S TATES OF M ATTER Chapter 10

State of Matter VolumeShapeDensity Compressibility Motion of Molecules Gas Liquid Solid Three States of Matter

Phase Diagrams phase diagram: graph that shows the relationship between the physical state of a substance and the temperature and pressure of the substance.

T HREE I MPORANT L INES Liquid-gas phase changes: Liquid-solid phase changes: Solid-gas phase changes:

T WO I MPORTANT P OINTS Triple Point : where all three lines meet, a specific temperature and pressure where all three phases exist at the same time

T RIPLE P OINT V IDEO

T WO I MPORTANT P OINTS Critical Point : a specific temperature and pressure where the gas can no longer be turned into a liquid, above this point a substance becomes a supercritical fluid

“N ORMAL ” C ONDITIONS Occur at standard atmospheric pressure: 1 atm or kPa To identify the normal boiling point of a substance: Locate the line between liquid and gas, and identify the temperature at 101 kPa __________________ To identify the normal freezing point of a substance: Locate the line between liquid and solid, and identify the temperature at 101 kPa __________________

G ASES Chapter 11

H 2 N 2 O 2 F 2 Cl 2 He Ne Ar Kr Xe Rn W HAT ELEMENTS EXIST AS A GAS AT ROOM TEMPERATURE ?

K INETIC M OLECULAR T HEORY OF G ASES Describing the _____________ of the ______________________ of a gas. Ideal gas: hypothetical gas that satisfies all 5 ideas of KMT Occurs at high temp and low pressure 1. A gas consists of very small particles, each of which has a ____________. 2. The ____________or dimensions of gas particles are considered to be __________ because of the large space between each particle. motion molecules mass zero volume

KMT CONT. 3. Gas molecules are in _______________________ in random directions. 4. Collisions among molecules or with the walls of their container are perfectly ____________. Gas molecules do not show attractive or repulsive forces on one another. 5. If gases are at the same ______________, they will have the same ______________energy. constant, rapid motion elastic kinetic temperature

1. Gases have very low densities. Solids and liquids have much higher density. Gas particles are spread out.

2. Gases have mass. A filled balloon is heavier than an empty balloon. 3. Gases are the most compressible state of matter. Gas particles can be squished closer together.

4. Gases take the shape and volume of their containers. Gases fill the entire space they are in. 5. Different gases will mix evenly and completely called diffusion. You can smell brownies baking in the oven when in a different room.

6. Gases exert pressure. You can feel the wind hit your face. 7. The pressure of a gas depends on its temperature. Temperature is a measure of kinetic energy. The more energy, the more force the gases hit a surface, the higher the pressure.

G AS M EASUREMENTS

M EASURING G ASES MeasurementSymbolUnitAbbrev. Amountnmolesmol VolumeVLitersL TemperatureTKelvinK PressurePatmosphereatm

R EMEMBER : 1 mol = 6.02 x particles 1 mL = 1 cm 3 K = o C + 273

K = 0 C K = ___ 0 Cabsolute zero 273 K = ___ 0 C freezing pt of water 373 K = ___ 0 Cboiling pt of water ____ K = 25 0 C room temperature ____ K = 37 0 C body temperature What temp would a gas be: in a boiling water bath? in an ice bath?

W HAT IS PRESSURE ? Force exerted on a certain area For gases: pressure is measured by the number of collisions the particles have with each other and the walls of the container Same Force Less Area More Pressure

Units of Pressure

Measuring Gas Pressure Atmospheric pressure is measured by a barometer. The pressure is then read on the column of mercury. Barometer 760 mm

Measuring Gas Pressure At sea level, the atmosphere keeps the mercury in a barometer at an average height of 760 mm (equals 1 atmosphere, atm.) One millimeter of mercury is also equal to a torr, after Evangelista Torricelli, the Italian physicist who invented the barometer.

Sea level1 atm 4 miles0.5 atm 10 miles0.2 atm Measuring Gases

Scientists have specified a set of standard conditions called standard temperature and pressure (STP) Standard Temp = 0°C = 273 K Standard Pressure = 1 atm = 760 mmHg = 760 torr = kPa

P RESSURE C ONVERSIONS The average atmospheric pressure in Denver, Colorado is atm. Express this pressure in: a. millimeters of mercury (mm Hg) and b. kilopascals (kPa) Given: atmospheric pressure = atm Unknown: a. pressure in mm Hg b. pressure in kPa

P RESSURE C ONVERSIONS A NSWERS A) B)

T HE G AS L AWS

W HAT IS VAPOR PRESSURE ? The pressure that exists above the surface of a liquid from particles escaping the surface of the liquid

V APOR P RESSURE IS EFFECTED BY HOW VOLATILE THE LIQUID IS

D ALTON ’ S L AW OF P ARTIAL P RESSURES John Dalton discovered that the pressure exerted by each gas in a mixture is independent of that exerted by other gases present. Gases mix evenly and completely to form a homogeneous mixture. Each gas in a mixture behaves as if it were the only gas present (assuming no chemical reactions). The pressure of each gas in a mixture is called the partial pressure.

