E.Q.: How do gases behave and what are the conditions that affect this behavior?

Airbags fill with NAirbags fill with N22 gas in gas in an accident. an accident.

Gas is generated by the Gas is generated by the decomposition of sodium decomposition of sodium azide, NaNazide, NaN33..

2 NaN2 NaN33 ---> 2 Na + 3 N ---> 2 Na + 3 N22

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

Gases can be expanded Gases can be expanded infinitely.infinitely.

Gases fill containers Gases fill containers uniformly and uniformly and completely.completely.

Gases diffuse and mix Gases diffuse and mix rapidly.rapidly.

Model used to describe the behavior of gases in terms of particles that are constantly moving and the forces between them

It assumes that the following concepts about gases are true….

Gas particles do not attract or repel each other and are free to move within the container they are in

Gas particles are much smaller than the distances between them

It assumes the gas particles have no volume

Volume of a gas is mainly empty space

Low density of particles = great compressibility

Gas particles are in constant, random motion

Particles move in straight lines and collide with each other and the walls of their container

No kinetic energy is lost when gas particles collide with one another or with the walls of their container

Collisions are completely elastic

If temperature remains the same, then…..

All gas particles have the same average KE at a given temperature

As temperature increases, the KE also increases and vice versa

Gas properties can be modeled Gas properties can be modeled using math. using math.

Model depends on—Model depends on— VV = = volumevolume of the gas ( of the gas (LL)) TT = = temperaturetemperature ( (KK))

Note: ALL temperatures Note: ALL temperatures MUSTMUST be in Kelvin!!! No be in Kelvin!!! No Exceptions!Exceptions!

nn = = amountamount ( (molesmoles)) PP = = pressurepressure

( (atmospheresatmospheres))

Pressure is force per unit area

Pressure of air is Pressure of air is measured with a measured with a BAROMETERBAROMETER (developed by (developed by Torricelli in 1643)Torricelli in 1643)

Hg rises in tube until force of Hg rises in tube until force of Hg (up) balances the force Hg (up) balances the force of atmosphere (down). (Just of atmosphere (down). (Just like a straw in a soft drink)like a straw in a soft drink)

P of Hg pushing down related P of Hg pushing down related to to

Hg densityHg density column heightcolumn height

Column height measures Column height measures Pressure of atmospherePressure of atmosphere

1 standard atmosphere 1 standard atmosphere (atm) *(atm) *

= 760 mm Hg (or 1 Torr) *= 760 mm Hg (or 1 Torr) *= 29.92 inches Hg = 29.92 inches Hg = 14.7 pounds/in= 14.7 pounds/in2 2 (psi)(psi)= 101.3 kPa (SI unit is = 101.3 kPa (SI unit is

PASCAL)*PASCAL)*= about 34 feet of water!= about 34 feet of water!

* Memorize these!* Memorize these!

A. What is 475 mm Hg expressed in atm?

1 atm 760 mm Hg

B. The pressure of a tire is measured as 29.4 psi.

What is this pressure in mm Hg? 760 mm Hg

14.7 psi

= 1.52 x 103 mm Hg

= 0.625 atm475 mm Hg x

29.4 psi x

A. What is 2 atm expressed in torr?

B. The pressure of a tire is measured as 32.0 psi.

What is this pressure in kPa?

P P αα 1/V 1/VThis means This means Pressure Pressure

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

PP11VV11 = P = P22 V V22

Robert Boyle Robert Boyle (1627-1691)(1627-1691)

P proportional to 1/VP proportional to 1/V

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

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

If n and P are If n and P are constant, constant, then then V V αα T T

V and T are V and T are directly directly proportional.proportional.

VV11 V V22

==

TT11 T T22 If temperature If temperature

goes up, the goes up, the volume goes up!volume goes up!

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

Charles’s original balloonCharles’s original balloon

Modern long-distance balloonModern long-distance balloon

If n and V are If n and V are constant, constant, then then P P αα T T

P and T are P and T are directly directly proportional.proportional.

PP11 P P22

==

TT11 T T22 If temperature goes If temperature goes

up, the pressure up, the pressure goes up!goes up!

