# 9 Ideal and Real Gases by JoshTheRiPPeR

VIEWS: 74 PAGES: 28

• pg 1
```									A Gas

Uniformly fills any container. Mixes completely with any other gas Exerts pressure on its surroundings.

1

Pressure

is equal to force/unit area
SI units = Newton/meter2 = 1 Pascal (Pa)

1 standard atmosphere = 101,325 Pa 1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr

2

Gases: Macroscopic Behavior

Boyle’s Law: P  1/V or PV = constant (at constant T, amount of gas) Charles’ Law: V  T (at constant P, amount of gas) Gay-Lussac’s Law: P  T (at constant V, amount of gas) Avogadro’s Law: V  n (at constant P, T; n = moles of gas)

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11_06

Boyle’s Law
P = 1.0 atm P = 2.0 atm P = 4.0 atm

V = 4.0L P x V = 4.0 atm • L

V = 2.0L P x V = 4.0 atm • L

V = 1.0L P x V = 4.0 atm • L

P1V1 = P2V2

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Plots of P vs. V assuming Boyle’s Law holds
05_06 5_6

3.0

1.5

Volume (L)

2.0 1.40 L 1.0 0.70 L

1.0

1/V(L–1)
0.25 0.50 Pressure (atm) A 0.75 1.00

0.5

0

0

0.25

0.50 Pressure (atm) B

0.75

1.00

5

11_11

Charles's Law

0.8 1.0 g O2 Extrapolation 0.4 t = –273ºc 0.2 1.0 g CO2

0.8

0.6

0.6

1.0 g O2 1.0 g CO2

Volume (L)

Volume (L)

0.4

Extrapolation

0.2

0

-250 -200 -150 -100 -50 0 Temperature (ºC)

50

0

50

100 150 200 250 300 350 Temperature (K)

A

B

V1 V2  T1 T2
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Additional Charles’ Law Plots
5_8

0.8

0.6

g 1.0

O2
O2

Volume (L)

gC 1.0
0.4 Extrapolation

g 0.5

O2
CO 2

0.5 g
0.2 t = -273C

0

- 250

-200

- 150

- 100

- 50

0

50

Temperature (°C)

7

Balloons Holding 0.041 mol of gas at 25º C and 1 atm pressure will all have a volume = 1.0 L)

V = an

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The Ideal (or Combined) Gas Law

PV = nRT
the “Equation of State” for ideal gases

R = proportionality constant = 0.08206 L atm  mol P = pressure in atm V = volume in liters n = moles T = temperature in Kelvins

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Gases – Example (1)

A gaseous compound has the empirical formula CHCl. A 256 mL flask, at 373 K and 750 torr pressure contains 0.800 g of the compound. Determine its molar mass and molecular formula.

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Gases – Example (2)

Molar mass = g of sample / moles in sample Moles in sample n = PV/RT n = PV/RT

1atm  1L    750.torr   256ml   760torr  1000mL    0.08205L  atm/mol  K 373K 
= 8.254 x 10-3 mol
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Gases – Example (3)

Molar mass = 0.800 g / 8.254 x 10-3 mol = 96.9 g/mol CHCl = 12.01 + 1.01 + 35.45 g/mol = 48.47 g/mol So the molecular formula is C2H2Cl2

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Dalton’s Law of Partial Pressures

For a mixture of gases in a container,

PTotal = P1 + P2 + P3 + . . .

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Kinetic Molecular Theory






Gas particles are extremely tiny and distances between them are great – particles have negligible volume Gas particles move continuously, rapidly and randomly in straight lines in all directions – the collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas For gases, both gravitational forces and forces of attraction between particles are negligible – the particles exert no forces on each other

14

Kinetic Molecular Theory




The average kinetic energy is the same for all gases at the same temperature; it varies proportionally with the temperature in Kelvin. When gas particles collide with one another, or with the walls of the container, no energy is lost; all collisions are perfectly elastic.

15

11_08

Explanation for Boyle’s Law

Larger volume Fewer collisions per unit area Lower pressure

Smaller volume More collisions per unit area Higher pressure

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Explanation of Charles’s Law: V  T

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5-15

Explanation for Gay-Lussac’s Law: P  T

Temperature is increased

P1 P2  T1 T2
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Meaning of Temperature • Molecules and atoms are in constant motion. • They always have a range of velocities: 0 Maxwell-Boltzmann distribution • Temperature measures how “spread out” that distribution is. • Higher temperatures mean more fast moving molecules.
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Maxwell-Boltzmann Distribution

The Meaning of Temperature

(KE)avg

3  RT 2

Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)

20

Molar Volume

“STP” P = 1 atmosphere T = 273.2 K The molar volume will be 22.42 liters

21

Real Gases
Z is called the compressibility
PV Z  1 nRT



Kinetic Molecular Theory predicts:

PV  nRT



or

This is true only at high temperatures or low pressures! At lower temperatures and higher pressures, the ideal gas equation does not hold:

PV  nRT
 

or

Z 

PV 1 nRT

The gas then has more complicated behavior. At high enough pressure or low enough temperatures, a gas will sometimes even turn to liquid or solid.
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Van der Waals Equation
In 1873, Johannes van der Waals figured out why gases show deviations from the ideal gas law
He realized that the individual gas molecules:  Repelled one another at short distances (higher pressures) – ideal volume is less than the measured volume by a constant related to the molecular volume  Attracted one another at longer distances (lower pressures) – pressure is reduced by attractions among the molecules

Van de Waals derived the following equation: 2

nRT an P  2 V  nb V
repulsions

attractions

a & b are constants that depend on the particular gas

 an2  P  V  nb   nRT  V2   

Alternate form
23

Real Gases: Volume of gas molecules

Gas molecules can’t invade each other’s “space”; available volume is reduced – measured volume exceeds ideal volume

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Real gases: Impact of attractive forces on pressure
5_28

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Plots of Z vs. P for Real Gases
5-24

2.0

Positive Deviations from Ideal Gas Law

N2

CH4

H2 PV nRT CO2 1.0
Negative Deviations from Ideal Gas Law

Ideal gas

0

• Different gases • Same temperature • T = 200 K

0

200

400

600

800

1000

P(atm)
26

Plots of Z vs. P for Nitrogen
5-25

203 K

1.8
Less ideal

293 K

PV nRT

1.4 673 K 1.0
More ideal

Ideal gas

0.6




Same Gas (N2) Different temperatures

0

200

400 P(atm)

600

800

27

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