Transcript A Gas

Gases
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1
A Gas
 Uniformly
fills any container.
 Can be compressed.
 Mixes completely with any other
gas
 Exerts pressure on its surroundings.
 Can diffuse into other gases.
 Can be described in terms of its
volume, temperature, pressure, and
the amount present.
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2
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
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3
A
Torricellian
Barometer
At sea level, latitude
45o north (or south),
the average
atmospheric pressure
supports a column of
mercury 760 mm
high in a simple
mercury barometer
at 0oC This average
pressure is called
one atmosphere.
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4
The Effects of Decreasing the Volume of a
Sample of Gas at Constant Temperature
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Boyle’s
*
Law
Pressure  Volume = Constant (T =
constant)
P1V1 = P2V2 (T = constant)
V  1/P (T = constant)
(*Holds precisely only at very low
pressures.)
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6
Plotting Boyle’s Data
from Table 5.1
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7
A Plot of
PV
versus P
for
Several
Gases at
Pressures
Below 1
ATM
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8
A gas that strictly obeys Boyle’s
Law is called an ideal gas.
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9
Example: Boyle’s Law
At 25 oC, a sample of oxygen occupies
100. mL under a pressure of 380. torr.
What volume would it occupy under a
pressure of 1.00 atm at the same
temperature?
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10
Answer
50.0 mL
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11
Example
At 100. oC a sample of neon occupies
200. mL under a pressure of 4.00
atmospheres. What must the pressure
be for it to occupy 800. mL at 100. oC?
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12
Answer
1.00 atm.
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13
The Effects of Increasing the Temperature of a
Sample of Gas at Constant Pressure
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14
Charles’s Law
The volume of a gas is directly proportional
to temperature, and extrapolates to zero at
zero Kelvin.
V = bT (P = constant)
b = a proportionality constant
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15
Charles’s Law
V1
V2

T1
T2
( P  constant)
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16
Amazing
Experiments have shown that when a
273 mL sample of gas at 0 oC is heated
to 1 oC, its volume increases by 1 mL
to 274 mL. Conversely each degree
the gas is cooled its volume decreases
1 mL. What will the volume of the gas
be at –273 oC?
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17
Plots of
V Versus
T (ºC)
for
Several
Gases
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18
The Kelvin Temperature Scale
The temperature at –273 oC, the lowest
temperature possible is known as
absolute zero. It is the basis of the
Kelvin (absolute) temperature.
K = oC + 273
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19
Plots
of V
Versus
T
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20
Example Charles’ Law
A sample of hydrogen, H2, occupies
100. mL at 25 oC and 740. torr. What
volume would it occupy at 50.0 oC and
740. torr?
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21
Answer
108 mL
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22
Example
A sample of oxygen, O2, occupies 200.
mL at 100. oC and 1.00 atm. At what
temperature (oC) will the oxygen
occupy 400. mL if the pressure remains
constant?
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23
Answer
746 K
473 oC
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24
The Effects of Increasing the Temperature of a
Sample of Gas at Constant Volume:
Who’s Law?
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25
Gay-Lussac’s Law
P1
T1
=
P2
T2
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26
Combined Gas Law
Boyle’s and Charles’ Laws can be
combined together into the following
mathematical expression:
P1V1 = P2V2
T1
T2
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A very convenient form:
V2= V1
P1 T2
P2 T1
The relationship has six
variables. If any five are known,
the sixth can be calculated.
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28
Example
A sample of nitrogen, N2, occupies
200. mL at 57 oC under a pressure of
840. torr. What volume would it
occupy at 0 oC and 1.00 atm pressure?
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29
Answer
183 mL
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30
Example
A sample of methane, CH4, the main
component of natural gas occupies
400. mL at 96 oC under a pressure of
0.500 atm. What volume would it
occupy at 0 oC under a pressure of
1200 torr?
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31
Answer
93.7 mL
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32
Avogadro’s Law
For a gas at constant temperature and
pressure, the volume is directly
proportional to the number of moles of
gas (at low pressures).
V = an
a = proportionality constant
V = volume of the gas
n = number of moles of gas
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33
Standard Temperature
and Pressure
“STP”
P = 1 atmosphere
T = C
The molar volume of an ideal gas is 22.42
liters at STP
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34
A Mole of Any Gas Occupies a Volume
of Approximately 22.4 L at STP
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35
Example
What volume does 36.3 g of oxygen, O2,
occupy at STP?
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36
Answer
25.4 L
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37
Molecular Weight
• Application of the gas laws provides a
method of calculating the molecular
weight of a gas.
• This plus elemental analysis provides
mechanism for determining molecular
formula
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38
Example
If 2.00 g of a gas occupies 560.mL at
STP, what is its molecular weight?
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39
Answer
80.0 g/mol
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40
Example
A compound containing only carbon
and hydrogen is 80.0% C and 20.0% H
by mass. At STP 280. mL of the gas
weighs 0.375 g. What is the molecular
formula for the compound?
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41
Answer
C2H6
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42
Ideal Gas Law
 An
equation of state for a gas.
 “state” is the condition of the gas at a given
time.
 Can be determined by combining Boyle’s
Law, Charles’ Law, and Avogadro’s Law
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Ideal Gas Law
PV = nRT
R = proportionality constant
= 0.0821 L atm  mol
P = pressure in atm
V = volume in liters
n = moles
T = temperature in Kelvins
Holds closely at P < 1 atm
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44
Example
What volume does 48.0 g of methane,
CH4, occupy at 140. oC under a
pressure of 1280 torr?
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45
Answer
60.4 L
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46
Example
A 250. mL flask contains a mixture of
nitrogen, oxygen, and helium at a
temperature of 27 oC and a pressure of
0.850 atm. How many moles of gas
are present?
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47
Answer
8.63 x 10-3 moles
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48
Example
What pressure in kilopascals is exerted
by 0.480 g of carbon dioxide in a 1.00
L flask at 100 oC?
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49
Answer
33.8 kPa
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50
Density
Density has the units of mass per unit
volume. We can arrange the ideal gas
equation to obtain density
D=
PM
RT
Where M is the gram molar mass;
D is in g/L
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51
Example
What is the density of formaldehyde,
CH2O, vapors at 95 oC and a pressure
of 650. torr?
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52
Answer
0.849 g/L
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53
Gram Molecular Mass
The Ideal Gas Equation can be rearranged
to solve directly for gram molecular mass.
M=
mRT
PV
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54
Example
A 0.1842 g sample of phosphorus
vapor in a 169 mL bulb exerts a
pressure of 45.6 kPa at 350. oC.
Calculate both the molecular mass and
molecular formula of phosphorus
vapor. (R = 8.31 kPa L/ mol K)
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55
Answer
124 g/mol
P4
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56
Dalton’s Law of
Partial Pressures
For a mixture of gases in a
container,
PTotal = P1 + P2 + P3 + . . .
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57
Partial Pressure of
Each Gas in a
Mixture
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58
Example
If 100 mL of hydrogen and 100. mL of
oxygen, both measured at 25 oC and
1.00 atm pressure, were forced into one
of the containers at 25 oC, what would
be the total pressure of the two gases?
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59
Answer
2 atm
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60
Collecting Gas Over Water
• A gas can be collected by displacement of water
• This results in a mixture of gases:
– The gas you are collecting
– Water vapor
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Collecting Gas Over Water
• Vapor pressure is temperature dependent.
• Ptotal = Pgas + Pwater
• How do we correct for the water vapor?
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62
Example
A sample of solid potassium chlorate (KClO3) was
heated in a test tube and decomposed by the
following reaction:
2KClO3(s)  2KCl(s) + 3O2(g)
The oxygen produced was collected by displacement
of water at 22.0 C at a total pressure of 754 torr. The
volume of the gas collected was 0.650 L, and the
vapor pressure of the water at 22.0 is 21 torr.
Calculate the partial pressure of O2 in the gas
collected and the mass of KClO3 in the sample that
was decomposed.
Solution
• First, find the partial pressure of O2 from
Dalton’s Law of partial pressures
• Next, use the ideal gas law to find the
number of moles of O2
• Calculate the moles of KClO3 needed to
produce this quantity of O2
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64
Answers
• PO2 = 733 torr
• nO2 = 2.59 x 10-2
• 2.12 g KClO3
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65
Kinetic Molecular Theory
1. Gases consist of tiny discrete molecules that
are relatively far apart.
2. Gases consist of molecules in continuous
random motion.
3. Molecular collisions are elastic
4. The average kinetic energy of gaseous
molecules is proportional to the absolute
temperature. KE = ½ mv2
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Examples
• Explain Gay Lussac’s Law on the basis of
the Kinetic Molecular Theory
• Explain Boyle’s Law on the basis of the
Kinetic Molecular Theory
• Explain Charles’ Law on the basis of the
Kinetic Molecular Theory
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Diffusion: describes the mixing of
gases. The rate of diffusion is the
rate of gas mixing.
Effusion: describes the passage of
gas into an evacuated chamber.
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The Effusion of a Gas into an
Evacuated Chamber
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Effusion:
Rate of effusion for gas 1

