Gas Laws
Characteristics of Gases
• Gases can be:
– Monatomic (noble gases)
– Diatomic (N2, Cl2, H2, O2, F2)
– Molecular compounds (ie CO, SO2, CH4, etc)
Low molar
mass
• Unlike liquids and solids, gases
– expand to fill their containers
•
So volume of container = volume of gas it is holding
– are highly compressible
– always form homogeneous mixtures with each other
– have extremely low densities
•
•
•
because individual molecules are far apart.
Thus each molecule behaves as though it were alone.
So all gases have similar physical properties, regardless of what
molecules they are made of.
2
Pressure
• Pressure is the
amount of force
applied to an area.
F
P=
A
• Atmospheric
pressure is the
weight of air per unit
of area.
Atmospheric pressure – air presses on
earth due to gravity
3
Units of Pressure
• Pascal (SI unit for pressure)
1 Pa = 1 N/m2
• N (newton) is a unit of force
• 1 N = 1 kg-m/s2
Memorize. All other
conversion factors
involving pressure will be
given to you
1000 Pa = 1 kPa
• Bar
1 bar = 105 Pa
4
Units of Pressure
• mm Hg or torr
1 mm Hg = 1 torr
These units are determined
by measuring the height (h),
measured in mm, of a
column of mercury
• Atmosphere (atm)
1.00 atm = 760 torr = 101,325 Pa
5
Standard Pressure
• Normal atmospheric pressure at sea level is
referred to as standard pressure.
• It is equal to 1.00 atm
6
Manometer
This device is used to
measure the difference in
pressure between
atmospheric pressure and
that of a gas in a vessel.
7
Examples
1. Convert 958 torr to atmospheres.
2. Convert 1.45 kPa to torr.
1.26 atm
10.9 torr
8
The Gas Laws
• We need four variables to define the physical
conditions, or state, of a gas:
Temperature (T)
Pressure (P)
Volume (V)
Amount of gas (usually in moles, n)
• We can study the effects of two variables at a
time by holding the others constant
9
The Gas Laws
• We need four variables to define the physical
conditions, or state, of a gas:
Temperature (T)
Pressure (P)
Volume (V)
Amount of gas (usually in moles, n)
• We can study the effects of two variables at a
time by holding the others constant
10
Boyle’s Law
• Constants:
– Amount of gas
– Temperature
• Variables:
– Pressure
– Volume
The pressure of the gas was
doubled by adding more
mercury, and the volume
decreased by half.
The volume of a fixed quantity of gas at constant
temperature is inversely proportional to the pressure.
11
Boyle’s Law
P and V are
inversely proportional
PV = k
(k is a constant)
Rearranging,
V = k (1/P)
This means a plot of V versus 1/P
will be a straight line.
We can use Boyle’s Law to predict the outcome in a change in
pressure and volume:
P1V1 = P2V2
12
Charles’s Law
• Constants:
– Amount of gas
– Pressure
• Variables:
– Temperature
– Volume
The volume of a fixed amount of gas at constant pressure is
directly proportional to its absolute temperature.
V
=k
T
So a plot of V versus T will be a straight line.
We can use Charles’s Law to predict the outcome in a change in
temperature and volume:
V
V
1
2
T1 = T2
13
Avogadro’s Law
• Constants:
– Temperature
– Pressure
• Variables:
– Amount of gas
– Volume
• The volume of a gas at constant
temperature and pressure is directly
proportional to the number of moles
of the gas.
• Mathematically, this means,
V1
V2
• So,
=
n1
n2
V
=k
n
14
Example
A fixed quantity of gas at 21 °C exhibits a pressure of 752 torr and
occupies a volume of 4.38 L.
A) Calculate the volume the gas will occupy if the pressure is increased to
1.88 atm and the temperature is held constant. Name which gas law you
used to determine this.
2.31 L, Boyle’s law
B) Calculate the volume the gas will occupy if the temperature is increased
to 175 °C while the pressure is constant. Name which gas law you used to
determine this.
L, Charles’s law
15
Ideal-Gas Equation
• So far we’ve seen that
V  1/P (Boyle’s law)
V  T (Charles’s law)
V  n (Avogadro’s law)
• Combining these, we get
nT
V
P
16
Ideal-Gas Equation
• The constant of
proportionality is known as
R, the gas constant.
• When working gas law
problems, the units of all
variables must agree with
the units of R.
– Temperature must always be
expressed in kelvin
– n is expressed in moles
– Volume is most often expressed in
liters
– Pressure is most often expressed in
atm
This is the one we
almost always use.
This one will be
given to you on the
17
exam.
Ideal-Gas Equation
The relationship
then becomes
or
nT
V
P
nT
V=R
P
PV = nRT
• This is the ideal-gas equation
- ideal gas – a hypothetical gas whose pressure,
volume, and temperature behavior are described
completely by the ideal-gas equation
18
Ideal-Gas Equation
Standard temperature and pressure (STP) – the conditions
0 °C and 1 atm
What is the volume of 1.000 mol of an ideal gas at STP?
PV = nRT
V = nRT/P
V = (1.000 mol)(0.08206 L-atm/mol-K)(273.15 K)
1.000 atm
V = 22.41 L
This is known as the molar volume of an ideal gas at STP.
19
Ideal-Gas Equation
We commonly face situations where P, V, and T all change
but n remains constant.
PV = nRT
PV/T = nR = constant
So,
P1V1
P2V2
=
T1
T2
Sometimes called the combined gas law
20
Examples
Calculate the following quantities (R = 0.08206 L-atm/mol-K):
a) The volume of the gas in liters if 1.50 mol has a pressure of 0.985 atm a
temperature of -6 °C
b)
The absolute temperature of the gas at which 3.33 x 10-3 mol occupies 325
mL at 750. torr
c)
The pressure in atmospheres if 0.0467 mol occupies 413 mL at 138 °C
d)
The quantity of gas in moles if 55.7 L at 54 °C has a pressure of 11.25 kPa
21
Examples
Calculate the following quantities (R = 0.08206 L-atm/mol-K):
a) The volume of the gas in liters if 1.50 mol has a pressure of 0.985 atm a
(33.4 L)
temperature of -6 °C
b)
The absolute temperature of the gas at which 3.33 x 10-3 mol occupies 325
(1170 K)
mL at 750. torr
c)
The pressure in atmospheres if 0.0467 mol occupies 413 mL at 138 °C
(3.81 atm)
d)
The quantity of gas in moles if 55.7 L at 54 °C has a pressure of 11.25 kPa
(0.230 mol)
22
What if we have a mixture of gases?
• Dalton’s Law of Partial Pressures
– The total pressure (Ptotal) of a mixture of gases
equals the sum of the pressures that each
would exert if it were present alone.
Ptotal = P1 + P2 + P3 + …
• Partial pressure – the pressure exerted by a
particular component of the mixture of gases
• Symbolized Px, where subscript x indicates the gas that exerted
that pressure
• Px = nxRT/V
23