# Chpt 5 (Chem 1050 - Spring 2019) (Notes - 1 slide) ```2019-05-12
CHEMISTRY
a molecular approach
NIVALDO J. TRO
Westmount College
TRAVIS D. FRIDGEN
Memorial University of
Newfoundland
LAWTON E. SHAW
Athabasca University
PowerPoint Slides prepared by
PHILIP J. DUTTON
University of Windsor
Chemistry, 2Ce
slide 1-1
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Chapter 5
Gases
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Properties of Gases
Gases
- Do not have definite volumes or
definite shapes
- Expand to occupy the entire volume
of the container
- Assume shape of the container
Other properties particular to gases:
1) The volume occupied by a gas changes significantly with pressure (unlike
liquids and solids)
2) The volume of a gas changes with temperature.
3) Gases are miscible – easily mixed unless they chemically react with one
another
4) Gases are typically less dense than liquids or solids – gas densities
expressed in g/L rather than in g/mL as are liquids and solids
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Understanding Pressure
(Sec. 5.1-5.2, p. 149-151)
Pressure: the ratio of force (F) to surface area (A)
kg&middot;m/s2 or N
kg
m/s2
P =
F
ma
=
A
A
kg/m&middot;s2 or N/m2
m2
Recall: F = ma
Force, Area and Pressure
same force, different area
different force, same area
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Pressure Units
(Sec. 5.2, p. 151-152)
Millimeters of Mercury and Unit Conversion
Dimensional Analysis and Unit Conversion
Mathematically, do things the
same way as always:
&raquo; cm &times; cm = cm2
&raquo; cm + cm = cm
&raquo; cm &divide; cm = 1
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The Manometer
(Sec. 5.2, p. 152-153)
Manometer: instrument used to measure the pressure of a gas sample in the
laboratory
Pgas = Patm - h
Gas pressure is less than
atmospheric pressure
Pgas = Patm + h
Gas pressure is less than
atmospheric pressure
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The Gas Law’s
(Sec. 5.3, p. 154-159)
Four quantities required to describe a gas:
1.) amount of gas (in moles)
2.) pressure (in bar)
3.) volume (in L)
4.) temperature (in K)
** gas laws describe the relationships between pairs of these properties
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The Gas Laws
(Sec. 5.3, p. 154-159)
P1V1 = P2V2
Boyle’s Law
V α 1/P
Charles’s Law
VαT
V1 = V2
T1
T2
Gas Laws
Vα n
V1 = V2
n1
n2
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The Ideal Gas Law
(Sec. 5.4, p. 160-162)
Charles’s Law
VαT
Boyle’s Law
V α 1/P
Constant T and n
Constant P and n
Ideal Gas Law
PV = nRT
Constant T and P
Vα n
Ideal Gas Constant (R):
= 0.08314 L&middot;bar
mol&middot;K
= 0.08314 L&middot;bar&middot;mol-1&middot;K-1
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The Ideal Gas Law: Applications
(Sec. 5.5, p. 162-165)
Molar Volume at Standard Temperature and Pressure (STP)
Standard Temperature and Pressure (STP)
Standard Temperature: 273.15 K
Standard Pressure: 1.00 bar
Molar Volume:
- the volume occupied by one
mole of a substance
V =
nRT
P
L bar
) (273 K)
mol K
1.00 bar
(1.00 mol) (0.08314
V =
V(273K) = 22.7 L
V(298K) = 24.8 L (Note: conditions!!)
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The Ideal Gas Law: Applications
Density of a Gas
a) Under standard conditions (at STP):
If,
(Sec. 5.5, p. 162-165)
m ,
V
then, density = molar mass
molar volume
** For gas: density α molar mass
d=
b) Under any conditions:
Using PV = nRT , and
knowing that Mm = m and rearranging to note that n = m
n
Mm
Substituting, PV = m x RT and again knowing that d = m
Mm
V
Then, rearranging:
m = d = PMm
V
RT
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The Ideal Gas Law: Applications
(Sec. 5.5, p. 162-165)
Molar Mass of a Gas
a) PV = nRT or PV = mRT
Mm
then rearranging Mm = mRT
PV
** requires mass measurements, and typical measurements for ideal gas
law
b) Use previously established density equation and knowing density of gas
and rearranging, then:
d = PMm
RT
then
Mm = dRT
P
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Dalton’s Law: Mixtures of Gases
(Sec. 5.6, p. 166-171)
Partial Pressure:
- pressure exerted by a
particular gas in a
mixture of gases
Mole Fraction (χa)
- the number of
moles of a component
in a mixture compared
to the total of moles in
the mixture
χa =
nnRT
n RT
…..
