Transcript Slide 1

OFB Chapter 5
The Gaseous State
5-1 The Chemistry of Gases
5-2 Pressure and Boyle’s Law
5-3 Temperature and Charles’s Law
5-4 The Ideal Gas Law
5-5 Chemical Calculations for Gases
5-6 Mixtures of Gases
5-7 Real Gases
7/18/2015
OFB Chapter 5
1
Chapter 5
The Gaseous State
Examples / Exercises
– 5-1 thru 5-13
Problems
– 8, 18, 26, 34, 38, 46, 68
7/18/2015
OFB Chapter 5
2
OFB Chapter 5
The Gaseous State
Early discoveries of gases formed by chemical
reactions:
heat
2 HgO(s)  2 Hg(l) + O2(g)
Lavoisier used this to establish the conservation of
mass theory
heat
Marble: CaCO3(s)  CaO(s) + CO2(g)
heat
NH4Cl(s)  HCl(g) + NH3(g)
Nitroglycerin: 4 C3H5(NO3)3(l) 
6 N2(g) + 12 CO2(g) + O2(g) + 10 H2O(g)
CaCO3(s) + HCl(aq) 
7/18/2015
OFB Chapter 5
CaCl2(aq)
+ H2O(g) + CO2(g)
3
Pressure and Boyle’s Law
force (F) = mass * acceleration =
Newton (N) = kg m s-2
acceleration (a) = velocity per
unit of time [m s-2]
mass (m) = quantity of matter [kg]
area (A) = m2
7/18/2015
OFB Chapter 5
4
Pressure and Boyle’s Law
7/18/2015
OFB Chapter 5
5
Pressure and Boyle’s Law
P = gdh
g = acceleration of gravity at the surface
of the Earth
= 9.80665 m s-2
d = density of the liquid = for Hg at 0ºC
= 13.5951 g cm-3 = 13.5951 kg m-3
h = height of mercury in the column
= 76 cm = 760 mm = 0.76 m
P = gdh = (9.80665 m s-2)(13.5951 kg m-3)
(0.76 m)
7/18/2015
OFB Chapter 5
6
A pressure of 101.325 kPa is need to
raise the column of
Hg 760 mm or 76 cm
Called standard pressure
7/18/2015
OFB Chapter 5
7
Boyle’s Law: The Effect of Pressure on
Gas Volume
The product of the pressure and volume,
PV, of a sample of gas is a constant at a
constant temperature:
7/18/2015
OFB Chapter 5
8
Boyle’s Law: The Effect of
Pressure on Gas Volume
STP
For 1 mole of any gas
(i.e., 32.0 g of O2; 28.0 g N2; 2.02 g H2),
STP = standard temperature and pressure =
0oC and 1 atm
7/18/2015
OFB Chapter 5
9
Boyle’s Law: The Effect of Pressure on Gas
Volume
Exercise 5-3
The long cylinder of a bicycle pump has a
volume of 1131 cm3 and is filled with air
at a pressure of 1.02 atm. The outlet
valve is sealed shut, and the pump handle
is pushed down until the volume of the
air is 517 cm3. The temperature of the air
trapped inside does not change. Compute
the pressure inside the pump.
7/18/2015
OFB Chapter 5
10
Temperature and Charles’ Law
Charles’ Law: The Effect of
Temperature on Gas Volume
V

t  273.15C   1) 
 V

7/18/2015
OFB Chapter 5
11
Charles’ Law: The Effect of
Temperature on Gas Volume
Absolute Temperature
V = Vo
(
t
1+
273.15oC
)
Kelvin temperature
scale
7/18/2015
OFB Chapter 5
12
Charles’ Law: The Effect of
Temperature on Gas Volume
7/18/2015
OFB Chapter 5
13
Exercise 5-4
The gas in a gas thermometer that has
been placed in a furnace has a
volume that is 2.56 times larger than
the volume that it occupies at 100oC.
Determine the temperature in the
furnace (in degrees Celsius).
7/18/2015
OFB Chapter 5
14
Boyle’s
Law
P1V1 = P2V2
(at a fixed
temperature)
Charles’
Law
V1 / V2 = T1 / T2
Avogadro
(at a fixed pressure
and temperature)
7/18/2015
(at a fixed pressure)
OFB Chapter 5
15
The Ideal Gas Law
V
7/18/2015
-1
nTP
OFB Chapter 5
16
The Ideal Gas Law
P1V1
R
n1T1
7/18/2015
P2V2
R
n2T2
OFB Chapter 5
17
Exercise 5-5
At one point during its ascent, a
weather balloon filled with helium at
a volume of 1.0  104 L at 1.00 atm
and 30oC reaches an altitude at which
the temperature is -10oC yet the
volume is unchanged. Compare the
pressure at that point.
P1V1 P2V2

n1T1 n2T2
7/18/2015
OFB Chapter 5
18
The Ideal Gas Law
R
universal gas constant
?
for fixed V, P, and T, the number of n
is fixed as well, and independent of
the particular gas studied
(22.414L)(
1atm)
PV

R
nT (1.00mol)(273.15 K)
(22.414x 10-3 m3 )(101.325x
103 N m-2 )
R
(1.00mol)(273.1
5K)
7/18/2015
OFB Chapter 5
19
PV = nRT
ideal gas law
R  0.082 L atm mol K
-1
R  8.31 J mol
7/18/2015
OFB Chapter 5
1
K
-1
1
20
Exercise 5-6
What mass of Hydrogen gas is
needed to fill a weather balloon
to a volume of 10,000 L at 1.00
atm and 30C?
Strategy
1.) use PV = nRT
2.)
3.)
7/18/2015
OFB Chapter 5
21
Exercise 5-6
What mass of Hydrogen gas is
needed to fill a weather balloon
to a volume of 10,000 L at 1.00
atm and 30C?
7/18/2015
OFB Chapter 5
22
Gas Density and Molar Mass
P V  nRT
m
P V  RT
M
7/18/2015
OFB Chapter 5
23
Gas Density and Molar Mass
Exercise 5-7
Calculate the density of gaseous
hydrogen at a pressure of 1.32 atm
and a temperature of -45oC.
P
d
M
RT
7/18/2015
OFB Chapter 5
24
Gas Density and Molar Mass
P V  nRT
m
P V  RT
M
Rearrange
m
P

