### Chapter 10 - Gases

```Chapter 10
Gases & Kinetic Molecular Theory
I) Gases, Liquids, Solids
Gases
Liquids
Solids
Particles
far apart
Particles
touching
Particles
closely packed
very
compressible
slightly
comp.
Incomp.
Dg
<< DR
<
Ds
No definite
vol.
def.
vol.
def.
vol.
No def.
shape
No def.
shape
def.
shape
1
II) Properties of Gases
A) Amount (mass or moles)
low molar masses
Independent of vol. (V),
pressure (P), temp. (T)
B) Volume
Gas takes shape of its container
& completely fills it.
vol. gas = vol. container
Dependent on P & T
2
C) Temperature
Both P & V depend on T
- MUST use Kelvin
D) All gases are miscible
- mix completely
homogeneous mixture
3
E) Pressure
Gas particles exert pressure by
colliding w. walls of container
Depends on V & T
SI unit : Pascal,
2
1 Pa = 1 N/m
4
1) Pressure Measurement
Barometer: measures pressure of
atmosphere
Manometer: measures press. of gas
or gas above a liquid
in a vessel
a) Units
Standard Atmospheric Pressure
Avg. atmospheric pressure at 0°C
at sea level that supports a column
of Hg 760 mm high. (1 atm)
1 atm = 760 mm Hg = 760 torr
= 101.325 k Pa = 14.7 lbs/in2
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6
7
III) Gas Laws
A) Boyle’s Law
Volume is inversely
proportional to Pressure
(constant T & fixed amt. gas)
8
B) Charles’s Law
Volume is directly
proportional to Absolute Temp.
(constant P & fixed amt. gas)
9
1) Ex: A gas occupies a vol. of
12.3 L at 177°C. What is its
vol. when the temp. is 27°C?
10
C) Avogadro’s Law
Avogadro’s Hypothesis:
Equal volumes of gases, at
same T & P, contain equal
numbers of particles.
Avogadro’s Law
Volume of a gas is directly
proportional to the number
of moles of gas
V = k3 C n
11
1) Determination of Mol. Wt.
If 2 gases have equal vol. then there
are equal numbers of particles &
mass 1 molecule B (amu)
mass 1 molecule A (amu)
=
mass B (g)
mass A (g)
Proof
12
2) Ex: There are 2 balloons at same
P & T. One balloon contains
H2 & the other contains an
unknown gas, B, each w. a vol.
of 1 L and masses as shown
below. What is the MW of B?
H2
1L
0.0900 g
B
1L
1.44 g
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IV) Ideal Gas Law
Replace proportionality & rearrange
14
Universal Gas Constant
Ideal Gas
Hypothetical gas that behaves according
to the Ideal Gas Law under all conditions
Real
Gas
Ideal
Gas
low P, high T
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A) Standard Temp. & Pressure
Temp. & Pressure affect Volume
Need a “standard” T & P
as a reference point
STP
T = 0 °C
(273.15 K)
P = 1 atm
16
B) Molar Volume
Volume of 1 mole of an
ideal gas, Vm, at a given T & P
At STP:
Standard Molar Volume
1) Ex: What volume does 3.0 mol
of gas occupy at STP?
17
C) Super Combined Gas Law
Alternate writing of IGL:
18
D) Calc. Using Ideal Gas Law
Given any three of P, V, n & T
calc. the unknown quantity
1) Ex: What is the pressure in a
container that holds 0.452 g of
NH3, in a vol. of 400.0 mL &
a temp. of 25°C?
19
2) Ex: A sample of gas occupies a vol.
of 5.0 L at a pressure of 650.0 torr
& a temp. of 24°C. We want to put
the gas in a 100.0 mL container
which can only withstand a pressure
of 3.0 atm. What temp. must be
maintained so that the container
doesn’t explode.
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V) Further Applications of IGL
A) Determine MW & Molecular Formula
MF = (EF)n
n
=
MF
EFW
Determine EF & EFW from
% composition data
Determine MW
PV = nRT
D =
= m/n
D = m/V
P
RT
22
1) Ex: An unknown gas has a mass of
0.50 g. It occupies 1.1 L at a
pressure of 252 torr & a temp. of
243°C. Its emp. formula is C2H5.
What is its molecular formula?
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B) Stoichiometry Problems Involving Gases
Moles of reactants & products
are related by balanced eqn.
Moles of gases related to P, V & T
Use Avogadro’s Law to express
quantities of gas in volumes
V% n
(constant T & P)
V = kn
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1) Ex 1: What volume of oxygen gas
would be required to produce
0.50 L of SO2 by the following rx.?
2 ZnS + 3 O2(g) v 2 ZnO + 2 SO2(g)
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2) Ex 2: When the following rxn.
was carried to completion at 27°C
& 0.987 atm 3.20 L of CO was
produced. How many moles of
Sb4O6 were initially present?