Joseph Louis Gay-Joseph Louis Gay-Lussac (1778-1850)Lussac (1778-1850)

P proportional to TP proportional to T

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 P2 V2

= T1 T2

If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law!

= P1 V1

T1

P2 V2

T2

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

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 = ??

P1 = 0.800 atm V1 = 180 mL T1 = 302 KP2 = 3.20 atm V2= 90 mL T2 = ??

P1 V1 P2 V2

= P1 V1 T2 = P2 V2 T1

T1 T2

T2 = P2 V2 T1

P1 V1

T2 = 3.20 atm x 90.0 mL x 302 K

0.800 atm x 180.0 mL

T2 = 604 K - 273 = 331 °C

= 604 K

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?

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?

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 deg

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

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?

Equal volumes of gases at the Equal volumes of gases at the same T and P have the same same T and P have the same number of molecules.number of molecules.

V = n (RT/P) = knV = n (RT/P) = knV and n are directly related.V and n are directly related.

twice as many twice as many moleculesmolecules

P proportional to nP proportional to n

The gases in this The gases in this experiment are all experiment are all measured at the measured at the same T and V.same T and V.

Brings together gas Brings together gas properties.properties.

Can be derived from Can be derived from experiment and experiment and theory.theory.

BE SURE YOU KNOW BE SURE YOU KNOW THIS EQUATION!THIS EQUATION!

P V = n R TP V = n R T

Chemists came up with a simple gas equation that “looks the other way” when small factors affect the behavior of gases.

In order for a gas to be ideal, the gas needs to follow the Kinetic Molecular Theory.

To simplify calculations involving gases, the assumption is that gas molecules are just specs (with no volume), moving in straight lines and with no attractive forces between them.

http://www.youtube.com/watch?v=BxUS1K7xu30

P = PressureP = PressureV = VolumeV = VolumeT = TemperatureT = Temperaturen = number of molesn = number of moles

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

all the possible unit combinations, we can all the possible unit combinations, we can just just memorizememorize oneone value and value and convert the convert the units to match R.units to match R.

R = 0.0821R = 0.0821

L • atm

mol • K

R = 0.0821 L*atmmol*K

R = 8.314 L*kPamol*K

R = 62.4 L*mmHgmol*K

1) How many moles of a gas does it take to occupy 120. L at a pressure of 2.30 atmospheres and a temperature of 340. K?

2) If I have a 50.0 L container that holds 45.0 moles of a gas at a temperature of 200. C, what is the pressure inside the container?

3) I have a balloon that can hold 100. L of air. If I blow up this balloon with 3.00 moles of O2 gas at a pressure of 1.00 atm, what is the temperature of the balloon?

How much NHow much N22 is required to fill a small is required to fill a small room with a volume of 960 cubic feet room with a volume of 960 cubic feet (27,000 L) to 745 mm Hg at 25 (27,000 L) to 745 mm Hg at 25 ooC?C?

SolutionSolution

1. Get all data into proper units1. Get all data into proper units V = 27,000 LV = 27,000 L

T = 25 T = 25 ooC + 273 = 298 KC + 273 = 298 K

P = 745 mm Hg (1 atm/760 mm Hg) P = 745 mm Hg (1 atm/760 mm Hg) = 0.98 atm = 0.98 atm

And we always know R, 0.0821 L atm / mol And we always know R, 0.0821 L atm / mol KK

How much NHow much N22 is req’d to fill a small room with a volume of is req’d to fill a small room with a volume of 960 cubic feet (27,000 L) to P = 745 mm Hg at 25 960 cubic feet (27,000 L) to P = 745 mm Hg at 25 ooC?C?

SolutionSolution

2. Now plug in those values and solve for 2. Now plug in those values and solve for the unknown.the unknown.

PV = PV = nnRTRT

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

(0.0821 L • atm/K • mol)(298 K)n =

(0.98 atm)(2.7 x 10 4 L)

(0.0821 L • atm/K • mol)(298 K)

n = 1.1 x 10n = 1.1 x 1033 mol (or about 30 kg of gas) mol (or about 30 kg of gas)

RT RTRT RT

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?

