Chapter 5 : Gases
Concept of Pressure
Outline
Pressure =
1)Pressure
Force
Area
2)The Simple Gas Laws
3)The Ideal Gas Law
50 Lb
4)Applications of the Gas Law
5)Mixtures of Gases
50 L
b
6)Gases in Chemical Reactions
7)“Real” Gases
Pressure
Gases Pushing
„
„
The Pressure of a Gas
„
gas molecules are constantly in
motion
as they move and strike a surface,
they push on that surface
„
„
if we could measure the total
amount of force exerted by gas
molecules hitting the entire surface
at any one instant, we would know
the pressure the gas is exerting
Pressure
result of the constant
movement of the gas
molecules and their
collisions with the surfaces
around them
the pressure of a gas
depends on several factors
Pressure
1
Measuring Pressure
Barometric pressure is the
pressure of the atmosphere.
It’s difficult to measure the total force exerted by a gas.
Need an indirect method to measure gas pressure.
Measuring the
pressure of a liquid is
much easier.
A = π r2
P=
d=
m
V
F
A
Usually, the liquid is mercury.
h
V = hπ r
2
A device that uses the height of a
liquid to measure the barometric
pressure is called a barometer.
The pressure exerted by 760 mm of mercury (mmHg)
is called a standard atmosphere (atm).
The pressure of a liquid is
proportional to its height
Pressure
Pressure
Units of Pressure
Why use Mercury ?
Lots of different units to measure pressure.
P = h× g ×d
Knowing that the density of mercury is 13.6 g/cm3, calculate
the height of a column of water (d = 1.00 g/cm3) that exerts the
same pressure as a 76.0 cm high column of Hg.
P = 0.760000m × 9.80665ms −2 × 13595.1kgm −3
P = 1.01325 x 105 kgm −1s −2
= N m-2 = Pa
If the pressure doubled, what would be the new height of the
column of water ?
Pressure
Pressure
2
Manometers
Example
Barometers are great for measuring the atmospheric
(barometric) pressure. Not nearly so helpful for
measuring the pressure of other gas pressures.
Pressure
The manometer pictured to the
left is filled with Hg (d = 13.6 g
cm-3). The barometric pressure is
748.2 mmHg and the difference
in the mercury heights is 8.6 mm.
What is the gas pressure, Pgas ?
Pressure
The Simple Gas Laws
Pressure, temperature, volume and amount of a
gas are all related. Some simple relationships
were noted very early.
Boyle’s Law
Foraafixed
fixed amount
amountof
of gas
gasat
ataaconstant
constanttemperature,
temperature,gas
gas
For
volume isisinversely
inverselyproportional
proportionalto
to gas
gaspressure.
pressure.
volume
P∝
1
V
OR
PV = a
Simple Gas Laws
Simple Gas Laws
3
Boyle’s Experiment
„
„
added Hg to a J-tube with
air trapped inside
used length of air column
as a measure of volume
Boyle’s Law and Diving
Length of Air
in Column
(in)
48
44
40
36
32
28
24
22
Difference in
Hg Levels
(in)
0.0
2.8
6.2
10.1
15.1
21.2
29.7
35.0
„
since water is denser
than air, for each 10 m
you dive below the
surface, the pressure
on your lungs
increases 1 atm
‰
if your tank
contained air at 1
atm pressure you
would not be
able to inhale it
into your lungs
at 20 m the total
pressure is 3 atm
Simple Gas Laws
Simple Gas Laws
Charles’ Law
Application of Boyle’s Law
For aa fixed
fixed amount
amount of
of gas
gas at
at aa constant
constant
For
pressure, the
the volume
volume is
is directly
directly proportional
proportional to
to
pressure,
the absolute
absolute temperature
temperature (Kelvin
(Kelvin temperature).
temperature).
the
T(K) = T(oC) + 273.15
One wants to determine the volume of the large, irregularly
shaped tank shown above. The tank is initially evacuated (P=0)
and then connected to a 50.0L cylinder of compressed air at a
pressure of 21.5 atm. After filling the tank, the pressure of the
cylinder is reduced to 1.55 atm. What is the tank’s volume ?
Simple Gas Laws
V ∝T
OR
V = bT
Simple Gas Laws
4
A Molecular View
As temperature increases, volume increases.
„
„
Simple Gas Laws
Application of Charles’ Law
Heat the gas…temperature goes up
Simple Gas Laws
the pressure of gas
inside and outside the
balloon are the same
at high temperatures,
the gas molecules are
moving faster, so they
hit the sides of the
balloon harder –
causing the volume to
become larger
Simple Gas Laws
Practice – The temperature inside a balloon
is raised from 25.0°C to 250.0°C. If the
volume of cold air was 10.0 L, what is the
volume of hot air?
