Chapter 5 Gases

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Chapter 5Gases
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Preview

• Properties of gases.
• Effects of temperature, pressure and volume.
• Boyles law.
• Charless law, and
• Avogadros law.
• The ideal gas law.
• Concepts of pressure
• and partial pressure.
• Real gases.

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States of Matter
Chapter 5 Section 1
Gas
Liquid
Solid
Unlike liquid and solid, gas fills up the
container and exerts force towards the inner
walls of the container.
4
Pressure
Chapter 5 Section 1

• Gas is always exerts pressure on its
  surroundings.
• Gas always has the volume of the container it
  occupies.

Water inside is boiling
After cooling water down
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The Atmospheric Pressure
Chapter 5 Section 1

• Pressure (P)
• At sea level average P is 760 mm Hg.
• At higher attitudes P goes
• down
• why??
• There is less air (and less gravitational force)
  pushing the Hg inside the column.

Force
Area
Pressure exerted by the atmosphere
Barometer was invented by Torricelli
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Manometer
Chapter 5 Section 1
Patm
Patm
Pgas gt Patm
Pgas lt Patm
Pgas Patm h
Pgas Patm h
Try http//www.chem.iastate.edu/group/Greenbowe/s
ections/projectfolder/flashfiles/gaslaw/manometer4
-1.html
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Units of Pressure
Chapter 5 Section 1
Chapter 5 Section 1

• 1 mm Hg 1 torr (after Torricelli)
• 760 mm Hg 1 atm standard atmospheric pressure
• P pascal
  (Pa)
• 1 atm 101,325 Pa 1.013105 Pa
• 1 atm 14.7 lb/in2.
• Pressure conversion.

Force
Newton
Area
m2
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Important Gas Laws
Chapter 5 Section 2

• Boyles Law
• PV k at constant T and n
• Charless Law
• V bT at constant P and n
• Avogadros Law
• V an at constant T and P
• Where V is volume, P is pressure, T is
  temperature, and n is number of moles.

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Boyles Law
Chapter 5 Section 2

• Boyle studied the relationship between pressure
  (P) and volume (V) for gases.
• Adding more Hg at constant T compresses the gas
  (less V and higher P).

opened
closed
h
A j-tube
gas
V a 1/P
V P k
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Plotting Boyles Results
Chapter 5 Section 2
V
Slope k
P
k
When P drops by half, V is doubled. Inverse
relationship. V a 1/P

• V
• y mx b

P
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Boyles Law
Chapter 5 Section 2

• Validity of Boyles law at different pressures.
• Not all gases obey Boyles law at higher
  pressures.
• A gas that strictly obeys Boyles law is called
  an ideal gas.
• You can get the new volume of a gas when pressure
  is changed (or vise versa).

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Application of Boyles Law
Chapter 5 Section 2

• Sample Exercise 5.2
• 1.53 L of SO2 is initially at a pressure of
  5.6104 Pa. If the pressure is changed to 1.5104
  Pa, what will be the new volume?
• PVk
• P1V1 k P2V2
• T is constant and the gas
• is assumed to be ideal.
• V2 0.57 L

P1V1
P2
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Charless Law
Chapter 5 Section 2

• He found that the V of a gas, at constant P,
  increases linearly with the increase of T.
• V bT
• The slope (b) for each gas is different because
  each sample contains different number of
  molecules (moles)
• All the lines extrapolate to zero volume at T
  -273.15 ºC.

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Charless Law
Chapter 5 Section 2

• T -273.15 ºC is defined as zero Kelvin or
  absolute zero.
• K ºC 273.15
• 110-6 K was reached in laboratories, but 0 K
  could not be attained.
• Another form of Charless law
• at constant pressure
• and T is in K

V1
V2
T1
T2
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Avogadros Law
Chapter 5 Section 2

• Avogadros law Equal volumes of gases at the
  same T and P contain the same number of
  particles.