P1P1 P2P2 P total = P 1 + P 2 Dalton’s law of partial pressures: the total pressure of a gas mixture is the sum of the partial pressures of each gas. P T = P gasA + P gasB + P gasC + etc.

Examples: 1. An organic chemist was considering the pressures exerted by three gases (M, N, L) in a flask. The total pressure inside the flask was 456 mmHg. If gas M contributes 200 mmHg, and gas L contributes 10 mmHg, what is the pressure exerted by gas N.

Examples: 2. An organic chemist was considering the pressures exerted by three gases (M, N, L) in a flask. The total pressure inside the flask was 644 mmHg. If gas M contributes to 21% of the pressure, and gas N contributes 54% what are the pressures exerted by all three gases in mmHg.

MOLE FRACTIONS Mole fraction of gas A = Moles of gas A_____ Total number of moles of gas GAS AMOUNT IN MOLES A B C 2.35 D 0.78 Examples: 1. Four gases are found in an atmospheric sample of gas. The data below indicates their respective amount. Determine the mole fraction of each.

What would be the pressure of each gas at standard pressure in kPa? GAS AMOUNT IN MOLES A B C 2.35 D 0.78

P a = X a P T H OW DO P ARTIAL P RESSURE AND M OLE F RACTION R ELATE ? Where: P a = partial pressure of a X a = mole fraction of a P T = total pressure Examples: Determine the mole fraction and partial pressure of oxygen, nitrogen, and argon using the following data. The total pressure of the system is 760 mmHg. GASAMOUN T IN GRAMS O2O N2N Ar

COLLECTING GASES OVER WATER Dalton ’ s Law can be used to calculate the pressure of gas collected over water Set-up for such a system is shown below

The collection flask initially contains all water When a reaction takes place in the reaction chamber gas travels through tubing and displaces the water in the collection flask When the reaction is complete and no more water is displaced the flask is stoppered and the gas is collected WITH WATER VAPOR

To find the pressure of the dry gas you need to subtract the pressure due to water vapor from the total pressure. All water vapor pressure values at a specific temperature are found by using the reference sheet. P total = P gas + P H2O

Examples: 1. A gas is collected over water at 50 o C and barometric pressure of 95 kPa. What is the pressure exerted by the dry gas? 2. Oxygen gas is collected over water from the reaction of Na 2 O 2 and water. The oxygen displaces 318 mL of water at 23 o C and 1.000atm. What is the pressure of dry O 2.

GAS EQUATIONS

As P (h) increases V decreases P RESSURE AND V OLUME R ELATIONSHIP

P 1 x V 1 = P 2 x V 2 Constant temperature Constant amount of gas pressure and volume are inversely related T HIS IS CALLED : BOYLE’S LAW Graphical Relationship:

A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL? P 1 x V 1 = P 2 x V 2 P 1 = 726 mmHg V 1 = 946 mL P 2 = ?V 2 = 154 mL P 2 = P 1 x V 1 V2V2 726 mmHg x 946 mL 154 mL = = 4460 mmHg

As T increasesV increases T EMPERATURE AND V OLUME R ELATIONSHIP

Temperature must be in Kelvin Constant pressure Constant amount of gas V 1 = V 2 T 1 T 2 temperature and volume are directly related T HIS IS CALLED : CHARLES’ LAW Graphical Relationship:

A sample of carbon monoxide gas occupies 3.20 L at C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant? V 1 = 3.20 L T 1 = 125 o C 398 K V 2 = 1.54 L T 2 = ? T 2 = V 2 x T 1 V1V L x 398 K 3.20 L = = 192 K V 1 = V 2 T 1 T 2

Temperature must be in Kelvin Constant volume Constant amount of gas temperature and pressure are ________related T HIS IS CALLED : G UY -L USSAC ’ S L AW Graphical Relationship:

G AY -L USSAC ’ S L AW P ROBLEM The gas in a container is at a pressure of 3.00 atm at 25°C. Directions on the container warn the user not to keep it in a place where the temperature exceeds 52°C. What would the gas pressure in the container be at 52°C? Remember: Temperature must be in KELVIN!!! P 1 = 3.00 atmP 2 = ? T 1 = 25°C T 2 = 52°C P 2 = P 1 T 2 = (3.00 atm) (325 K) = 3.27 atm T K

O THER R ELATIONSHIPS What would an equation look like for: pressure and amount? volume and amount?

Temperature must be in Kelvin Constant amount of gas Boyle’s law and Charles’s law can be combined into a single equation that can be used for situations in which temperature, pressure, and volume, all vary at the same time. T HIS IS CALLED : C OMBINED G AS L AW

C OMBINED G AS L AW P ROBLEM A helium-filled balloon has a volume of 50.0 L at 25°C and 1.08 atm. What volume will it have at atm and 10.0°C? Remember: Temperature must be in KELVIN!!!

