Transcript Document

Chapter 5
Gases
John A. Schreifels
Chemistry 211
1
Overview
• Gas Laws
–
–
–
–
–
Gas Pressure and its measurement
Empirical gas laws
Ideal gas laws
Stoichiometry and gases
Gas Mixtures; Law of partial pressures
• Kinetic and Molecular Theory
– Kinetic theory of an Ideal gas
– Molecular speeds: diffusion and effusion
– Real gases
John A. Schreifels
Chemistry 211
2
Gases and Gas Pressure
• They form homogeneous solutions. All gases dissolve in each
other.
– Gases are compressible.
– Large molar volume.
• Barometer usually mercury column in tube; mm Hg is a
measure of pressure.
• Manometer tube of liquid connected to enclosed container
makes it possible to measure pressure inside the container.
• Pressure
– One of the most important of the measured quantities for
gases
– defined as the force/area P = f/area.
– Pressure has traditionally been measured in units relating to
the height of the Hg and is thus expressed as mm Hg = 1
Torr.
John A. Schreifels
Chemistry 211
3
Gas Pressure
• Pressure is directly proportional to the height of the column in a
barometer or manometer.
F mg dVg
P 

A
A
A
 dgh
• Mercury often used but other low density liquids are used for low
pressure changes:
P = dHgghHg = doilghoil or dHghHg = doilhoil.
• E.g. Water is sometimes used to determine pressure; determine
the height of water if the barometer pressure was 750 mmHg.
The density of Hg = 13.596 g/cm3 and 1.00 g/cm3 respectively.
• Solution:
hH2O  hHg 
dHg
dH2O
 750 mmHg 
13.596 g / cm3
1.00 g / cm3
 10197 mmH 2O
John A. Schreifels
Chemistry 211
4
The Gas Laws
John A. Schreifels
Chemistry 211
60
50
40
30
20
10
0
0
0.5
1
Pressure, atm
Volume vs Temperature
Volume, L
Boyle's Law: For a fixed amount of gas and
constant temperature, PV = constant.
• Charles's Law: at constant pressure the volume
is linearly proportional to temperature. V/T =
constant
• Avagadro’s law for a fixed pressure and
temperature, the volume of a gas is directly
proportional to the number of moles of that gas.
V/n = k = constant.
E.g. 1 The volume of some amount of a gas was 1.00
L when the pressure was 10.0 atm; what would
the volume be if the pressure decreased to 1.00
atm?
E.g. 2 A gas occupied a volume of 6.54 L at 25°C
what would its volume be at 100°C?
E.g. 3 The volume of 0.555 mol of some gas was
100.0 L; what would be the volume of 15.0 mol of
the same gas at the same T and P?
60
50
40
30
20
10
0
0
100
200
300
Temperature, K
Volume vs # mol
Volume, L
•
Volume, L
Volume vs Pressure
60
50
40
30
20
10
0
0
0.5
1
Moles
1.5
5
2
The Ideal Gas Equation
•
•
•
Ideal gas law the functional relationship between the pressure, volume,
temperature and moles of a gas. PV = nRT; all gases are ideal at low pressure.
PV =nRT. Each of the individual laws is contained in this equation.
Boyle's Law: PV = k1 = nRT.
•
Charles's Law:
•
•
V nR

 k2
T P
Avagadro’s law: V  nRT  nk
3
P
When any of the other three quantities in the ideal gas law have been
determined the last one can be calculated.
E.g. Calculate the pressure inside a TV picture tube, if it's volume is 5.00 liters,
it's temperature is 23.0C and it contains 0.0100 mg of nitrogen.
John A. Schreifels
Chemistry 211
6
Further Applications of Ideal-Gas
Equation
•
The density of a gas the density of a gas can be related to the
pressure from the ideal gas law using the definition of density: d =
mass/vol.
m n  FM
d 
V
V
P  FM

