1

Bellringer

In the three boxes, draw what the molecules look like in a solid, liquid, and gas.

Solid Liquid Gas

2

GASES

3

Importance of Gases

• Airbags fill with N2 gas in an accident.

• Gas is generated by the decomposition of sodium azide, NaN3.

• 2 NaN3 ---> 2 Na + 3 N2

4

THREE STATES OF MATTER

THREE STATES OF MATTER

5

• Have a definite shape

• Have a definite volume

Molecules are held close together and there is very little movement

between them.

Kinetic Molecular Theory

6

• Have an indefinite shape

• Have a definite volume

Kinetic Molecular Theory:Atoms and molecules have more space between them than a solid does, but less than a gas (ie. It is more

“fluid”.)

7

•Have an indefinite shape•Have an indefinite volume

Kinetic Molecular Theory:

Molecules are moving in random patterns with varying amounts of

distance between the particles.

8

At 100°C, water

becomes water vapor,

a gas. Molecules can move randomly over large distances.

Below 0°C, water solidifies to become ice.

In the solid state, water

molecules are held together

in a rigid structure.

Between 0°C and 100 °C, water is a

liquid. In the liquid state,

water molecules are close together, but can move about freely.

9

Changing states requires energy in either the form of heat. Changing states may also be due to the change in

pressure in a system.

10General Properties of

Gases• There is a lot of “free” space in a gas.

• Gases can be expanded infinitely.

• Gases fill containers uniformly and completely.

• Gases diffuse and mix rapidly.

11

Properties of Gases

Gas properties can be modeled using math. Model depends on—

• V = volume of the gas (L)• T = temperature (K)

–ALL temperatures in the entire chapter MUST be in Kelvin!!! No Exceptions!

• n = amount (moles)• P = pressure

(atmospheres)

12Temperature

• T = temperature (K)–ALL temperatures in the entire

chapter MUST be in Kelvin!!! No Exceptions!

Converting is simple!

K = C + 273C = K - 273

Convert the temperature of this room (23 C) to Kelvin

13

Pause for a Cause

Convert the following to Kelvin:Water freezes at 0o CWater boils at 100o CHuman Body Temperature is 37o C

Convert the following to Celsius:Absolute Zero is 0 KStandard Pressure is 273.15 K

14ForcePressure =

Area

15

Pressure Is caused by the collisions of

molecules with the walls of a container is equal to force/unit

area.

SI units = Newton/meter2 = 1 Pascal (Pa) 1 standard atmosphere (atm) = 101,325 Pa 1 standard atmosphere (atm) = 760 mm Hg 1 standard atmosphere (atm) = 760 torrs 1 standard atmosphere (atm) = 14.7 psi

1 standard atmosphere (atm) = 101.325 kPa

16PressureColumn height measures Pressure of atmosphere

• 1 standard atmosphere (atm) *

= 760 mm Hg (or torr) *= about 34 feet of water!

17

Sea level 1 atm

4 miles 0.5 atm

10 miles 0.2 atm

5.2

18

Pressure Conversions

What is 475 mm Hg expressed in atm?

1 atm 760 mm Hg

= 0.625 atm475 mm Hg x

19

Pressure Conversions

A. What is 2 atm expressed in torr?

20

Pause for a Cause• Convert a pressure of 1.75 atm to kPa and to mm Hg.

• Convert a pressure of 570. torr to atmospheres and to kPa.

• Convert a pressure of 550 mm of Hg into atm and Pa

• Convert a pressure of 150. KPa to mm of Hg and atm

21Bellringer – answer in complete sentences

1. If you want to reduce the pressure of gas in a tire, what could you do?

2. As you let the gases in a hair spray can escape, what happens to the volume and pressure of the gas?

3. If you want air to enter your lungs, what must you do to the space inside your chest cavity?

22Boyle’s LawP α 1/VThis means Pressure

and Volume are INVERSELY PROPORTIONAL if moles and temperature are constant (do not change). For example, P goes up as V goes down.