; Pb = nbRT ; Pn =
Pa = a
Vtot
V
Vtot
tot
Pa
Ptot = Pa + Pb + Pc …
Ptot = (na + nb + nc+…)
Ptot
RT
Vtot
= (ntotal)
RT
Vtot
=
na
ntot
naRT/Vtot
ntotRT/Vtot
=
na
ntot
Pa = χaPtot
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Dalton’s Law: Mixtures of Gases
(Sec. 5.6, p. 166-171)
Collecting Gases Over Water
Zn (s) + HCl (aq)
25&ordm;C
758.2 mmHg
ZnCl2 (aq) + H2 (g)
Ptotal = PH2 + PH2O
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Gases is Chemical Reactions: Stoichiometry
(Sec. 5.7, p. 171-174)
Gases and Balanced Chemical Equation
- use given information about one gas, and stoichiometric factors of
balanced chemical equation to determine desired information about
another gas
Molar Volume and Stoichiometry
2 H2(g) + O2(g)
2 H2O(l)
If you are working at STP:
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Kinetic Molecular Theory: A Model for Gases
(Sec. 5.8, p. 174-180)
Kinetic Molecular Theory
- theories – give underlying reasons for scientific behaviour
- simplest model for behaviour of gases
- gas sample modelled as collection of particles
- gas particles move in constant straight-line motion
- size of particles is negligibly small
- particle collisions are elastic
Postulates (assumptions) of the theory:
1.
2.
3.
The size of each gas particle is
negligibly small.
The average kinetic energy of a
particle is proportional to the
temperature in kelvins.
The collision of one particle with
another (or with the walls of the
container) is completely elastic.
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Kinetic Molecular Theory: A Model for Gases
(Sec. 5.8, p. 174-180)
-
ideal gas law follows directly from kinetic molecular theory:
- explanations p.175-176
Boyle’s Law
at constant T:
1
V
V
collisions
P
V∝ T
T
collisions
Pconst V
Vconst P
V∝ n
n
collisions
Pconst V
Vconst P
collisions
Pconst V
P∝
Charles’s Law
at constant P:
at constant T an P:
Dalton’s Law
(Ptot = Pa + Pb + Pc + …)
at constant V and T:
n
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Kinetic Molecular Theory: A Model for Gases
Temperature and Molecular Velocities
-
all populations of gas particles at given temperature have same average
kinetic energy (regardless of mass)
kinetic energy of single particle (atom or molecule) of gas calculated as
KE =
-
-
(Sec. 5.8, p. 174-180)
1
2
mv2
m = mass
v = velocity or speed
this means, at any given moment, not all gas molecules are traveling at
exactly the same velocity (ie. collisions between gas molecules may cause
molecules in any sample to have range of speeds)
only way for all particles to have same kinetic energy is if lighter particles
travel faster (on average) than heavier ones
Therefore, kinetic molecular theory says we define the root-mean square
velocity as
urms =
u2
u2 = the average of the squares of the
particle velocities
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Kinetic Molecular Theory: A Model for Gases
(Sec. 5.8, p. 174-180)
Temperature and Molecular Velocities
- so, average kinetic energy of one mole of gas particles is now given with
respect to the root-mean square velocity as
now, the 2nd assumption of the kinetic molecular theory says average
kinetic energy is proportional to the kelvin temperature
- the constant of proportionality in this relationship is (3/2R) so
-
Note: R is the gas constant in units of
8.314 J mol-1 K-1
-
combining these two equations
and solving for u2,
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Kinetic Molecular Theory: A Model for Gases
(Sec. 5.8, p. 174-180)
Temperature and Molecular Velocities
- Now, with
m = in kg
so NAm = kg&middot;mol-1, (molar mass in kg&middot;mol-1) expressed as M, and
- the root mean square velocity of a collection of gas particles is
proportional to the square root of the temperature in kelvins
- and is inversely proportional to the square root of the molar mass of the
particles (Note: M has units of kg&middot;mol-1)
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Kinetic Molecular Theory: A Model for Gases
(Sec. 5.8, p. 174-180)
-
-
the lower the molecular mass,
the higher the root-mean
the distribution of speeds
temperature is the same for
all the gases (ie. same KEavg)
Temperature and Molecular Velocities
As the temperature increases for a particular gas
- the root mean square velocity increases
- the distributions broaden; that is, a smaller
fraction of the molecules moves at any given
speed
- more speeds are represented by a significant
fraction of the population
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Mean Free Path, Diffusion, and Effusion of Gases
(Sec. 5.9, p. 180-181)
Mean free path
-
