AP Notes Chapter 11Properties Of Gases

TemperatureTemperature An indirect measure of the An indirect measure of the

average kinetic energy of a average kinetic energy of a collection of particlescollection of particles

KEKEavgavg = kT = kT

BoltzmanBoltzman Plot Plot

PressurePressureMeasure of the number of Measure of the number of

collisions between gas collisions between gas particles and a unit area of particles and a unit area of

the wall of the containerthe wall of the container

Pressure = force / unit areaPressure = force / unit area

Force/areaForce/area

English system:English system:

pounds/inpounds/in22 (psi) (psi)

Metric system:Metric system:

Newton/mNewton/m22 (pascal) (pascal)

Torricelli Barometer

h = 760 mm Hg1 atmospherepressure

1 atm = 760 torr (mm Hg)

= 101.325 kPa

= 1.01325 bar

=14.70 psi

Manometer

Pgas

Patm

h

Manometer

Pgas

Patm

h

VolumeVolume

Total space of a container that Total space of a container that gases occupy due to the free gases occupy due to the free

random motion of the gas random motion of the gas moleculesmolecules

Relationship between Volume & Pressure of

Gases

P-V

V

P (at constant T)

V

1/P (at constant T)

Slope = kP

1 V

P

kV or

b P

1m V

In mathematical terms:y = mx + b

Boyle’s Law

Relationship between Volume & Temperature

of Gases

V-T

In mathematical terms:y = mx + bV = mT + b

Charles’ Law

kTV

Where T must be in Kelvin (K) temperature

K = 0C + 273

Relationship between Pressure &

Temperature of Gases

P-T

In mathematical terms:y = mx + bP = mT + b

Gay-Lussac’s Law

kTP

Relationship between Volume & Moles

of Gases

V-n

In mathematical terms:y = mx + bV = mn + b

Avogadro’s Law

knV

Avogadro’s HypothesisAvogadro’s Hypothesis

At constant temperature and At constant temperature and pressure, equal volumes of pressure, equal volumes of

gases contain equal number gases contain equal number of particlesof particles

3. Hydrogen gas [8.3 liters] reacts in the presence of 2.5 liters of nitrogen gas at 370C and 100 kPa. What volume of ammonia is produced at

these same conditions?

Combined Gas LawCombined Gas Law

constant anT

PV

kn VkT P

kT V P

kV

Ideal & RealGasses

Kinetic Molecular Kinetic Molecular TheoryTheory

1. Gases consist of small 1. Gases consist of small particles that are far apart in particles that are far apart in comparison to their own size. comparison to their own size. These particles are These particles are considered to be tiny points considered to be tiny points occupying a negligible occupying a negligible volume compared to that of volume compared to that of their container. their container.

2. Molecules are in rapid and 2. Molecules are in rapid and random straight-line motion. random straight-line motion. This motion can be This motion can be described by well-defined described by well-defined and established laws of and established laws of motion.motion.

Kinetic Molecular Kinetic Molecular TheoryTheory

3. The collisions of molecules 3. The collisions of molecules with the walls of a container with the walls of a container or with other molecules are or with other molecules are perfectly elastic. That is, no perfectly elastic. That is, no loss of energy occurs.loss of energy occurs.

Kinetic Molecular Kinetic Molecular TheoryTheory

4. There are no attractive 4. There are no attractive forces between molecules or forces between molecules or between molecules and the between molecules and the walls with which they collide.walls with which they collide.

Kinetic Molecular Kinetic Molecular TheoryTheory

5. At any particular instant, the 5. At any particular instant, the molecules in a given sample molecules in a given sample of gas do not all possess the of gas do not all possess the same amount of energy.same amount of energy.

Kinetic Molecular Kinetic Molecular TheoryTheory

Have 1 particle, with mass m, with velocity

PARTICLEIN THE

BOX

A

fP

2

fP

Consider the P exerted:

But: f = ?

But: f = mawhere

time

velocity in change a

Change in velocity = (

t

2a

Thus, the pressure exerted by one particle on a wall is:

21

t2

)m(P

But, ?

But,t

d

and, the distance a particle travels between collisions with the same wall is ?

2t

ort

2

21

t2

)m(P

Substitutinginto

we get:

21

22

)m(

P

Simplifying: 3

2

1

mP

V

mP

V2

1

3

but,

This represents the pressure (P) that

one particle exerts striking opposite walls in the box.

Now assume the box contains N

particles. Then, N/3 particles are

traveling between opposite walls.

Thus, the total pressure on

opposite walls is:

V

m

3

NP

2

2

1

3

2

3

1

Substitute & rearrange

2m2

1

V

N

3

2P

KE3

N2PV

KEm2

1 2

From classical physics

kT2

3KE

where k is theBoltzman constant

0N

Rk

where R = universal gas constant N0 = Avogadro’s number

TN

R

2

3KE

0

TN

R

2

3

3

N2PV

0

nRTPV

Ideal Gas Equation

Kmol

torrL 62.36

Kmol

kPaL 8.314

Kmol

atmL 08206.0R

RnT

PVNote that

is similar to theCombined Gas Lawderived earlier.