P1V1 = P2 V2

Robert Boyle (1627-1691). Son of Early of Cork, Ireland.

23

Boyle’s LawBoyle’s Law

A bicycle pump is a good example of Boyle’s law.

As the volume of the air trapped in the pump is reduced, its pressure goes up, and air is forced into the tire.

24

Boyle’s Law Problem• A sample of oxygen gas has a volume of

150 mL when its pressure is 0.923 atm. If the pressure is increased to 0.987 atm and the temperature remains constant, what will the new volume be?

25You try!

• A balloon filled with helium gas has a volume of 500 mL at a pressure of 1 atm. The balloon is released and reaches an altitude of 6.5 km,

where the pressure is 0.5 atm. Assuming that the temperature has remained the same, what volume does the gas occupy at this height?

26

Charles’s Law

If n and P are constant, then V α T

V and T are directly proportional.

V1T2= V2T1

• If the temperature goes up, the volume goes up!

Jacques Charles (1746-1823). Isolated boron and studied gases. Balloonist.

27

Charles’s original balloon

Modern long-distance balloon

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Charles’s Law

29Practice

A sample of neon gas occupies a volume of 752 mL at 25°C. What volume will

the gas occupy at 50°C if the pressure remains constant?

30

You try!

• A helium-filled balloon has a volume of 2.75 L at 20°C. The volume of the balloon decreases to 2.46 L after it is placed outside on a cold day. What is the outside temperature in K and in °C?

31

Gay-Lussac’s Law

If n and V are constant, then P α T

P and T are directly proportional.

P1T2= P2T1

• If one temperature goes up, the pressure goes up!

Joseph Louis Gay-Lussac (1778-1850)

32

Practice• The gas in an aerosol can is at a pressure of 3.00 atm

at 25°C. Directions on the can warn the user not to keep the can in a place where the temperature exceeds 52°C. What would the gas pressure in the can be at 52°C?

33

Before a trip from New York to Boston, the pressure in an automobile tire is 1.8 atm at

20°C. At the end of the trip, the pressure gauge reads 1.9 atms. What is the new

Celsius temperature of the air inside the tire?

34

Combined Gas Law

• The good news is that you don’t have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION!

P1 V1 T2 = P2 V2 T1

No, it’s not related to R2D2

35

Combined Gas Law Problem

A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29°C. What is the new temperature(°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm?

Set up Data Table

P1 = 0.800 atm V1 = 180 mL T1 = 302 K

P2 = 3.20 atm V2= 90 mL T2 = ??

36

Learning Check

A gas has a volume of 675 mL at 35°C and 0.850 atm pressure. What is the temperature in °C when the gas has a volume of 0.315 L and a pressure of 802 mm Hg?

37

Practice• The gas in an aerosol can is at a pressure of 3.00 atm

at 25°C. Directions on the can warn the user not to keep the can in a place where the temperature exceeds 52°C. What would the gas pressure in the can be at 52°C?

38

You try! The volume of a gas is 27.5 mL at 22.0°C and 0.974 atm. What will the volume be at 15.0°C and 0.993 atm?

39

One More Practice Problem

A balloon has a volume of 785 mL on a fall day when the temperature is 21°C. In the winter, the gas cools to 0°C. What is the new volume of the balloon?

40And now, we pause for this commercial message from STP

OK, so it’s really not THIS kind of STP…

STP in chemistry stands for Standard Temperature and

Pressure

Standard Pressure = 1 atm (or an equivalent)

Standard Temperature = 0 C

(273 K)

STP allows us to compare amounts of

gases between different pressures and temperatures

STP allows us to compare amounts of

gases between different pressures and temperatures

41

Try This One

A sample of neon gas used in a neon sign has a volume of 15 L at STP. What is the volume (L) of the neon gas at 2.0 atm and –25°C?

