P2)(15015 L*mol*K)

66384 atm*L*mol*K = (P2) 15015 L*mol*K

0.42517 atm = P2

Use 2 sig figs 0.43 atm= P2

Homework

Complete pg. 8 in your packet.

Soda Can Activity

OBJECTIVES• Students will demonstrate the effects of air

pressure. • Students will demonstrate that as a gas is

heated it expands and as it cools it will contract.

SAFETY• Be careful of hot water.

What caused the can to collapse?

• As the water boils, the can becomes full of steam.

• When the can is inverted into the cold water bath, the temperature of the gas inside the can drops and some of the water condenses.

• Since the temperature drops and there are fewer gas particle collisions, the pressure inside the can decreases.

• Since the pressure outside the can is now much greater, this higher pressure crushes the can.

The Crushing Can in Real Life

Day 3: Boyle’s, Charles’, and Avogadro’s Laws

The Effect of Changing Size of Container – Boyle’s Law

WHAT IF…temperature and moles do not change and we just look at the relationship between pressure and volume. Our equation would look like this:

P1 V1 = P2 V2 Boyle’s Law Boyle’s Law states that at a constant temperature, the volume of a gas is inversely proportional to the pressure exerted by that gas.

The Effect of Changing Size of Container – Boyle’s Law

Think of two kids (Paul Pressure and Victor Volume) on a see-saw. If Paul goes up, Victor goes down. If Victor goes up, Paul goes down. This is an inverse relationship.

http://www.grc.nasa.gov/WWW/k-12/airplane/boyle.htmlTo show animation

Examples:• If a gas is compressed from 2L

to 1L, the pressure will _____________ by a factor of 2.

• If a gas is expanded from 1L to 3L, the pressures will _______________ by a factor of 3.

• Gases cool when they expand and heat when they compress. Why?

Thus, if you forget to wear your suit in space, you will_EXPLODE_!!!

increase

decrease

If the volume of a container decreases in size, the pressure of gas particles in the container increases.

Example Problems

1. The pressure of a 3.5L balloon was determined to be 1.5atm. Assuming that the temperature remained constant, what would be the volume of the balloon if the pressure was decreased to 0.45atm?

2.  At 45oC, a certain container of gas has the volume of 580mL and a pressure of 980mmHg. What would be the new volume of the gas at 250 mmHg and 45oC?

P1 V1 = P2 V2

The Effect of Temperature changes on Volume – Charles’s

Law• As the gas inside a balloon cools, the

average KE of molecules decreases. • With fewer and less collisions, the gas

molecules move closer together and occupy a smaller volume than they previously did.

• The volume decreases, assuming no change in the amount of gas and pressure.

Charles law states: At a constant pressure, the volume of a gas is directly proportional to the temperature in Kelvin.

Charles’ Law

As temperature increases, the volume increasesAs temperature decreases, the volume decreases.

2

2

1

1

T

V

T

V

• Observe what happens to the balloon as liquid nitrogen is being poured on it.

Helpful Hint!!!

Guided PracticeTemperature must be in Kelvin!

1. The temperature of a 0.65L sample of carbon dioxide gas is 580K. If the pressure remains constant, what is the new volume of the gas if the temperature increases to 1300K?

2. A balloon has a volume of 5.6L at a temperature of 98oC. If the volume of balloon increases to 9.5L, what will be the temperature of the gas in Celsius? Assume that the pressure remains constant.

Avogadro’s Law

Avogadro's Law (Avogadro's theory; Avogadro's hypothesis) is a principle stated in 1811 by the Italian chemist Amedeo Avogadro (1776-1856) that "equal volumes of gases at the same temperature and pressure contain the same number of molecules regardless of their chemical nature and physical properties“. This number (Avogadro's number) is 6.02 X 1023. It is the number of molecules of any gas present in a volume of 22.41 L and is the same for the lightest gas (hydrogen) as for a heavy gas such as carbon dioxide or bromine.

Avogadro’s LawOr to put it another way, "the principle that equal volumes of all gases at the same temperature and pressure contain the same number of molecules.

Thus, the molar volume of all ideal gases, at 0° C and a pressure of 1 atm., is 22.4 liters"

V = the volume of the gas n = the amount of substance of the gas

Avogadro’s Law states that that equal volumes of all gases at the same temperature and pressure contain the same number of molecules or moles.

V1 = V2 V = the volume of the gas

n1 n2 n = the amount of substance of the gas

Example #1: 5.00 L of a gas is known to contain 0.965 mol. If the amount of gas is increased to 1.80 mol, what new volume will result (at an unchanged temperature and pressure)?

Example #2: A cylinder with a movable piston contains .005 mol of helium, He, at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many moles of helium were added to the cylinder if the volume was changed from 2.00 L to 2.70 L? (The temperature was held constant.)

Homework

Complete pg. 12-13 in your packet.

Remember, quiz is on Monday.

State Boyle’s Law

For a constant temp and mass, the pressure

of a gas varies INVERSELY with

volume.

Graph for Boyle’s Law

P

V

P1V1 = P2V2

Equation for Boyle’s Law

Inverse

Inverse or Direct?

Boyle’s Law

State Charles’s Law

For a given mass and constant pressure, the volume of a gas varies

directly with temp.

Graph for Charles’s Law

V

T

Equation for Charles’s Law

Direct

Inverse or Direct?

Charles’s Law

1 2

1 2

V V

T T

Temperature must be in Kelvin.

State Avogadro’s Law

For a given gas at a constant temperature

and pressure, the moles varies directly

with volume

Graph for Avogadro’s Law

n

V

Equation for Avogadro’s Law

Direct

Inverse or Direct?