V an
(linear relationship between V and n at
constant P and T)

V1
V2
n1
n2
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Avogadros Law
Chapter 5 Section 2

• Sample Exercise 5.5
• 12.2 L sample containing 0.50 moles of O2 at P
  1 atm and T 25 ºC is converted into O3 at
  the same T and P. What would be the
  volume of O3?
• 3O2 2O3
• mol of O3 produced 0.50 mol O2
  0.33 mol O3
• Equal volumes of gases at the same T and P
  contain the same number of particles.
• V2 ( ) V1 8.1 L

0.50 mol O2
0.33 mol O3
12.2 L
8.1 L
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The Ideal Gas Law
Chapter 5 Section 3

• Boyles law V k 1/P
• Charless Law V b T
• Avogadros Law V a n
• V a gt V R
  
• R is the universal gas constant
• R 0.08206
• Ideal Gas Law PV nRT

T n
T n
P
P
L atm
K mol
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Applications of the Ideal Gas Law
Chapter 5 Section 3

• Sample Exercise 5.6
• A sample of H2 gas has V 8.56 L _at_ T 0 ºC and
  P 1.5 atm. How many H2 molecules are present?
• ? Dont forget to state T in K.

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Applications of the Ideal Gas Law
Chapter 5 Section 3

• Sample Exercise 5.8
• A sample methane with V 3.8 L _at_ 5ºC is heated
  to 86ºC with constant P, what is the new volume?
• (Charless
  Law)
• V2 V1T2 / T1 (359 K)(3.8 L) / 278 K
  4.9 L
• ? Again, dont forget to state T in K.
• ? Does the answer make physical sense to you?

V1
nR
V2
T2
T1
P
V1
V2
T1
T2
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The Molar Volume
Chapter 5 Section 4

• What is the volume of 1.000 mole of gas at
  standard temperature and pressure (STP)?
• STP T 0ºC P 1 atm.
• V
• 22.42 L (Molar volume)
• ? For an ideal gas
• 1 mol 22.42 L

nRT
(1.000 mol)(0.0821 L atm / K mol)(273.15 K)
T
(1.000 atm)
22.42L
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Ideal Gas Law
Chapter 5 Section 4

• Sample Exercise 5.12
• CaCO3 (s)
  CaO (s) CO2 (g)
• 152 g
  
  V?

_at_STP
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Molar Volume
Chapter 5 Section 4

• 2NaN3 (s)
  2Na (s) 3N2 (g)
• ? g
  
  V 65L
• NaN3 is an explosive material.
• It explodes very gast and
• completes the reaction in 40 ms.

_at_ 25oC and 1.0 atm
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Gas Stoichiometry
Chapter 5 Section 4

• Sample Exercise 5.13
• CH4 2O2
  CO2 H2O
• Pressure 1.65 atm
  1.25 atm 2.50 atm
• Volume 2.80 L
  35.0 L ?
• Temperature 298 K
  304 K 398 K
• n 0.189 mol 1.75 mol
• VCO2

PV RT
gt 0.189 mol
Limiting reactant because it requires 0.189 mol
2 0.378 mol of O2
nRT P
(0.189 mol)(0.0821 Latm/Kmol)(398K) (2.50 atm)
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Molar Mass of a Gas
Chapter 5 Section 4

• For a gas
• n
• P
• Since the density of a gas (d)
• Then, P d or MM d

mass MM
(mass)RT V (MM)
nRT V
(mass/MM)RT V
mass V
RT MM
RT P
g/L
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Daltons Law of Partial Pressures
Chapter 5 Section 5

• For a mixture of gases in a container at constant
  V and T, the total pressure exerted (PTot) is the
  sum of the pressures that each gas would exert if
  it were alone.

Partial pressures
n1 RT V
n2 RT V
n3 RT V
PTot P1 P2 P3
PTot (n1 n2 n3 )
nTot ( )
RT V
RT V
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Important Observations from Daltons Theory
Chapter 5 Section 5
RT V
PTot nTot ( )

• When you calculate the total vapor pressure of a
  mixture of gases
• The identity or composition of each gas is not
  important, only the total number of moles (nTot)
  of particles are important.
• The volume of each gas is not important, only the
  total volume of gases is important.
• The forces among the particles (attraction or
  repulsion) are not important, as long as no
  chemical reaction is taking place within them.