42Avogadro’s Law

V a number of moles (n)

V = constant x n

V1/n1 = V2/n2

5.3

Constant temperatureConstant pressure

43

Dalton’s Law of Partial Pressures

44

Dalton’s Law of Partial Pressures

For a mixture of gases in a container,

PTotal = P1 + P2 + P3 + . . .

This is particularly useful in calculating the pressure of gases collected over water.

Patm = Pgas + Pwater

45

Dalton’s Law of Partial Pressure Problem

Three of the primary components of air are carbon dioxide, nitrogen, and oxygen. In a sample containing only a mixture of these gases at exactly 1.00 atm., the partial pressure of the carbon dioxide and nitrogen are given as PCO2 = 0.285 torr, PN2= 593.525 torr. What is the partial pressure of oxygen?

46

Dalton’s Law- You Try!

Three of the primary components of air are carbon dioxide, nitrogen, and

oxygen. In a sample containing only a mixture of these gases. The partial

pressure of the carbon dioxide, nitrogen, and oxygen are given as PCO2

= 0.350 atm, PN2= 75.2 kPa, and PO2 = 410. torr. What is the partial pressure of oxygen in atm? What is the total

pressure?

47Consider a case in which two gases, A and B, are in a container of volume V.

PA = nART

V

PB = nBRT

V

nA is the number of moles of A

nB is the number of moles of B

PT = PA + PB XA = nA

nA + nB

XB = nB

nA + nB

PA = XA PT PB = XB PT

Pi = Xi PT

5.6

mole fraction (Xi) = ni

nT

48A sample of natural gas contains 8.24 moles of CH4,

0.421 moles of C2H6, and 0.116 moles of C3H8. If the total pressure of the gases is 1.37 atm, what is the partial

pressure of propane (C3H8)?

Pi = Xi PT

Xpropane = 0.116

8.24 + 0.421 + 0.116

PT = 1.37 atm

= 0.0132

Ppropane = 0.0132 x 1.37 atm = 0.0181 atm

5.6

49

2KClO3 (s) 2KCl (s) + 3O2 (g)

Bottle full of oxygen gas and water vapor

PT = PO + PH O2 2 5.6

50

IDEAL GAS LAW

Brings together gas properties.

Can be derived from experiment and theory.

BE SURE YOU KNOW THIS EQUATION!

P V = n R T

51Ideal Gases

Ideal gases are imaginary gases that perfectly fit all of

the assumptions of the kinetic molecular theory.

Gases are most ideal at high temperatures, low

pressures, with few molecules.

Under these conditions there are less

intermolecular forces.

52

Deviation of Real Gases from Ideal Behavior

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

Kinetic-molecular theory holds true for noble gases.

53Deviations from Ideal Behavior

1 mole of ideal gas

PV = nRT

n = PVRT

= 1.0

5.8

Repulsive Forces

Attractive Forces

54Effect of intermolecular forces on the pressure exerted by a gas.

5.8

55

Using PV = nRTP = PressureV = Volumen = number of molesT = Temperature

R is a constant, called the Ideal Gas ConstantInstead of learning a different value for R for all the

possible unit combinations, we can just memorize one value and convert the units to match R.

R = 0.0821L • atm

Mol • K

56

Using PV = nRTHow much N2 is required to fill a small room

with a volume of 960 cubic feet (27,000 L) to 745 mm Hg at 25 oC?

Solution1. Get all data into proper units V = 27,000 L T = 25 oC + 273 = 298 K P = 745 mm Hg (1 atm/760 mm Hg)

= 0.98 atmAnd we always know R, 0.0821 L atm / mol K

57

Using PV = nRTHow much N2 is req’d to fill a small room with a volume of 960

cubic feet (27,000 L) to P = 745 mm Hg at 25 oC?

Solution2. Now plug in those values and solve for

the unknown.

PV = nRT

n = (0.98 atm)(2.7 x 10 4 L)

(0.0821 L • atm/K • mol)(298 K)

n = 1.1 x 103 mol (or about 30 kg of gas)

RT RT

58

Learning Check

Dinitrogen monoxide (N2O), laughing gas, is used by dentists as an anesthetic. If 2.86 mol of gas occupies a 20.0 L tank at 23°C, what is the pressure (mm Hg) in the tank in the dentist office?

