The Ideal Gas Law and Stoichiometry

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The Ideal Gas Lawand Stoichiometry
Lecture 14

• Chemistry 142 B
• Autumn Quarter, 2004
• J. B. Callis, Instructor

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Ideal Gas Law

• An ideal gas is defined as one for which both the
  volume of molecules and forces between the
  molecules are so small that they have no effect
  on the behavior of the gas.
• The ideal gas equation is
• PVnRT
• R Ideal gas constant 8.314 J / mol K 8.314
  J mol-1 K-1
• R 0.08206 L atm mol-1 K-1

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The Ideal Gas Law Subsumes the Other Gas Laws

• During chemical and physical processes, any of
  the four variables in the ideal gas equation may
  be fixed.
• Thus, PVnRT can be rearranged for the fixed
  variables
• for a fixed amount at constant temperature
• PV nRT constant Boyles
  Law
• for a fixed amount at constant volume
• P/T nR/V constant Amontons
  Law
• for a fixed amount at constant pressure
• V/T nR/P constant Charless
  Law
• for a fixed volume and temperature
• P/n RT/V constant Avogadros
  Law

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Many gas law problems involve a change of
conditions, with no change in the amount of gas.

• constant Therefore, for a
  change
• of
  conditions
• T1
  T2

P x V
T
P1 x V1
P2 x V2

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Problem 14-1 Change of Three Variables - I

• A gas sample in the laboratory has a volume of
  45.9 L at 25 oC and a pressure of 743 mm Hg. If
  the temperature is increased to 155 oC by
  compressing the gas to a new volume of 31.0 L
  what is the pressure?
• P1
• P2
• V1 V2
• T1
• T2

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Problem 14-1 Change of Three Variables - II
P1 x V1
P2 x V2

• 
  
• 
  

T1
T2

P2
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Problem 14-2 Gas Law
Problem Calculate the pressure in a container
whose Volume is 87.5 L and it is filled with
5.038kg of Xenon at a temperature of 18.8
oC. Plan Convert all information into the units
required, and substitute into the Ideal Gas
equation ( PVnRT ). Solution
nXe
T
P
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Problem 14-3 Ideal Gas Calculation - Nitrogen

• Calculate the pressure in a container holding 375
  g of Nitrogen gas. The volume of the container is
  0.150 m3 and the temperature is 36.0 oC.

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Problem 14-4 Sodium Azide Decomposition - I

• Sodium Azide (NaN3) is used in some air bags in
  automobiles. Calculate the volume of Nitrogen gas
  generated at 21 oC and 823 mm Hg by the
  decomposition of 60.0 g of NaN3 .
• 2 NaN3 (s) 2
  Na (s) 3 N2 (g)

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Problem 14-4 Sodium Azide Decomposition - II
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Problem 14-5 Ammonia Density

• Calculate the Density of ammonia gas (NH3) in
  grams per liter at 752 mm Hg and 55 oC.
• Density mass per unit volume
  g / L
• P
• T
• n mass / Molar mass g / M
• d

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Calculation of Molar Mass

• n
• n

Mass
Molar Mass
P x V
Mass
R x T
Molar Mass
Mass x R x T
Molar Mass MM
P x V
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Problem 14-6 Dumas Method of Molar Mass
Problem A volatile liquid is placed in a flask
whose volume is 590.0 ml and allowed to boil
until all of the liquid is gone, and only vapor
fills the flask at a temperature of 100.0 oC and
736 mm Hg pressure. If the mass of the flask
before and after the experiment was 148.375g and
149.457 g, what is the molar mass of the
liquid? Plan Use the ideal gas law to calculate
the molar mass of the liquid. Solution
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Problem 14-7 Calculation of Molecular Weight of
a Natural Gas - Methane
Problem A sample of natural gas is collected at
25.0 oC in a 250.0 ml flask. If the sample had a
mass of 0.118 g at a pressure of 550.0 torr, what
is the molecular weight of the gas? Plan Use the
ideal gas law to calculate n, then calculate the
molar mass. Solution
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Gas Mixtures

• Gas behavior depends on the number, not the
  identity, of gas molecules.
• The ideal gas equation applies to each gas
  individually and to the mixture as a whole.
• All molecules in a sample of an ideal gas behave
  exactly the same way.