Rate of effusion for gas 2
M2
M1
Diffusion:
Distance traveled by gas 1

Distance traveled by gas 2
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M2
M1
70
Example
The average speed of oxygen
molecules at 25 oC is 4.8 x 104 cm/s.
What would be the average speed of
sulfur dioxide molecules at the same
temperature?
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71
Answer
3.39 x 104 cm/s
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72
Example
The time required for a volume of an
unknown gas to effuse through a pin
hole was 71.5 sec. The time required
for the same volume of oxygen was
63.0 sec. Calculate the molecular
weight of the unknown gas.
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Answer
41.2 g/mol
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74
HCI(g) and NH3(g) Meet in a
Tube
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Real Gases
• At ordinary temperatures and
pressures, most gases obey the gas
laws reasonably well.
• Under what conditions does a gas
deviate significantly form ideality?
Why?
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Real Gases
Must correct ideal gas behavior
when at high pressure (smaller
volume) and low temperature
(attractive forces become important).
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Real Gases
van der Waals Equation
(
n2 a
P+
V2

corrected pressure
)
(V – n b) = nRT

corrected volume
Pideal
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Videal
78
Van der Waals’ Constants
Gas
a (L2atm/mol2 b (L/mol)
He
0.03412
0.02370
O2
1.360
0.03803
Cl2
6.493
0.05622
NH3
4.170
0.03707
H2O
5.464
0.03049
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79
Example
Calculate the pressure in atmospheres
exerted by 48.0 g of ammonia, NH3, in
a 1.00 L container at 100. oC using the
ideal gas equation.
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80
Answer
86.5 atm
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81
Now…
Solve the previous problem using the
van der Walls equation.
(
n2 a
P+
V2
)
(V – n b) = nRT
Gas
a (L2atm/mol2 b (L/mol)
NH3
4.170
0.0371
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82
Answer
63.3 atm
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83
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.)
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84
Path of
One
Particle
in a
Gas
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A Plot of
the Relative
Number of
O2
Molecules
That Have a
Given
Velocity at
STP
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A Plot of the
Relative
Number of
N2
Molecules
That Have a
Given
Velocity at
Three
Temperature
s
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87