59

Learning Check

A 5.0 L cylinder contains oxygen gas at 20.0°C and 735 mm Hg. How many grams of oxygen are in the cylinder?

60

Ideal Gas Law Problem

What is the pressure in atmospheres exerted by a 0.500 mol sample of nitrogen

gas in a 10.0L container at 298 K?

61

Ideal Gas Law Problem #2

How many moles of helium gas would it take to fill a balloon with a volume of 1000.0 cm3 (1 cm3 = 1mL) when the temperature is 320C and the atmospheric pressure is 752 mm of Hg?

62

• A tank with a volume of 658 mL contains 1.50 grams of neon gas. The maximum safe pressure that the

tank can withstand is 4.50 X 102 kPa. At what temperature will the tank have that pressure?

63Deviations from Ideal Gas Law

• Real molecules have

volume.The ideal gas consumes the

entire amount of available volume. It does not account for the volume of the molecules themselves.

• There are intermolecular forces.

An ideal gas assumes there are no attractions between molecules. Attractions slow down the molecules and reduce the amount of collisions.– Otherwise a gas could not

condense to become a liquid.

64Health NoteWhen a scuba diver is several hundred feet under water, the high pressures cause N2 from

the tank air to dissolve in the blood. If the diver rises too fast, the dissolved N2 will form

bubbles in the blood, a dangerous and painful condition called "the bends". Helium, which is inert, less dense, and does not dissolve in the blood, is mixed with O2

in scuba tanks used for deep descents.

65

Density (d) Calculations

d = mV =

PMRT

m is the mass of the gas in g

M is the molar mass of the gas

Molar Mass (M ) of a Gaseous Substance

dRTP

M = d is the density of the gas in g/L

5.4

Solve for n, which = mass/molar mass

Or,

66

67A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and

27.00C. What is the molar mass of the gas?

5.3

68Gas Stoichiometry

What is the volume of CO2 produced at 370 C and 1.00 atm when 5.60 g of glucose are used up in the reaction:

C6H12O6 (s) + 6O2 (g) 6CO2 (g) + 6H2O (l)

g C6H12O6 mol C6H12O6 mol CO2 V CO2

5.60 g C6H12O6

1 mol C6H12O6

180 g C6H12O6

x6 mol CO2

1 mol C6H12O6

x = 0.187 mol CO2

V = nRT

P

0.187 mol x 0.0821 x 310.15 KL•atmmol•K

1.00 atm= = 4.76 L

5.5

69

Stoichiometry of gases

• Steps in Solving Mass-Volume Stoichiometry Problems– 1. Write a balanced equation.

– 2. Find the number of moles of a given substance.– 3. Use the ratio of moles of a given substance to

moles of a required substance to find the moles of a gas.--4. Express moles of a gas in terms of volume of a gas.

70

Sample Mass- Volume Problem• Pg. 900 #315. Sodium reacts vigorously with water to

produce hydrogen and sodium hydroxide according to the following equation:

2Na(s) + 2H2O(l) 2 NaOH(aq) + H2(g)

If 0.027 g of sodium reacts with excess water, what volume of hydrogen at STP is formed?

71

Pg. 900 #321. Urea, (NH2)2CO is an important fertilizer that is manufactured by the following

reaction:

2NH3(g) + CO2(g) (NH2)2CO(s) + H2O(g)

What volume of NH3 at STP will be needed to produce 8.50 X 104 kg of urea?

Mass-Volume Problem- You Try!

72

Sample Volume Mass Problem

Pg. 900 #318. Dinitrogen monoxide can be prepared by heating ammonium nitrate, which decomposes according to the following equation:

NH4NO3(s) N2O (g) + 2H2O(l)

What mass of ammonium nitrate should be decomposed in order to produce 250. mL of N2O measured at STP?