M ULTI -S TEP P ROBLEM Carbon dioxide gas is collected over water at a temperature of 30.0 o C and a pressure of 728 torr. The volume of gas plus water vapor collected is 27.8mL. What is the volume of dry carbon dioxide at STP? (The partial pressure of water vapor at 30 o C is 31.8 mmHg) Remember: Temperature must be in KELVIN!!!

E ND OF M ATERIAL FOR Q UIZ #1

A VOGADRO ’ S L AW When amount ______________, volume ____________ Amount of moles & volume are _____________ related. Variables: volume, moles Constants: pressure, temperature V 1 = V 2 n 1 n 2

Because of Avogadro’s law equal volumes of gases at constant temperature and pressure contain equal numbers of molecules. Avogadro determined one mole of any gas (regardless of mass differences) will expand to the same volume every time standard molar volume of a gas: L (rounded to 22.4 L)

M OLAR V OLUME V IDEO

D ERIVING THE I DEAL G AS L AW Review: Write down the combined gas law; where do you think “n” fits in? If both sides must equal each other, we can set one side equal to a constant. We’ll call this constant “R.”

T HE I DEAL G AS L AW E QUATION PV = nRT ideal gas law: relates all variables – pressure, volume, moles, temperature

D ERIVING THE I DEAL G AS L AW C ONSTANT R: ideal gas constant Its value depends on the units chosen for pressure, volume, and temperature in the rest of the equation. What are the standard conditions for an ideal gas? P = n = V = T = Plug in values into the equation and calculate. What is the constant that you get? Usually rounded to (Latm/molK)

N UMERICAL V ALUES OF T HE G AS C ONSTANT “R” ALWAYS MATCH UP YOUR UNITS!!!!

G AS S TOICHIOMETRY Avogadro’s law can be applied in calculating the stoichiometry of reactions involving gases. The coefficients in chemical equations of gas reactions reflect not only mole ratios, but also volume ratios (assuming conditions remain the same). Discovered by Dalton, while exploring why water was a ratio of 2H to 1O example 2H 2 (g) + O 2 (g) → 2H 2 O(g) 2 molecules 1 molecule2 molecules 2 mole 1 mole2 mol 2 volumes 1 volume 2 volumes

G AS S TOICHIOMETRY P ROBLEM Number 1 on Practice Sheet What volume of nitrogen at STP would be required to react with mol of hydrogen to produce ammonia? N H 2  2 NH 3

G AS S TOICHIOMETRY P ROBLEM S OLUTION mol H 2 x 1 mol N 2 x 22.4 L N 2 3 mol H 2 1 mol N 2 = L N 2

I DEAL G AS L AW S AMPLE P ROBLEM A sample of carbon dioxide with a mass of g was placed in a 350. mL container at 400 K. What is the pressure exerted by the gas? P = ? V = 350. mL = L n = g = ? mol T = 400 K

I DEAL G AS L AW P ROBLEM S OLUTION P = nRT = mol (.0821 Latm/molK) 400 K V.350 L = atm

G AS S TOICH AND I DEAL G AS L AW Number 2 on Practice Sheet What volume of nitrogen at 215 O C and 715 mmHg would be required to react with mol of hydrogen to produce ammonia? N H 2  2 NH 3 Note: This system is NOT at STP!!

G AS S TOICHIOMETRY P ROBLEM S OLUTION mol H 2 x 1 mol N 2 = mol N 2 3 mol H 2 P = 715 mmHg V = ? n = mol N 2 R = 62.4 LmmHg/molK T = 25 O C = 488 K

D IFFUSION AND E FFUSION REMEMBER: EFFUSION: process when the molecules of a gas confined in a container randomly pass through a tiny opening in the container DIFFUSION: the gradual mixing of two or more gases due to their spontaneous, random motion

G RAHAM ’ S L AW OF E FFUSION

Graham’s law of effusion: the rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses.

Sample Problem What is the rate of effusion of hydrogen if oxygen has a velocity of 175 m/s at the same temperature and pressure.

Substitute the given values into the equation: Hydrogen rate of effusion is … Graham’s Law of Effusion, continued

G RAHAM ’ S L AW - V ISUAL P ROBLEM

Gas Stoichiometry What is the volume of CO 2 produced at 37 0 C and 1.00 atm when 5.60 g of glucose are used up in the reaction: C 6 H 12 O 6 (s) + 6O 2 (g) 6CO 2 (g) + 6H 2 O (l) g C 6 H 12 O 6 mol C 6 H 12 O 6 mol CO 2 V CO g C 6 H 12 O 6 1 mol C 6 H 12 O g C 6 H 12 O 6 x 6 mol CO 2 1 mol C 6 H 12 O 6 x = mol CO 2 V = nRT P mol x x K Latm molK 1.00 atm = = 4.76 L