9/22/2015 1 Chapter 12 The Behavior of Gases Chemistry.

04/19/231

Chapter 12Chapter 12The Behavior of GasesThe Behavior of Gases

Chemistry

04/19/232

The Kinetic Theory RevisitedThe Kinetic Theory Revisited

Have you ever noticed that a balloon shrinks when it gets cold and expands when it is warmed? You saw a balloon shrink to nothing when placed in liquid nitrogen and then expand when removed from the liquid nitrogen!

04/19/233

The Kinetic Theory RevisitedThe Kinetic Theory RevisitedGases consist of hard spherical particlesThese particles are so small that in relation

to the distances between them that their individual volumes can be assumed to be insignificant.

There is considerable empty space between the particles

Between the particles is empty space. No attractive or repulsive forces exist between the particles.

04/19/234

The Kinetic Theory RevisitedThe Kinetic Theory Revisited

The particles move in constant random motion. They travel in straight paths, independently of

each other. The gas particles change direction only from collision with one another or with other objects.

Gases fill their containers regardless of the shape and volume of the containers.

Uncontained gases diffuse into space without limit.

04/19/235

The Kinetic Theory RevisitedThe Kinetic Theory Revisited

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

04/19/236

The Kinetic Theory RevisitedThe Kinetic Theory Revisited

Compressibility is a measure of how much the volume of matter decreased under pressure.

Gases are easily compressed (unlike solids or liquids)

Compressibility is why air bags work.

04/19/237

The Kinetic Theory RevisitedThe Kinetic Theory Revisited

Remember that the average kinetic energy of a collection of gas particles is directly proportional to the Kelvin temperature of a gas

04/19/238

The Kinetic Theory RevisitedThe Kinetic Theory Revisited

The four variables that describe a gas are:

– Pressure in kilopascals, kPa

– Volume in liters, L

– Temperature in Kelvin degrees – K has no° sign

– Number of moles, n

04/19/239

Factors Affecting Gas PressureFactors Affecting Gas Pressure

The limitation of how many gas particles can be added to a container is the strength of the container.

Halving the number of gas particles, halves the pressure.

04/19/2310

Factors Affecting Gas PressureFactors Affecting Gas Pressure

Raising the temperature of a gas in a closed container increases the pressure.

The speed and kinetic energy increases as the temperature increases. Faster moving particles impact the walls of the container with more energy, exerting greater pressure.

Doubling the Kelvin temperature doubles the gas pressure.

04/19/2311

Factors Affecting Gas PressureFactors Affecting Gas Pressure

Heating an aerosol can can cause the can to burst. Why?

As the temperature increases the gas pressure increases. At some point, the aerosol can cannot withstand the increased pressure and it bursts open.

04/19/2312

Factors Affecting Gas PressureFactors Affecting Gas Pressure

You can raise the pressure of a contained gas by decreasing the volume. The more gas is compressed, the greater the gas pressure.

Reducing the volume by half doubles the gas pressure.

Doubling the volume halves the gas pressure.

04/19/2313

Boyle’s LawBoyle’s LawP P αα 1/V 1/VThis means Pressure and This means Pressure and

Volume are INVERSELY Volume are INVERSELY PROPORTIONAL if moles PROPORTIONAL if moles and temperature are and temperature are constant (do not change).constant (do not change).

For example, P goes up as V For example, P goes up as V goes down.goes down.

PP11VV11 = P = P22 V V22

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

04/19/2314

The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s Law

Boyle’s Law is the pressure-volume relationship

Boyle’s Law states that for a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure. In an inverse relationship the product of the two variable quantitative is constant.

P1 V1 = P2 V2

04/19/2315

The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s Law

Now, let's look at how these ideas relate to diving. It is well known among divers that diving at the surface can be more dangerous than deeper diving. We can understand this by first noting that for every 10 meters you descend in the water, the pressure increases by about 1 atm.

04/19/2316

The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s Law

04/19/2317

The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s Law

Therefore, when you hold your breath, you create a closed system with your lungs and thus Boyle's law will hold. If you are down at 90 meters (at 10 atm) and you rise 10 meters to 80 meters (at 9 atm), the pressure has decreased by about 10%, and since PV is a constant your lungs expand by about 10% (probably not too bad).