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Examples on Daltons Law
Chapter 5 Section 5

• Sample Exercise 5.15
• He 46 L _at_ 25ºC and 1.0 atm
• O2 12 L _at_ 25ºC and 1.0 atm
• They are pumped into a 5.0 L tank _at_ 25ºC.
  Calculate PHe , PO2 and PTot .
• nHe 1.9 mol.
• Similarly, nO2 0.49 mol.

P VHe RT
nHe RTHe Vtank
PHe 9.3 atm. Also PO2
2.4 atm. PTot PHe PO2 11.7 atm
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The Mole Fraction in a Mixture
Chapter 5 Section 5
n1 n1 n2 n3

• Mole fraction of substance 1 (?1)
• 
  
• Also, simple derivation gives ?1
• or
  P1 ?1 PTot
• Look at the mathematical derivation on page 196.
• Also note that

n1 nTot
P1 PTot
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Examples on Daltons Law
Chapter 5 Section 5

• Calculate the mole fraction of oxygen in air
  where the values above are pressures in kPa.
• ?O2 0.206
• Also, P1 ?1 PTot (From the mole fraction of
  one component you can calculate its partial
  pressure)

PO2 Pair
20.9 kPa 101.3 kPa
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Collecting a Gas Over Water
Chapter 5 Section 5
and water vapor
2KClO3 (s) 2KCl (s) 3O2 (g)
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Collecting O2 Gas Over Water
Chapter 5 Section 5

• Sample Exercise 5.18
• 2KClO3 (s) 2KCl (s) 3O2 (g)
• O2 was collected _at_ 22ºC and PTot (PO2 PH2O) of
  754 torr.
• The volume of the gas collected is 0.650 L.
• Calculate PO2 and the mass of KClO3 that was
  consumed.
• PO2 PTot PH2O 754 torr 21 torr 733
  torr.
• nO2 2.5910-2 mol.
• Mass of KClO3 decomposed
• 2.5910-2 mol O2
  2.12 g

PO2 V RT
2 mol KClO3 3 mol O2
122.6 g KClO3 1 mol KClO3
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The Kinetic Molecular Theory of Gases
Chapter 5 Section 6

• Theories (or models) attempt to describe physical
  observations (laws).
• The kinetic molecular theory (KMT) attempts to
  explain the properties of ideal gas atoms or
  molecules

1 mol N2(g)
1 mol N2(l )
Volume Density
35 mL 0.81 g/mL
22.4 L 0.0012 g/mL
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The Kinetic Molecular Theory of Gases
Chapter 5 Section 6

• The KMT for ideal (NOT real) gases can be stated
  as follow
• 1- The particles are so small comparing with the
  distances between them. Thus, the volume of the
  individual particle can be assumed to be
  negligible (zero).
• 2- The particles are constantly in random
  motion. The collisions of the particles with the
  walls of the container are the cause of the
  pressure exerted by the gas.
• 3- The particles are assumed neither to attract
  nor to repel each other (No interaction).
• 4- The average kinetic energy (KE) of a
  collection of gas particles is assumed to be
  directly proportional to the Kelvin temperature
  of the gas.

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Pressure and Volume
Chapter 5 Section 6

• Boyles law (constant n and T).
• P (nRT)
• The decrease in V means the particles will hit
  the wall of the container more often, resulting
  in an increase of P.

1 V
constant
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Pressure and Temperature
Chapter 5 Section 6

• Constant n and V.
• P ( )T
• When T increases, the speed of particles
  increases (increase in KE), causing the particles
  to hit the wall of the container more often and
  with greater force (higher P)

nR V
constant
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Volume and Temperature
Chapter 5 Section 6

• Charless law (constant n and P).
• V ( )T
• When T becomes higher, the only way to keep P
  constant is to increase V to minimize collision
  forces on the wall.

nR P
constant
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Volume and Number of Moles
Chapter 5 Section 6

• Avogadros law (constant P and T)
• V ( )n
• When n increases at constant V, P will become
  larger. Thus, in order to keep P constant, V must
  be increases

RT P
constant
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Mixture of Gases
Chapter 5 Section 6

• Daltons law.
• KMT account for Daltons law because it assumes
  that all gas particles are independent of each
  other (assumption 3 of KMT) and that the
  volumes of individual particles are not important
  (assumption 1 of KMT). Thus the identities of
  the gas particles are not important.
• The Total P the sum of the Ps exerted by each
  type of particles, no matter what volumes they
  occupy or what kinds of particles they are.