Sb4O6 + 6 C v 4 Sb + 6 CO(g)
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3) Ex 3: What vol. of N2(g) at STP
would be produced by the rxn.
of 0.86 g of NO(g)?
2 NO(g) + 2 H2(g) v 2 H2O(g) + N2(g)
Remember: 1 mol gas = 22.41 L at STP
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VI) Gas Mixtures & Partial Pressures
Each gas acts independently.
Total pressure depends only on
the total # particles & not kind.
A) Partial Pressures
Pressure each gas would exert if it
were the only gas present at same
T & V as for mixture.
Dalton’s Law of Partial Pressures
Ptot = P1 + P2 + P3 + CCC
29
N
Ptot = 3 Pj
j=1
Assume each gas behaves ideally
Pj = nj (
RT
V
N
N
j=1
j=1
)
Ptot = 3Pj = (RT/V)3nj = (RT/V)ntot
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1) Mole Fraction
Pj
nj
=
nT
Related to partial pressures
Pj
PT
nj (RT/V)
=
nT (RT/V)
=
Pj
Pj = Pj PT
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2) Ex: A mixture of 40.0 g of O2 &
40.0 g of He has a total pressure of
0.900 atm. What is the partial
pressure of O2?
32
VII) Kinetic-Molecular Theory
Explains behavior of ideal gases
A gas consists of molecules
in constant random motion
K.E. = ½ m (urms)
2
urms = root-mean-square (rms) speed
1
N
E si )
2 1/2
urms = (
N
i
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5 Postulates of Kinetic Theory
(1) Molecules move continuously and randomly in straight lines in all
directions and various speeds.
--
Properties of a gas that depend on motion of molecules, such as
pressure, will be the same in all directions.
(2) Gases are composed of molecules whose size is negligible compared
to the average distance between them.
--
Most of the volume occupied by a gas is empty space.
--
Ignore the volume occupied by the molecules.
(3) Intermolecular forces (attractive and repulsive forces between
molecules) are negligible, except when the molecules collide with
each other.
--
A molecule continues moving in a straight line with
undiminished speed until it collides with another gas molecule
or with the walls of the container.
(4) Molecular collisions are elastic.
--
Energy can be transferred between molecules but the total
average kinetic energy remains constant.
(5) The average kinetic energy of the molecules is proportional to the
absolute temperature, K (kelvin).
--
At any given temperature, the molecules of ALL gases have the
SAME average kinetic energy.
– The higher the temperature, the greater the average kinetic energy.
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A) Ideal Gas
Hypothetical gas which conforms
to all the assumptions
of the K.M.T.
B) Real Gases
Obey K.M.T. (behave ideally) at
high temp. & low pressure
High Temp: K.E. great enough to
overcome I.A.F.
Low Pressure:
few particles in a
large volume
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C) Molecular Speeds
Distribution of KE & u is
dependent on Temperature
Total KE of
1 mole of gas
=
3/2 (RT)
Avg. KE of
1 molecule
=
½ m u2
1
3
½ m u = ----- C ---- RT
NA
2
2
3 RT
3 RT
u = ------- = ------NAm
2
3 RT 1/2
u = ( -------- )
37
1) Ex: Calc. the speed of a molecule
of O2 that has the avg. KE at room
temp, 20°C.
3 RT 1/2
u = ( -------- )
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D) Qualitative Interpretation of Gas Laws
Pressure caused by collisions of
molecules w. container’s walls
- frequency of collisions/unit area
- force/collision
Molecular conc. & avg. speed
determines the freq. of coll.
Avg. molecular speed
determines avg. force/coll.
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1) Boyle’s Law
T constant | KE constant | u constant
ˆ avg.
molecular force/coll.
remains constant
Inc. Volume
Molecular conc. dec.
- freq. of coll./unit area dec.
ˆ P dec.
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1) Charles’s Law
T inc.
|
KE inc.
|
u inc.
- inc. force/coll.
- inc. freq. of coll.
Keep P constant
Volume must inc. so the
# molecules/unit vol. &
freq. of coll. will dec.
ˆ T inc., V inc.
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VIII) Diffusion & Effusion
A) Diffusion
Dispersion of a gas throughout a vessel
Why does it take so long
for a gas to diffuse?
- have molecular collisions
Avg. distance traveled between
collisions is called the mean free path
Higher density
of gas
|
Smaller
m.f.p.
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2) Ex: The rate of effusion of an
unknown gas is 2.91 times faster
than that of NH3. What is the
molecular wt. of the gas?
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B) Calculations
1) Ex 1: The pressure of 2.50 mol of
Xe in a 2.000 L flask is 31.6 atm at
75°C. Is the gas behaving ideally?
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