73

Pg. 900 #325. Oxygen can be generated in the laboratory by heating potassium chlorate. The reaction is

represented by the following equation:

2KClO3(s) 2KCl(s) + 3O2(g)

What mass of KClO3 must be used in order to generate 5.00 L of O2, measured at STP

Volume- Mass Problem- You Try!

74

The principal source of sulfur is in the form of deposits of free sulfur occurring in volcanically active regions.

The sulfur was initially formed by the reaction between the two volcanic vapors SO2 and H2S to form H2O(l) and

S (s). What volume of each gas, at 730 mm of Hg and 22oC, was needed to form a sulfur deposit of 4.50 X 105

kg on the slopes of a volcano in Hawaii?

Practice Problem on Using Stoichiometry Under Nonstandard Conditions

75

Practice Problem on Using Stoichiometry Under Nonstandard Conditions- You Try!

• A 3.25-g sample of solid calcium carbide (CaC2) reacts with water to produce acetylene gas (C2H2) and aqueous calcium hydroxide. If the acetlylene is at 17oC and 740 mm of Hg, how many mL of acetylene were produced?

CaC2 + H2O C2H2 + Ca(OH)2

76

Practice Problem on Using Stoichiometry Under Nonstandard Conditions

• What volume of oxygen gas in liters can be collected at 0.987 atm pressure and 25oC when 30.6 g of KClO3 decompose by heating according to the following equation?

2KClO3(s) 2KCl(s) + 3O2(g)

77

Practice Problem on Using Stoichiometry Under Nonstandard Conditions- You Try!

How many liters of gaseous carbon monoxide at 27oC and 0.247 atm can be produced from the burning of 65.5 g of carbon according to the

following equation:

2C(s) + O2(g) 2CO2(g)

78

The distribution of speedsfor nitrogen gas molecules

at three different temperatures

The distribution of speedsof three different gases

at the same temperature

5.7

urms = 3RTM

Velocity of a Gas

79Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties.

5.7

NH3

17 g/molHCl

36 g/mol

NH4Cl

80GAS DIFFUSION AND EFFUSION

• diffusion is the gradual mixing of molecules of different gases.

• effusion is the movement of molecules through a small hole into an empty container.

81GAS DIFFUSION AND

EFFUSION

Graham’s law governs effusion and diffusion of gas molecules. KE=1/2 mv2

Thomas Graham, 1805-1869. Professor in Glasgow and London.

Rate of effusion is inversely proportional

to its molar mass.

Rate of effusion is inversely proportional

to its molar mass.

M of AM of B

Rate for B

Rate for A

82

GAS DIFFUSION AND EFFUSION

Molecules effuse thru holes in a rubber balloon, for example, at a rate (= moles/time) that is

• proportional to T• inversely proportional to M.Therefore, He effuses more rapidly

than O2 at same T.

He

83

Gas Diffusionrelation of mass to rate of

diffusion

Gas Diffusionrelation of mass to rate of

diffusion

• HCl and NH3 diffuse from opposite ends of tube.

• Gases meet to form NH4Cl

• HCl heavier than NH3

• Therefore, NH4Cl forms closer to HCl end of tube.

• HCl and NH3 diffuse from opposite ends of tube.

• Gases meet to form NH4Cl

• HCl heavier than NH3

• Therefore, NH4Cl forms closer to HCl end of tube.

84

Graham’s Law Problem 1

1 mole of oxygen gas and 2 moles of ammonia are placed in a container and allowed to react at 850 degrees celsius according to the equation:

4 NH3(g) + 5 O2(g) --> 4 NO(g) + 6 H2O(g)

Using Graham's Law, what is the ratio of the effusion rates of NH3(g) to O2(g)?

85

Graham’s Law Problem 2

What is the rate of effusion for H2 if 15.00 ml of CO2 takes 4.55 sec to effuse out of a container?

86

Graham’s Law Problem 3

What is the molar mass of gas X if it effuses 0.876 times as rapidly as N2(g)?

87