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Deriving the Ideal Gas Law from the KMT
Chapter 5 Section 6

• Deriving the ideal gas law from applying the
  principles of physics to the KMT.

From physics background. Details are in appendix
2
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Deriving the Ideal Gas Law from the KMT
Chapter 5 Section 6

• From the assumption 4 of the KMT.

This result is identical to the ideal gas
equation if the proportionality constant is taken
to be R
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The Meaning of Temperature
Chapter 5 Section 6

• From the previous conclusion

The Kelvin temperature is an index of the random
motions of gas particles.
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Root Mean Square Velocity
Chapter 5 Section 6
Average of the square of the velocity of a
particle
Root mean square velocity
m is the mass of a particle in Kg. NA is 1 mole
of particles.

• Because NAm M

M is the molar mass in (Kg/mol). R 8.314 J /
K .mol
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Root Mean Square Velocity
Chapter 5 Section 6

• Sample Exercise 5.19
• Calculate urms for the atoms in a sample of He
  gas _at_ 25oC.

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Molecular Velocity
Chapter 5 Section 6

• The path and speed of a particle in a gas are not
  constant or systematic.
• Collides with other particles.
• Collides with the walls.
• Velocity distributions of different gases at
  constant T and P.
• The peak value corresponds to the most probable
  velocity not the root mean squared velocity.

Mean free path of order of 10-7 m
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Molecular Velocity
Chapter 5 Section 6

• The velocity distributions of N2 molecules at
  three different temperatures.
• The higher the temperature is, the greater the
  most probable velocity is.

Interesting Experiment
(a)
(b)
(c)
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Effusion and Diffusion
Chapter 5 Section 7
Effusion is the passage of gas particles through
a pinhole to an evacuated chamber.
Diffusion is rate of mixing of gases with each
other.
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Effusion
Chapter 5 Section 7

• Grahams law of effusion

Study the derivation of Grahams law form the KMT
as presented on page 207
Sample Exercise 5.20 Calculate the ratio of
effusion rates of H2 and UF6. MH2 2.016
g/mol. MUF6 352.02 g/mol.
13.2
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Diffusion
Chapter 5 Section 7

• NH3(g) HCl(g)
  NH4Cl(s)

White solid forms after few minutes
NH3
CH4
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Diffusion
Chapter 5 Section 7

• Approximation to get the diffusion rate gives

• The velocities for HCl and NH3 are 450 and 660
  m/s, respectively.
• So, why does it take several minutes for them to
  meet?

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Real Gases
Chapter 5 Section 8

• No gas exactly follows the ideal gas law.
• Many gases behave close to ideality at low P
  and/or high T.

At constant T PV/nRT approaches 1 when P lt 1
atm. At higher T, real gases behave nearly
ideal.
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Real Gases
Chapter 5 Section 8

• PV nRT describes the behavior of a hypothetical
  gas that
• has no volume, and
• its particles dont interact with each other.
• Johannes van der Waals made some modification to
  the ideal gas low.
• He suggested that the volume of gas particles
  are finite.
• V (real gas) V (ideal gas) nb
• Number of moles of gas Empirical constant

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Real Gases
Chapter 5 Section 8

• Van der Waals also suggested that there are
  attractions taking place between the real gas
  particles, giving rise to Pobs.
• Pobs lt Ptheor

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Real Gases
Chapter 5 Section 8

• Pobs P correction factor
• The correction factor is
  proportional to (n/V)2.
• The of possible pairs
• 10(9)/2 45 distinct pairs.
• For large number of particles
• n/V (n-1)/V, then
• n(n-1)/V2/2 n2/V2/2

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Real Gases
Chapter 5 Section 8

• At low P van der Waals model behaves nearly
  ideal.
• At high T the model also behaves nearly ideal.
• b constant a the size of the molecule particles.