the average distance
that a molecule travels
between collisions
-
Diffusion
mean free path increases with
decreasing pressure
-
the process by which gas molecules spread
out in response to a concentration gradient
(high to low concentration) despite the fact
the particles undergo many collisions
-
heavier molecules diffuse more slowly than
lighter ones
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Mean Free Path, Diffusion, and Effusion of Gases
(Sec. 5.9, p. 180-181)
Effusion and Graham’s Law of Effusion
- the process by which a gas escapes from a container
into a vacuum through a small hole
- heavier molecules effuse more slowly than lighter
ones
- rate of effusion related to urms
rate α
1
√M
Graham’s Law of Effusion
- ratio of effusion rates of two
different gases

rateA =
rateB
MB
MA
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Real gases: The effects of Size and Intermolecular Forces
(Sec. 5.7, p. 181-185)
Until now, our assumptions:
1) all gases are behaving ideally
- this is acceptable since under typical
atmospheric pressures and
temperatures, most gases do behave
ideally
- all gases acting nearly ideally at STP
2) the volume occupied by individual gas particles is negligible compared
to the total volume occupied by the gas
3) there are no interactions between gas particles other than random elastic
collisions (ie. forces between gas particles are not significant)
***these assumptions are all acceptable for most gases at STP
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Real gases: The effects of Size and Intermolecular Forces
The Effect of the Finite Volume of Gas Particles
Low pressure
(Sec. 5.7, p. 181-185)
High pressure
Low Pressures
- molar volume of argon is nearly identical
to that of ideal gas
High Pressures
- molar volume of argon becomes greater
than that of ideal gas
Molar volume of Ideal gas and Argon
at varying pressures
Conclusion
- finite volume of gas particles (ie. actual size) is important at higher pressure
since volume of particles themselves occupies significant portion of total gas
volume
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Real gases: The effects of Size and Intermolecular Forces
(Sec. 5.7, p. 181-185)
The Effect of the Finite Volume of Gas Particles
- comparison of molar volume at various pressures of argon gas shows
ideal gas law predicts a molar volume that is too small
- small correction, made by Johannes van der Waals, accounts for volume
of the gas particles themselves
V = nRT
P
+ nb
Note: n = number of moles
b = constant that depends
on the gas
V - nb = nRT
P
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Real gases: The effects of Size and Intermolecular Forces
(Sec. 5.7, p. 181-185)
Intermolecular forces:
- attractions between atoms or molecules that compose any substance
- typically negligible in gases due to kinetic energy of molecules is great
enough to overcome these forces of attraction
a) High temp. affects on intermolecular forces
- weak attractions between molecules, compared with relatively large
kinetic energy between them, do not affect their collisions
b) Lower temp. affects on intermolecular forces
- collisions occur with less kinetic energy, with weak attractions affecting
molecular collisions and even direction of motion
Conclusion
- effect of weak attractions between particles is a lower number of collisions
with the surfaces thereby lowering the pressure compared to that of ideal
gas
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Real gases: The effects of Size and Intermolecular Forces
(Sec. 5.7, p. 181-185)
Effect of Intermolecular Forces
High temp.
- pressure of xenon gas nearly
identical to that of ideal gas
Low temp.
- pressure of xenon gas is less
than that of ideal gas
- significant interaction between
xenon atoms result in few
collisions with walls of
container; lower pressure
Pressure of 1.0 mol of Ideal gas and 1.0 mol of
Xenon at varying pressures (constant volume)
**graph shows that ideal gas law predicts pressure too large at low temps.
-
small correction, made by Johannes van der Waals, accounts for intermolecular
forces between gas particles
P = nRT
V
-
a n 2 and rearranged to P + a n 2 = nRT
V
V
V
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Real gases: The effects of Size and Intermolecular Forces
(Sec. 5.7, p. 181-185)
Van der Waals Equation
- used to calculate properties of gas under non-ideal conditions
P +a n
V
2
x V - nb = nRT
- describes non-ideal behaviour of gases
Real Gas (or nonideal gas)
- one that does not obey the assumptions
that define an ideal gas
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