04/19/2318

The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s Law

Now if you are at 10 meters (at 2 atm), and you rise 10 meters to the surface (at 1 atm) the pressure had decreased by 50% and expanding your lungs by this factor could cause significant damage, maybe death!

04/19/2319

The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s Law

04/19/2320

The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s Law

A balloon contains 30.0 L of helium gas at 103 kPa. What is the volume when the balloon rises to an altitude where the pressure in only 25.0 kPa?

04/19/2321

The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s LawKnowns: P1 = 103 kPa V1 = 30.0 L

P2 = 25.0 kPa V2 = UNK

P1 V1 = P2 V2 (Rearrange for V2)

V2 = P1 V1 V2 = 103 kPa 30.0 L =

P2 25.0 kPa124 L1.24 102 L

04/19/2322

Charles’s LawCharles’s Law

Timberlake, Chemistry 7th Edition, page 259

Raising the temperature of a gas increases the pressure if the volume is held constant.

The molecules hit the walls harder.

TemperatureTemperature

If you start with 1 liter of gas at 1 atm pressure and 300 K

and heat it to 600 K one of 2 things happens

300 K

Either the volume will increase to 2 liters at 1 atm

300 K600 K

300 K 600 K

….or the pressure will increase to 2 atm.

04/19/2327

Charles’s Charles’s LawLawIf n and P are constant, If n and P are constant,

then V then V αα T TV and T are directly V and T are directly

proportional.proportional.VV11 V V22

==

TT11 T T22

If one temperature goes up, the If one temperature goes up, the

volume goes up!volume goes up!

Jacques Charles Jacques Charles (1746-1823). (1746-1823).

04/19/2328

Charles’s LawCharles’s Law

Timberlake, Chemistry 7th Edition, page 259

04/19/2329

Charles’s LawCharles’s Law

04/19/2330

Gay-Lussac’s LawGay-Lussac’s LawIf n and V are If n and V are

constant, constant, then P then P αα T T

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

PP11 P P22

==

TT11 T T22

If one temperature goes up, If one temperature goes up,

the pressure goes up!the pressure goes up!

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

04/19/2331

Combined Gas LawCombined Gas LawThe 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

04/19/2332

Kelvin vs. CelsiusKelvin vs. Celsius

Remember that all gas laws must be applied in Kelvin

If your given a problem in Celsius Temp you must convert it to Kelvin

K = C + 273 degrees

04/19/2333

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

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

STP in chemistry stands for Standard Temperature and

Pressure

Standard Pressure = 101.3 kPa, 1 atm, or

760 mm Hg

Standard Temperature = 0 deg

C (273 K)

04/19/2334

Ideal Gas EquationIdeal Gas Equation

5.4

Charles’ law: V T(at constant n and P)

Avogadro’s law: V n(at constant P and T)

Boyle’s law: V (at constant n and T)1P

V nT

P

V = constant x = RnT

P

nT

PR is the gas constant

PV = nRT

04/19/2335

The conditions 0 0C and 101.3 kPa are called standard temperature and pressure (STP).

PV = nRT

R = PVnT

=(101.3kPa)(22.414L)

(1 mol)(273.15 K)

R = 8.31 L • kPa / (mol • K)

5.4

Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L.

04/19/2336

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

04/19/2337

A 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

dRTP

M = d = mV

4.65 g2.10 L

= = 2.21 g

L

M =2.21

g

L

101.3 kPa

x 8.31 x 300.15 KL•kPamol•K

M = 54.6 g/mol

04/19/2338

Gas 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 8.31 x 310.15 KL•kPamol•K

101.3 kPa= = 4.76 L

5.5

04/19/2342

Gas 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

04/19/2343

GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION 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 molecules movement of molecules through a small hole through a small hole into an empty into an empty container.container.

04/19/2344

GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

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

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

04/19/2345

GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

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

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

than Othan O22 at same T. at same T.

HeHe

04/19/2346

Gas DiffusionGas Diffusionrelation of mass to rate of diffusionrelation of mass to rate of diffusionGas DiffusionGas Diffusionrelation of mass to rate of 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.