M
V RT
RT
 m  RT
M  
d
P
V P
RT
M d
P
7/18/2015
P
d
M
RT
OFB Chapter 5
25
Exercise 5-8
Fluorocarbons are compounds of
fluorine and carbon. A 45.60 g
sample of a gaseous fluorocarbon
contains 7.94 g of carbon and 37.66
g of fluorine and occupies 7.40 L at
STP (P = 1.00 atm and T = 273.15
K). Determine the approximate
molar mass of the fluorocarbon and
give its molecular formula.
7/18/2015
OFB Chapter 5
26
Exercise 5-8
Fluorocarbons are compounds of fluorine and carbon. A
45.60 g sample of a gaseous fluorocarbon contains 7.94 g
of carbon and 37.66 g of fluorine and occupies 7.40 L at
STP (P = 1.00 atm and T = 273.15 K). Determine the
approximate molar mass of the fluorocarbon and give its
molecular formula.
RT
M d
P
1 1

 45.60g 0.082L atm mol K x 273K



1atm
 7.40L 

M  138g mol1
 1molC 
  0.661molC
n C  7.94g C x 
 12 g C 
 0.661mol  1 part C
 1molF 
  1.982mol F
n F  37.66g F x 
 0.661mol  3 partsF
 19 g F 
7/18/2015
OFB Chapter 5
27
Chemical Calculations for Gases
Why use Volume for gases in
chemical reaction calculations?
The volume of a gas is easier to
measure than the mass of a gas.
Exercise 5-9
Ethylene burns in oxygen:
C2H4(g) + 3 O2(g)  2 CO2(g) + 2H2O(g)
A volume of 3.51 L of C2H4(g) at a
temperature of 25oC and a pressure of 4.63
atm reacts completely with O2(g). The water
vapor is collected at a temperature of 130oC
and a pressure of 0.955 atm. Calculate the
volume of the water vapor.
7/18/2015
OFB Chapter 5
28
Exercise 5-9
Ethylene burns in oxygen:
C2H4(g) + 3 O2(g)  2 CO2(g) + 2H2O(g)
A volume of 3.51 L of C2H4(g) at a temperature of 25oC and a
pressure of 4.63 atm reacts completely with O2(g). The water
vapor is collected at a temperature of 130oC and a pressure of
0.955 atm. Calculate the volume of the water vapor.
P1V1 P2V2 PC2 H 4VC2 H 4 PH 2OVH 2O


n1T1 n2T2 nC H TC H
nH 2OTH 2O
2 4
2 4
Condit ion1 is C 2 H 4
and Condit on2 is H 2 O
1partC 2 H 4 for 2 part sH 2 O
n C2H 4  2 n
H2 0
PC 2 H 4  4.63at m
VC 2 H 4  3.51L
TC 2 H 4  298K
PH 2O  0.955at m
TH 2O 7/18/2015
 403K
VH 2O  x
OFB Chapter 5
29
Exercise 5-9
Ethylene burns in oxygen:
C2H4(g) + 3 O2(g)  2 CO2(g) + 2H2O(g)
A volume of 3.51 L of C2H4(g) at a temperature of 25oC and a
pressure of 4.63 atm reacts completely with O2(g). The water
vapor is collected at a temperature of 130oC and a pressure of
0.955 atm. Calculate the volume of the water vapor.
P1V1 P2V2

n1T1 n2T2
PC2 H 4VC2 H 4
nC2 H 4 TC2 H 4

PH 2OVH 2O
nH 2OTH 2O
VH2O
PC2H4 VC2H4n H2O TH2O

nC2H4TC2H4 PH2O
VH2O
PC2H4 VC2H4n H2O TH2O

2n H2O TC2H4 PH2O
VH2O
PC2H4 VC2H4TH2O

2TC2H4 PH2O
7/18/2015
VH2O  46.0L
OFB Chapter 5
30
Mixtures of Gases
Dalton’s Law of Partial
Pressures
The total pressure of a mixture
of gases equals the sum of the
partial pressures of the
individual gases.
7/18/2015
OFB Chapter 5
31
Mole Fractions and Partial Pressures
The mole fraction of a component in a
mixture is define as the number of
moles of the components that are in the
mixture divided by the total number of
moles present.
Mole Fractionof A  X A
nA
nA
XA 

n tot n A  n B  ...  n N
PA V  n A RT
Ptot V  n tot RT
divide equat ions
PA V  n A RT
PA
nA
nA
or

or PA 
Ptot
Ptot V  n tot RT Ptot n tot
n tot
PA  X A Ptot
7/18/2015
OFB Chapter 5
32
Exercise 5-11
A solid hydrocarbon is burned in air in a
closed container, producing a mixture of gases
having a total pressure of 3.34 atm. Analysis
of the mixture shows it to contain 0.340 g of
water vapor, 0.792 g of carbon dioxide, 0.288
g of oxygen, 3.790 g of nitrogen, and no other
gases. Calculate the mole fraction and partial
pressure of carbon dioxide in this mixture.
7/18/2015
OFB Chapter 5
33
Section 5-7
Kinetic Theory of Gases
Section 5-8
Real Gases
7/18/2015
OFB Chapter 5
34