Avogado’s Law

Dalton’s Law of Partial Pressures

• Partial pressure of a gas in a mixture of gases is the pressure which that gas would exert if it were the only gas present in the container.

• Dalton’s Law of Partial Pressures states that that the total pressure in a gas mixture is the sum of the partial pressures of each individual gas.

Ptotal = Pgas a + Pgas b + Pgas c + etc

• Dalton’s Law of Partial Pressures assumes each gas in the mixture is behaving like an ideal gas

A partial pressure is the pressure a gas would have or would exert if it were alone in the container.

Example Problems

1. Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure of oxygen (Poxygen) at 101.3kPa if the partial pressures of nitrogen, carbon dioxide, and other gases are 79.10kPa, 0.040kPa, and 0.94kPa, respectively.

2. A mixture of gases contains oxygen, nitrogen, and helium. The partial pressure of oxygen is 2.1atm. The partial pressure of nitrogen in 0.21atm, and the partial pressure of helium is 7.80atm. Determine the total pressure of this mixture.

Ptotal = Pgas a + Pgas b + Pgas c + etc

Homework

Complete pg. 15 in your packet.

Ideal Gas Law• An ideal gas is one that follows the gas laws at

________________________________________.

• Such a gas would have to conform precisely to the assumptions of ________ ________.

• As you probably suspect, there is _________ for which this is true. An ideal gas __________ exist. Nevertheless, at many conditions of temperature and pressure, _____________ behave very much like an ideal gas.

all conditions of pressure and temperature

kinetic theory

no gasdoes not

real gases

• An important behavior of real gases that differs from that of a hypothetical ideal gas is that real gases can be ___________ and sometimes ____________ by cooling and by applying pressure. Ideal gasses cannot be. For example, when water vapor is cooled below 100oC at standard atmospheric pressure, it condenses to a liquid. The behavior of other real gases is similar, although lower temperature and greater pressures may be required.

• • ****Gases behave ideally at

___________________________________.

liquifiedsolidfied

high temperatures and low pressure

If we look at one side of the Combined Gas Law:

P Vn T

and solve it for one mole at STP, you would get a “constant” (symbolized as R). (101.3 kPa)(22.4 L) = 8.31 (L . kPa)/(K . mol) (1 mole)(273 K)

P = PressureV = Volumen = molesT = Temperature

We call this the ideal gas constant (R):

If pressure is measured in:

The ideal gas constant (R) is:

kPa 8.31 (L . kPa)/(K . mol)

atm 0.0821 (L . atm)/(K . mol)

mmHg 62.4 (L . mmHg)/(K . mol)

torr 62.4 (L . torr)/(K . mol)

SO… P = Pressure

V = Volume (must be in liters)

n = moles

T = Temperature (must be in Kelvin)

R = Ideal gas constant

Temp must be in Kelvin!!!!

Givens and Unknowns:P = V =

n =

R = T =

Equation: PV = nRTSubstitute & Solve:

1. Calculate the number of moles of oxygen in a 12.5 L tank containing 250 atm, measured at 22oC.

Givens and Unknowns:P = V =

n =

R = T =

Equation: PV = nRTSubstitute & Solve:

2. If 4.5 g methane gas (CH4) is introduced into an evacuated 2.00 L container at 35oC, what is the pressure in the container, in atm?

Givens and Unknowns:P = V =

n =

R = T =

Equation: PV = nRTSubstitute & Solve:

3. A balloon is filled with 0.34 moles of pure nitrogen. If the balloon is at 37 oC and is under pressure of 100 kPa, calculate the volume of the balloon.

Homework

Complete pg. 18 in your packet.

Example ProblemExample 1: 3.00 liters of nitrogen (N2) gas is reacted with excess hydrogen (H2) gas to form ammonia (NH3) gas at 304°K and a pressure of 1.02 atm. How many liters of ammonia gas is formed? Step 1: Write the balanced chemical reaction.

N2 (g) + 3 H2 (g) 2 NH3 (g) Step 2: Convert liters of N2 to moles of N2. NOTE: Since the gas is not at STP, you must convert using the Ideal Gas Law before you can do Stoichiometry!!! PV = nRT: (1.02atm) (3.00L) = (n)(0.0821 L • atm) (304K)

mole • K

n = 0.123 mol of N2

Example ProblemStep 3: Convert moles of N2 to moles of NH3 using the mole ratio of the balanced chemical equation. 0.123 mol N2 2 mol NH3

1 mol N2 = 0.246 mol NH3

Step 4: Convert moles of NH3 to liters of NH3 using the ideal gas law.PV = nRT: (1.02atm) (V) = (0.246mol)(0.0821 L • atm) (304K)

mole • K

V = 6.02 L of NH3

Example 2: Calculate the volume of hydrogen gas produced at 0.0°C and 1.00 atm of pressure by reacting 12.0 g of zinc metal with excess sulfuric acid.

Step 1: Write the balanced chemical reaction.Zn (s) + H2SO4 (aq) H2 (g) + ZnSO4 (aq)

Step 2: Convert grams of zinc to moles of H2 using the mole ratio from the balanced equation.

12.0 g zinc 1 mole zinc 1 mol H2 = 0.183 mol H2

65.4 g zinc 1 mole zinc 

Step 3: Convert moles of H2 to liters of H2 using the ideal gas law.

PV = nRT (1.00 atm) (V) = (0.183 mol) (0.0821 L • atm ) (273 K) mole • K

V = 4.10 L of H2

Class Practice: 3. How many grams of calcium carbonate will be needed to form 4.29 liters of carbon dioxide? The following reaction takes place at a pressure of 1 atm and a temperature of 298o K.

CaCO3(s) CO2(g) + CaO(s)

Homework

Complete pg. 21 in your packet.