Gases
A. Properties of Gases
1.
2.
3.
4.
Gases uniformly fill any container
Gases are easily compressed
Gases mixed completely with any other gas
Gases exert pressure on their surroundings
a. Pressure = force/unit area
B. Measuring barometric pressure
1. Barometer - Evangelista Torricelli (1643)
2. Units
a. mmHg (torr)
1 standard atmosphere = 1 atm = 760 mmHg = 760 torr
b. Pascal (Pa) = Newtons/meter2 (Pa = N/m2)
1 standard atmosphere = 101,325 Pa
C. The Gas Laws of Boyle, Charles and Avogadro’s Hypothesis
1. Boyle’ s Law
a. At constant temperature the product of pressure times volume is constant, PV = k
b. P is inversely proportional to V
c. The graph P vs V is hyperbolic
d. Volume increases linearly as the pressure decreases (1/P)
2. At constant temperature, Boyle’s law can be used to find a new volume or a new pressure
PV
1 1 = PV
2 2 or
P1 V2
=
P2 V1
3. Boyle’s law works best at low pressures (ideal gases)
D. Charles’ Law
a. At constant pressure the volume of gas increases linearly with temperature
b. V = bT, V/T = b, V1 / T1= b= V2 / T2 or
V
T
V1 V2
and consequently, 1 = 1
=
V2 T2
T1 T2
c. Temperature is measured in Kelvin, K = oC + 273.15
d. 0 K is “absolute zero”
E. Avogadro’s Hypothesis
1. For a gas at constant temperature and pressure, the volume is directly proportional to the
number of moles, n
2. V = an or V/n = a
F. The Ideal Gas Law
1. From existing laws
V=
k
at constant T and n (Boyle)
P
V = bT at constant P and n (Charles)
V = an at constant T and P (Avogadro)
1
 Tn 
V = ( k )(b)( a )  
 P
2. The constants ( k )(b)( a ) are combined into universal gas constant R and
PV = nRT where R = 0.08206 L atm K-1 mol-1
3. Limitations of the Ideal Gas Law
a) Works well at low pressures and high temperatures
b) Most gases do not behave ideally above 1 atm pressure
c) Does not work well near the condensation conditions of a gas
4. Solving for new volumes, temperatures or pressures while n remains the same
PV PV
PV
PV
1 1
= nR
= 2 2 or 1 1 = 2 2
T1
T2
T1
T2
G. Gas Stoichiometry
1. Standard temperature and pressure (STP): 0oC, 273.15 K and 760 torr, 1 atm
2. Molar Volume: one mole of an ideal gas occupies 22.42 L of volume at STP
3. Molar mass
grams of gas
mass
m
m
and density, d =
= =
molar mass molar mass MM
V
dRT
dRT
and MM =
P=
P
MM
n
=
H. Dalton’s Law of Partial Pressures
1. For a mixture of gases in a container, the total pressure exerted is the sum of the pressures
each gas would exert if it were alone
2. It is the number of moles of particles that is important, not the identity of the composition
of the gas particles
3.
PTOTAL = P1 + P2 + P3 + ... =
n1RT n2 RT n3 RT
 RT
+
+
+ ... = ( n1 + n2 + n3 + ...) 
V
V
V
 V

 RT 
 = nTOTAL 


 V 
4. Mole fraction
a) The ratio of the number of moles of a given component in a mixture to the total number
of moles in the mixture
b) For an ideal gas, the mole fraction,=
x: x1
n1
P1
=
nTOTAL PTOTAL
The Kinetic Molecular Theory of Gases
A. Postulates related to ideal gases
1. The particles are so small compared to the distances between them that the volume of the
individual particles can be assumed to zero
2. The particles are in constant motion. Collision of the particles with the walls of the container
cause pressure
3. Assume that the particles exert no forces on each other
4. The average kinetic energy of a collection of gas particles is assumed to be directly
proportional to the Kelvin temperature of the gas, ( KE ) average =
3
RT
2
2
B. Explaining observed behavior with Kinetic Molecular Theory
1. P and V (T is constant)
a. As V is decreases, P increases:
V decrease causes a decrease in the surface area. Since
P = force/unit area, the decrease in V causes the area to decrease, increasing P
2. P and T (V is constant)
a. As T increase, P increases:
The increase in T causes an increase in the average kinetic energy. Molecules moving
faster collide with the walls of the container more frequently, and with greater force
3. V and T (P is constant)
a. As T increases, V also increases:
Increased T creates more frequent, more forceful collisions. V must increase
proportionally to increase the surface area and maintain P
4. V and n (P and T is constant)
a. As n increases, V must increase
Increasing the number of particles increases the number of collisions. This can be
balanced by an increase in V to maintain constant P.
5. Dalton’s Law of Partial Pressures
a. P is independent of the type of gas molecule
Kinetic Molecular Theory states that particles are independent, and V is assumed to be
zero. The identity of the molecule is therefore unimportant.
C. Root Mean Square Velocity
1. Velocity of a gas is dependent on mass and temperature
2. Velocity of gases is determined as an average, urms =
3RT
where M is the mass of one
M
mole of the gas particles in kg and R = 8.314 J K-1 mol-1 (universal gas constant)
D. Mean Free Path
1. Average distance a molecule travels between collisions
Effusion and Diffusion
A. Effusion
1. Movement of gas through a small opening into an evacuated container (vacuum)
2. Graham’s Law
rate of effusion for gas 1
=
rate of effusion for gas 2
MM 2
where M1 and M2 are the molar masses of gases
MM 1
B. Diffusion
1. The mixing of gases
2. Complicated topic to describe theoretically and mathematically
Real Gases and the van der Waals equation
A. Volume
1. Real gases do have volume
3
2. Volume available is not 100% of the container
n is the number of moles and
b is an empirical constant, determined by experimental results
nRT
We correct volume, V – nb
V
nRT
Real gas: P =
V − nb
Ideal gas: P =
B. Pressure
1. Molecules of real gases do experience attractive forces
2. We correct pressure , by making the observed pressure smaller than it would be if the gas
particles did not interact
 nRT

Pobs =
− correction factor 
( P ' − correction factor) =

 V − nb

2
n
Pobs= P − a   where a is can be determined from observing the actual behavior of the
V 
'
gas.
3. van der Waals Equation
2
nRT
n
=
Pobs
− a   and by rearranging…
V − nb
V 
2

n 
P
+
a
nRT
 obs
   (V − nb ) =
 V  

Chemistry in the Atmosphere
A. Composition of the Troposphere
B. Photochemical Smog – the problem of nitrogen oxides
C. Coal and Acid Rain
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