RT
E.g. Estimate the density of air at 20.0C and 1.00 atm by supposing that
air is predominantly N2.
E.g. From the results above determine the density of He.
• Rearrangement permits the determination of molecular mass of a gas
from a measure of the density at a known temperature and pressure.
dRT
P
E.g. A certain gas was found to have a density of 0.480 g/L at 260C and
103 Torr. Determine the FM of the compound.
FM 
John A. Schreifels
Chemistry 211
7
Stoichiometric Relationships with
Gases
• When gases are involved in a reaction, das
properties must be combined with stoichiometric
relationships.
E.g. Determine the volume of gas evolved at 273.15 K
and 1.00 atm if 1.00 kg of each reactant were used.
Assume complete reaction (i.e. 100% yield)
CaO(s) + 3C(s)  CaC2(s) + CO(g).
• Strategy:
– Determine the number of moles of each reactant to which
this mass corresponds.
– Use stoichiometry to tell us the corresponding number of
moles of CO produced.
– Determine the volume of the gas from the ideal gas law.
John A. Schreifels
Chemistry 211
8
Partial Pressure and Dalton’s Law
•
•
•
•
Dalton's Law = the sum of the partial pressures of the gases in a
mixture = the total pressure or P = PA + PB + PC + ...where Pi = the
partial pressure of component i.
Dalton found that gases obeying the ideal gas law in the pure form will
continue to act ideally when mixed together with other ideal gases.
The individual partial pressures are used to determine the amount of
that gas in the mixture, not the total pressure, PA = nART/V.
Since they are in the same container T and V will be the same for all
gases.
E.g. 1.00 g of air consists of approximately 0.76 g nitrogen and 0.24 g
oxygen. Calculate the partial pressures and the total pressure when
this sample occupies a 1.00 L vessel at 20.0C.
– Solution:
• Determine the number of moles of each gas.
• Using the ideal gas law determine the pressure of each and sum to determine the
total pressure.
John A. Schreifels
Chemistry 211
9
Partial Pressure and Dalton’s Law2
•
•
Mole fraction another quantity commonly determined for gas mixtures.
It is defined the number of moles of one substance relative to the total
number of moles in the mixture or
nA
PA
XA 

n A  nB     PA  PB    
X can be calculated from
– moles of each gas in the mixture or
– the pressures of each gas
E.g. determine the mole fraction of N2 in the above example.
• Collection of a gaseous product over water is another example of
Dalton's Law. Subtract the vapor pressure of water to find the pressure
of the gaseous product.
E.g. Suppose KClO3 was decomposed according to
2 KClO3(s)+   2KCl(s) + 3O2(g).
PT = 755.2 Torr and 370.0 mL of gas was collected over water at
20.0C. Determine the number of moles of O2 if the vapor pressure of
water is 17.5 torr at this temperature.
John A. Schreifels
Chemistry 211
10
The Behavior of Real Gases
• The molar volume is not constant as is expected for
ideal gases.
• These deviations due to an attraction between some
molecules.
• Finite molar molecular volume.
• For compounds that deviate from ideality the van der
Waals equation is used:
2a 

n
P +
(V - nb) = nRT

2 
V 

where a and b are constants that are characteristic of
the gas.
• Applicable at high pressures and low temperatures.
John A. Schreifels
Chemistry 211
11
The Kinetic Theory – Molecular Theory
of Gases
• Microscopic view of gases is called the
kinetic theory of gases and assumes that
– Gas is collection of molecules (atoms) in
continuous random motion.
– The molecules are infinitely small point-like
particles that move in straight lines until they
collide with something.
– Gas molecules do not influence each other except
during collision.
– All collisions are elastic; the total kinetic energy is
constant at constant T.
– Average kinetic energy is proportional to T.
John A. Schreifels
Chemistry 211
12
The Kinetic Theory – Molecular Theory
of Gases
•
•
Theory leads to a description of bulk properties i.e. observable properties.
The average kinetic energy of the molecule is
Ek 
•
3RT
2N A
Average kinetic energy of moving particles can also be obtained from
1
E  mu 2
2
•
•
where NA = Avagadro’s number.
where u = average velocity
1 2
u=
(u1 + u22 +    + uk2)
k
All speeds are possible giving really a distribution of speeds.
Combine 1 & 2 to get a relationship between the velocity, temperature and molecular
mass.
u
3RT
M
• Express M in kg/mol and R = 8.3145 J/mol*K.
E.g. determine average velocity of He at 300 K.
E.g.2 predict the ratio of the speeds of some gas if the temperature increased from 300
K to 450 K.
John A. Schreifels
Chemistry 211
13
Graham’s Law: Diffusion and Effusion
of Gases
• Diffusion the process whereby a gas spreads out through another
gas to occupy the space with uniform partial pressure.
• Effusion the process in which a gas flows through a small hole in
a container.
• Graham’s law of Effusion the rate of effusion of gas molecules
through a hole is inversely proportional to the square root of the
molecular mass of the gas at constant temperature and pressure.
k
Rate 
MW
E.g. determine the molecular mass of an unknown compound if it
effused through a small orifice if it effused 3.55 times slower than
CH4.
E.g. A compound with a molecular mass of 32.0 g/mol effused
through a small opening in 35 s; determine the effusion time for
the same amount of a compound with a molecular mass of 16.0.
John A. Schreifels
Chemistry 211
14