Chapter 10: Gases
Characteristics of gases
Generally composed of nonmetallic
elements; e.g., HCN, CO2, CH4, SO2
Simple molecular formulas; low
molar mass
Highly compressible
Form homogeneous
mixtures regardless of the
identities or proportions of
the component gases
The characteristic properties
of gases arise because the
individual gas molecules are
far apart from one another
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What measurable variables are required to define the
state of a gas?
We will consider P, V, T, and n
Why choose these variables?
Pressure
F
, or the force
A
F which acts on a given area, A
Defined by P 
Units of pressure
SI:
1 Pa = 1 N/m2 ( 1 N = 1 kg-m/s2)
1 atm = 1.01325 x 105 Pa
non-SI: 1 torr = 1 mm Hg
1 atm = 760 mm Hg
How do we measure pressure?
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Hg barometer: used to measure atmospheric pressure
Standard atmospheric pressure: pressure necessary to
support a column of Hg 760 mm in height, typically at sea
level
hence, 1 atm = 760 mm Hg
How to measure the pressure of an enclosed gas? (i.e.,
gas in a flask)
manometer (open or closed-type)
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Gas Laws
We have chosen P, V, T, and n to describe the state of a
gas
How are these quantities related mathematically?
Pressure-volume relationship: Boyle's Law
Volume of a fixed quantity of a gas at constant
temperature is inversely proportional to pressure
i.e., P 
1
(constant n, T)
V
Or P 
c
(constant n and T)
V
Or PV=c (constant n,T)
Boyle's law in graphical form: plot P vs V
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Temperature-Volume relationship: Charles's Law
Volume of a fixed quantity of a gas at constant pressure is
directly proportional to absolute temperature
V  T (constant n, P)
Or
V = cT (constant n, P)
graphically,
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Quantity - Volume relationship: Avogadro's law
Volume of a gas at constant temperature and pressure is
directly proportional to n
V  n (constant T, P) or
V  cn (constant T, P)
How can we combine Boyle's, Charles's, and Avogadro's
laws to obtain a general relation between P, V, T, and n?
The ideal gas law
Recall
Boyle:
V  1/ P, constant n, T
Charles:
V  T, constant n, P
Avogadro:
V  n, constant P,T
Combine these results:
V
ncT
P
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Let the proportionality constant = R; then,
PV = nRT
This is the ideal gas law
Ideal gas: gas whose P,V,T behavior is described by the
ideal gas law
Note that R = gas constant
Value & units of R depend on the units of P, V, n, T
T always expressed in K
quantity, n : moles
P : usually atm
V : usually in liters
Numerical values of R:
R  0.08206
R  8.314
liter atm
mol K
joule
(SI units)
mol K
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What is the volume of 1.000 mol of an ideal gas at 273.15 K
and 1.000 atm?
273.15 K (0o C) and 1.00 atm are referred to as standard
temperature & pressure (STP)
V for 1 mol of an ideal gas at STP is known as the molar
volume of an ideal gas at STP
Sample calculations
E.g., At 37oC and 740 mm Hg, an ideal gas occupies a
volume of 1.05 L. How many gas molecules are in the
sample?
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E.g., At what temperature would 0.270 mol of an ideal gas
occupy a volume of 15.0 L at 2.54 atm?
Now, consider a process carried out involving a fixed
quantity of an ideal gas
A fixed quantity of an ideal gas confined to a cylinder
fitted with a movable piston is a nice way to think about
this, e.g.
Let the initial state of the n mol of gas be given by P1, T1,
V1
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Since n = constant, the ideal gas law gives
PV
 nR = constant
T
1
1
1
Now, move the piston up or down - take the system from
P1, T1, V1 to P2, V2, T2
Since the quantity of gas is fixed, n does not change
during the process, and
PV P V

T
T
1
1
1
2
2
2
This is known as the combined gas law
What happens to this relation:
At constant P?
At constant T?
At constant V?
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E.g., at 36oC and 1.00 atm, a gas occupies a volume of
0.600 L. How many liters will it occupy at 0oC and 0.205
atm?
130
Problems du Jour
Assume that you have a cylinder with a movable piston.
What would happen to the gas pressure inside the
cylinder if you:
(a) Decrease the volume to one-third the original volume
at constant T
(b) Reduce the Kelvin temperature to half the original
value at constant V
(c) Reduce the amount of gas to half while keeping the
volume and temperature constant
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