CnT

PV

Variations onIdeal Gas Equation

RTMM

massPV

4. What is the molar mass of methylamine if 0.157 g of the gas occupies 125 mL with a pressure of 99.5 kPa at 220C?

Variations onIdeal Gas Equation

RT

MMP

volume

massdensity

RTMM

massPV

Bromine

5. Calculate the 5. Calculate the density of fluorine density of fluorine gas at:gas at:

303000C and 725 torr.C and 725 torr.STPSTP

Real GasBehavior

Ideal Gas Equation

P V = n R T

Idealgas

0 200 400 600 800 1000 P (atm)

PVnRT

0

1.0

2.0

CO2

H2

N2

CH4

“correct” for volume of molecules

(V - b)

also “correct” for attractive forces

between molecules

2V

aP

van der Waals’ Equation

for 1 mole

RTbVV

aP

2

van der Waals’ Equation

for n moles

nRTbnVV

anP

2

2

from CRC Handbook

a* b*He 0.03412 0.02370

Ne 0.2107 0.01709

*when P(atm) & V(L)

from CRC Handbook

a* b*NH3 4.170 0.03707

H2O 5.464 0.03049

*when P(atm) & V(L)

from CRC Handbook

a* b*CCl4 20.39 0.1383

C5H12 19.01 0.1460

*when P(atm) & V(L)

ClCl22 gas has gas has aa = 6.49, = 6.49, bb = 0.0562 = 0.0562

For 8.0 mol ClFor 8.0 mol Cl22 in a 4.0 L tank at 27 in a 4.0 L tank at 27ooC.C. P (ideal) = nRT/V = 49.3 atmP (ideal) = nRT/V = 49.3 atm P (van der Waals) = 29.5 atmP (van der Waals) = 29.5 atm

T & P conditionswhere a real gas

approximatesan ideal gas?

203 K

293 K

673 K

Idealgas

0 200 400 600 800 P (atm)

0.6

1.0

1.4

1.8

PVnRT

N2 gas

T & P conditionswhere a real gas

approximatesan ideal gas?

high temperaturelow pressure

GaseousMolecularMovement

Partial Pressurepressure exerted by

each component in a mixture of gases

this assumes thatNO interactionsoccurs between

the molecules of gas

must concludemust conclude1. each gas acts as if it is 1. each gas acts as if it is

in container alonein container alone

2. each gas collides with 2. each gas collides with the container wall as an the container wall as an “event”“event”

n

1iiT PP

where n = # components

or

PT = P1 + P2 + P3 + ...

Pi V = ni R T

or

PnRT

Vii

thus:

Pn RT

V

n RT

VT 1 2 ...

or

PRTV

n nT 1 2 ...

therefore:

nT = ni

and PT sum of mols of gas

Mole Fraction

Xn

nii

T

1... n

n

n

n

n

n 321

Since:

and

PnRT

Vii

Pn RT

VTT

T

i i

T

i

P

PX

n

n

Then

and

Pi = Xi PT

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

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

rate of averageeffusion speed

cr

or

r

B

A

B

A

c

c

r

r

B

A

B

A

r

r

But ...

where

MMnmMM

mn

nRT2

3m

2

1KE

2

thus

then

2

1

2

MM

RT3

nRT2

3MMn

2

1

RMS speed

2

1

B

2

1

A

B

A

MMRT3

MMRT3

r

r

substituting:

simplifying

A

B

B

A

MM

MM

r

r

Graham’s LawNH3-HCl

rdt

A

B

A

B

B

A

B

A

MM

MM

t

t

td

td

r

r

if “d” is constant

A

B

B

A

B

A

B

A

MM

MM

d

d

td

td

r

r

if “t” is constant

GAS LAWSTOICHIOMETRY

1. Ethanol, C2H5OH, is often prepared by fermentation of sugars such as glucose, C6H12O6, with carbon dioxide as the other product.

[A] What volume of CO2 is produced from 125 g of glucose if the reaction is 97.5% efficient?

[B] Ethanol can also be made from ethylene, C2H4 according to the following chemical system:

3 C2H4(g) + 2 H2SO4

C2H5HSO4 + (C2H5)2SO4

then

C2H5HSO4 + (C2H5)2SO4 + 3H2O

3C2H5OH + 2 H2SO4

What volume (mL) of 95% ethanol is produced from 142.5 dm3 of C2H4? The density of 95% ethanol is 0.8161 g/mL.

2. What is the final pressure [kPa] if 1000. g uranium reacts with sufficient fluorine gas to produce gaseous uranium hexafluoride at 32oC in a 300. L container?

3. What mass of sodium metal is needed to produce 250 mL of hydrogen gas at 24oC and 740 Torr?