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Daltons Law of Partial Pressures - I

• Definition In a mixture of gases, each gas
  contributes to the total pressure the pressure
  it would exert if the gas were present in the
  container by itself.
• To obtain a total pressure, add all of the
  partial pressures Ptotal P1P2P3PN

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Daltons Law of Partial Pressure - II

• Pressure exerted by an ideal gas mixture is
  determined by the total number of moles
• P(ntotal RT)/V
• ntotal sum of the amounts of each gas pressure
• the partial pressure is the pressure of gas if it
  was present by itself.
• P (n1 RT)/V (n2 RT)/V (n3RT)/V ...
• the total pressure is the sum of the partial
  pressures.

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Problem 14-8 Daltons Law of Partial Pressures

• A 2.00 L flask contains 3.00 g of CO2 and 0.10
  g of Helium at a temperature of 17.0 oC.
• What are the Partial Pressures of each gas, and
  the total Pressure?

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Problem 14-8 Daltons Law of Partial
Pressurescont.
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Problem 14-9 Daltons Law using mole fractions

• A mixture of gases contains 4.46 mol Ne, 0.74 mol
  Ar and 2.15 mol Xe. What are the partial
  pressures of the gases if the total pressure is
  2.00 atm ?
• Total moles
• XNe
• PNe XNe PTotal
• XAr
• PAr
• XXe

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Relative Humidity

• Rel Hum
  x 100
• Example the partial pressure of water at 15oC
  is 6.54 mm Hg, what is the relative humidity?

Pressure of Water in Air
Maximum Vapor Pressure of Water
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Relative Humidity

• Rel Hum
  x 100
• Example the partial pressure of water at 15oC
  is 6.54 mm Hg, what is the relative humidity?
• Rel Hum (6.54 mm Hg/ 12.788 mm Hg )x100
• 51.1

Pressure of Water in Air
Maximum Vapor Pressure of Water
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Problem 14-10 Collection of Hydrogen gas over
Water - Vapor pressure - I

• 2 HCl (aq) Zn(s) ZnCl2
  (aq) H2 (g)
• Calculate the mass of Hydrogen gas collected over
  water if 156 ml of gas is collected at 20oC and
  769 mm Hg.

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Problem 14-10 Collection of Hydrogen gas over
Water - Vapor pressure - II

• PV nRT n PV / RT
• n
• n
• mass

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Chemical Equation Calc - III
Mass
Atoms (Molecules)
Molecular Weight
Avogadros Number
g/mol
6.02 x 1023
Molecules
Reactants
Products
Moles
Molarity
PV nRT
moles / liter
Solutions
Gases
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Problem 14-11 Gas Law Stoichiometry
Problem A slide separating two containers is
removed, and the gases are allowed to mix and
react. The first container with a volume of 2.79
L contains Ammonia gas at a pressure of 0.776 atm
and a temperature of 18.7 oC. The second with a
volume of 1.16 L contains HCl gas at a pressure
of 0.932 atm and a temperature of 18.7 oC. What
mass of solid ammonium chloride will be formed,
and what will be remaining in the container, and
what is the pressure? Plan This is a limiting
reactant problem, so we must calculate the
moles of each reactant using the gas law to
determine the limiting reagent. Then we can
calculate the mass of product, and determine what
is left in the combined volume of the container,
and the conditions. Solution
Equation NH3 (g) HCl (g)
NH4Cl (s)
TNH3 18.7 oC 273.15 291.9 K
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Problem 14-11 Gas Law Stoichiometry
PV
n
RT
RRNH3
RRHCl
Therefore the product will be
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Answers to Problems in Lecture 14

1. 2.08 atm
2. 10.5 atm
3. 2.26 atm
4. 30.8 liters
5. 0.626 g / L
6. 58.03 g/mol
7. 15.9 g/mol
8. PCO2 0.812 atm, PHe 0.30 atm, PTotal 1.11
   atm
9. 1.21 atm for Ne, 0.20 atm for Ar, 0.586 atm for
   Xe
10. 0.0129 g hydrogen
11. 2.28 g NH4Cl made remaining NH3 at a pressure of
    0.274 atm