Chapter 5 Gases
Chapter 5 Gases
Chapter 5 Gases
Chapter 5
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Elements that exist as gases at 250C and 1 atmosphere
5.1
5.1
Physical Characteristics of Gases
• Gases assume the volume and shape of their containers.
• Gases are the most compressible state of matter.
• Gases will mix evenly and completely when confined to
the same container.
• Gases have much lower densities than liquids and solids.
5.1
Force
Pressure = Area
(force = mass x acceleration)
Units of Pressure
1 pascal (Pa) = 1 N/m2
1 atm = 760 mmHg = 760 torr
1 atm = 101,325 Pa
Barometer
5.2
10 miles 0.2 atm
5.2
Manometers Used to Measure Gas Pressures
5.2
Apparatus for Studying the Relationship Between
Pressure and Volume of a Gas
P 1/V
P x V = constant Constant temperature
Constant amount of gas
P1 x V1 = P2 x V2
5.3
A sample of chlorine gas occupies a volume of 946 mL
at a pressure of 726 mmHg. What is the pressure of
the gas (in mmHg) if the volume is reduced at constant
temperature to 154 mL?
P x V = constant
P1 x V1 = P2 x V2
P1 = 726 mmHg P2 = ?
V1 = 946 mL V2 = 154 mL
Charles’ &
Gay-Lussac’s
Law
V1 /T1 = V2 /T2
V1 = 3.20 L V2 = 1.54 L
T1 = 398.15 K T2 = ?
T1 = 125 (0C) + 273.15 (K) = 398.15 K
V2 x T1 1.54 L x 398.15 K
T2 = = = 192 K
V1 3.20 L
5.3
Avogadro’s Law
V number of moles (n)
Constant temperature
V = constant x n Constant pressure
V1 / n1 = V2 / n2
5.3
Ammonia burns in oxygen to form nitric oxide (NO) and
water vapor. How many volumes of NO are obtained
from one volume of ammonia at the same temperature
and pressure?
At constant T and P
5.3
5.3
5.3
5.3
Ideal Gas Equation
1
Boyle’s law: V (at constant n and T)
P
Charles’ law: V T(at constant n and P)
Avogadro’s law: V n(at constant P and T)
nT
V
P
nT nT
V = constant x =R R is the gas constant
P P
PV = nRT
5.4
The conditions 0 0C and 1 atm are called standard
temperature and pressure (STP).
Experiments show that at STP, 1 mole of an ideal
gas occupies 22.414 L.
PV = nRT
PV (1 atm)(22.414L)
R= =
nT (1 mol)(273.15 K)
5.4
What is the volume (in liters) occupied by 49.8 g of HCl
at STP?
T = 0 0C = 273.15 K
P = 1 atm
PV = nRT
1 mol HCl
nRT n = 49.8 g x = 1.37 mol
V= 36.45 g HCl
P
L•atm
1.37 mol x 0.0821 mol•K
x 273.15 K
V=
1 atm
V = 30.6 L
5.4
Argon is an inert gas used in lightbulbs to retard the
vaporization of the filament. A certain lightbulb
containing argon at 1.20 atm and 18 0C is heated to
85 0C at constant volume. What is the final pressure of
argon in the lightbulb (in atm)?
5.4
Density (d) Calculations
dRT
M= d is the density of the gas in g/L
P
5.4
A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm
and 27.0 0C. What is the molar mass of the gas?
dRT m 4.65 g g
M= d= = = 2.21
P V 2.10 L L
g L•atm
2.21 x 0.0821 mol•K
x 300.15 K
L
M=
1 atm
M = 54.6 g/mol
5.4
Gas Stoichiometry
L•atm
0.187 mol x 0.0821 x 310.15 K
nRT mol•K
V= = = 4.76 L
P 1.00 atm
5.5
Dalton’s Law of Partial Pressures
V and T
are
constant
P1 P2 Ptotal = P1 + P2
5.6
Consider a case in which two gases, A and B, are in a
container of volume V.
nART
PA = nA is the number of moles of A
V
nBRT nB is the number of moles of B
PB =
V
nA nB
PT = PA + PB XA = XB =
nA + nB n A + nB
PA = XA PT PB = XB PT
ni
Pi = Xi PT mole fraction (Xi) =
nT
5.6
A sample of natural gas contains 8.24 moles of CH4,
0.421 moles of C2H6, and 0.116 moles of C3H8. If the
total pressure of the gases is 1.37 atm, what is the
partial pressure of propane (C3H8)?
Pi = Xi PT PT = 1.37 atm
0.116
Xpropane = = 0.0132
8.24 + 0.421 + 0.116
5.6
Bottle full of oxygen
gas and water vapor
PT = PO2 + PH 2O
5.6
5.6
Chemistry in Action:
Scuba Diving and the Gas Laws
Depth (ft) Pressure
(atm)
0 1
33 2
66 3
P V
5.6
Kinetic Molecular Theory of Gases
1. A gas is composed of molecules that are separated from
each other by distances far greater than their own
dimensions. The molecules can be considered to be points;
that is, they possess mass but have negligible volume.
2. Gas molecules are in constant motion in random directions,
and they frequently collide with one another. Collisions
among molecules are perfectly elastic.
3. Gas molecules exert neither attractive nor repulsive forces
on one another.
4. The average kinetic energy of the molecules is proportional
to the temperature of the gas in kelvins. Any two gases at
the same temperature will have the same average kinetic
energy
KE = ½ mu2
5.7
Kinetic theory of gases and …
• Compressibility of Gases
• Boyle’s Law
P collision rate with wall
Collision rate number density
Number density 1/V
P 1/V
• Charles’ Law
P collision rate with wall
Collision rate average kinetic energy of gas molecules
Average kinetic energy T
PT
5.7
Kinetic theory of gases and …
• Avogadro’s Law
P collision rate with wall
Collision rate number density
Number density n
Pn
• Dalton’s Law of Partial Pressures
Molecules do not attract or repel one another
P exerted by one type of molecule is unaffected by the
presence of another gas
Ptotal = Pi
5.7
Apparatus for studying molecular speed distribution
5.7
The distribution of speeds
of three different gases
at the same temperature
urms = 3RT
M
5.7
Chemistry in Action: Super Cold Atoms
Gaseous Rb Atoms
1.7 x 10-7 K
Bose-Einstein Condensate
Gas diffusion is the gradual mixing of molecules of one gas
with molecules of another by virtue of their kinetic properties.
r1 M2
=
r2 M1
NH4Cl
NH3 HCl
17 g/mol 36 g/mol
5.7
Gas effusion is the is the process by which gas under
pressure escapes from one compartment of a container to
another by passing through a small opening.
r1 t2 M2
= =
r2 t1 M1
5.8
Effect of intermolecular forces on the pressure exerted by a gas.
5.8
Van der Waals equation
nonideal gas
an
( P + V2 ) (V – nb) = nRT
2
}
}
corrected corrected
pressure volume
5.8