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?

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.

The % of gases in air Partial pressure (STP)

78.08% N2 593.4 mm Hg

20.95% O2 159.2 mm Hg

0.94% Ar 7.1 mm Hg

0.03% CO2 0.2 mm Hg

PAIR = PN + PO + PAr + PCO = 760 mm Hg 2 2 2

Total Pressure 760 mm Hg

What is the total pressure in the flask?What is the total pressure in the flask?

PPtotaltotal in gas mixture = P in gas mixture = PAA + P + PBB + ... + ...Therefore, Therefore,

PPtotaltotal = P = PHH22OO + P + POO22 = 0.48 atm = 0.48 atm

Dalton’s Law: total P is sum ofDalton’s Law: total P is sum of PARTIALPARTIAL pressures.pressures.

2 H2 H22OO2 2 (l) ---> 2 H(l) ---> 2 H22O (g) + OO (g) + O2 2 (g)(g)

0.32 atm 0.32 atm 0.16 0.16 atmatm

John DaltonJohn Dalton1766-18441766-1844

When 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.

Gases, since they mix with other gases readily, must be collected in an environment where mixing can not occur. The easiest way to do this is under water because water displaces the air. So when a gas is collected “over water”, that means the container is filled with water and the gas is bubbled through the water into the container. Thus, the pressure inside the container is from the gas AND the water vapor. This is where Dalton’s Law of Partial Pressures becomes useful.

A student collects some hydrogen gas over water at 20 degrees C and 768 torr. What is the pressure of the H2 gas?

768 torr – 17.5 torr = 750.5 torr

HighHigh densitydensity

Low Low densitydensity

22.4 L of ANY gas AT STP = 1 mole

2 H2 H22OO2 2 (l) ---> 2 H(l) ---> 2 H22O (g) + OO (g) + O2 2 (g)(g)

Decompose 1.1 g of HDecompose 1.1 g of H22OO22 in a flask with a in a flask with a volume of 2.50 L. What is the volume of volume of 2.50 L. What is the volume of OO22 at STP? at STP?

Bombardier beetle Bombardier beetle uses decomposition uses decomposition of hydrogen peroxide of hydrogen peroxide to defend itself.to defend itself.

2 H2 H22OO2 2 (l) ---> 2 H(l) ---> 2 H22O (g) + OO (g) + O2 2 (g)(g)

Decompose 1.1 g of HDecompose 1.1 g of H22OO22 in a flask with a volume of 2.50 L. in a flask with a volume of 2.50 L. What is the volume of OWhat is the volume of O22 at STP? at STP?

SolutionSolution1.1 g1.1 g HH22OO22 1 mol H 1 mol H22OO22 1 mol O 1 mol O22 22.4 L O 22.4 L O22

34 g H34 g H22OO22 2 mol H 2 mol H22OO22 1 mol O 1 mol O22

= 0.36 L O2 at STP

A. What is the volume at STP of 4.00 g of CH4?

B. How many grams of He are present in 8.0 L of gas at STP?

1. Do the problem like it was at STP. (V1)

2. Convert from STP (V1, P1, T1) to the stated conditions (P2, T2)

How many L of O2 are needed to react 28.0 g NH3 at 24°C and 0.950 atm?

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

diffusiondiffusion is the is the gradual mixing of gradual mixing of molecules of molecules of different gases.different gases.

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

HONORS HONORS onlyonly

Graham’s law Graham’s law governs effusion governs effusion and diffusion of and diffusion of gas molecules.gas molecules.

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

Rate of effusion is Rate of effusion is inversely proportional inversely proportional to its molar mass.to its molar mass.

Rate of effusion is Rate of effusion is inversely proportional inversely proportional to its molar mass.to its molar mass.

M of AM of B

Rate for B

Rate for A

HONORS HONORS onlyonly

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

proportional to Tproportional to T inversely proportional to M.inversely proportional to M.Therefore, He effuses more Therefore, He effuses more

rapidly than Orapidly than O22 at same T. at same T.

HeHe

HONORS HONORS onlyonly

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.

HONORS HONORS onlyonly