Simple Gas Laws
5
The Ideal Gas Equation
Avogadro’s Law
Recall the following relationships ;
Foraafixed
fixed temperature
temperatureand
and pressure,
pressure,the
the volume
volumeof
ofaa
For
gasisisdirectly
directlyproportional
proportionalto
tothe
the amount
amountof
ofgas.
gas.
gas
V ∝n
„
„
OR
V = cn
V∝
1
P
V ∝T
count number of gas
molecules by moles
equal volumes of gases
contain equal numbers of
molecules
Combine all these proportionalities
V ∝n
PV = nRT
V∝
nT
P
V=
R = 0.082057 L atm mol-1 K-1
Simple Gas Laws
The Ideal Gas Equation
The Ideal Gas Equation
Predicting Changes with the I.G.E.
PV
1 1 = n1 RT1
What is an “ideal gas” ?
An “ideal gas” is a hypothetical gas where the gas’ atoms
or molecules have no interaction with each other.
PV = nRT
RnT
P
R = 0.082057 L atm mol-1 K-1
Example :
What is the volume occupied by 1.75 moles of Argon gas
at a pressure of 700 torr and a temperature of 25oC ?
The Ideal Gas Equation
PV
2 2 = n2 RT2
“1” denotes initial conditions
PV
1 1
=R
n1T1
“2” denotes final conditions
PV
2 2
=R
n2T2
PV
PV
1 1
= 2 2
n1T1 n2T2
The Ideal Gas Equation
6
Using the IGE to identify an unknown gas
Old Exam Question:
Carbon monoxide (CO) is a toxic gas that causes rapid
asphyxiation whereas carbon dioxide (CO2) is much less
toxic.
In a particular reaction, a gas is produced that is known to
be either CO or CO2. In an effort to determine the identity
of the gas the following experiment was performed.
A glass vessel weighs 40.1305 g when clean, dry and
completely evacuated. When completely filled with water it
weighs 138.2410 g (density of water = 1.000 g/mL) and it
weighs 40.2402 g when completely filled with the unknown
gas (CO or CO2) at 740.3 mmHg and 24.0oC. What’s the
identity of the gas ?
The Ideal Gas Equation
The Ideal Gas Equation
STP
Molar Volume
Not a band fronted by Scott Weiland…stands for
Standard Temperature and Pressure.
„
Because gas properties depend on temperature
and pressure, when comparing one gas to another
it is important to choose a set of standard
conditions.
solving the ideal gas equation for the volume
of 1 mol of gas at STP gives 22.4 L
‰
‰
„
we call the volume of 1 mole of gas at STP
the molar volume
‰
T = 0oC (273.15K)
6.022 x 1023 molecules of gas
notice: the gas is immaterial
it is important to recognize that one mole of
different gases have different masses, even
though they have the same volume
P = 1 atm (760 mmHg)
The Ideal Gas Equation
Applications of the IGE
7
Gas Densities
General observations….
Density is defined as mass divided by volume ;
m
d=
V
Mass equals molar mass, M, (g/mol) multiplied by
number of moles, n.
d=
Replacing in the I.G.E.,
Mn
V
d=
MP
RT
As the pressure increases, the density of a gas increases.
The higher the molar mass, the larger the density of a gas.
As temperature increases, the density of a gas decreases.
PV = nRT , gives
Applications of the IGE
Which of the following gases would be best suited for a
hot-air balloon ?
Applications of the IGE
Question on Gas Densities
(H2, He, Ar)
Hydrogen is very
light, cheap, but
extremely
flammable.
Argon is extremely
inert, but heavy.
The “average” density of air is 29 g/mol. Which of these
gases is lighter than air (at the same temperature and
pressure) ?
Helium is inert and
light. Much more
expensive than H.
Applications of the IGE
Applications of the IGE
8
Mixtures of Gases
Mixtures of Gases
„
when ideal gases are mixed together, their
molecules behave independent of each other
all the gases in the mixture have the same volume
all gases in the mixture are at the same temperature
‰
‰
„
Therefore the mixture can be thought of as one gas
‰
‰
we can measure the pressure, volume, and temperature of
the mixture as if it were a pure substance
we can calculate the total moles of molecules in a mixture
knowing P, V, and T, even though they are different
molecules
„
the pressure of a single gas in a mixture of gases is
called its partial pressure
Dalton’s Law
Lawof
of Partial
Partial Pressures
Pressuresstates
statesthat
thatthe
thetotal
total
Dalton’s
pressureof
ofaamixture
mixtureof
of gases
gases isisthe
thesum
sumof
ofall
allthe
the partial
partial
pressure
pressuresof
ofthe
the components
componentsof
ofthe
themixture
mixture
pressures
Mixtures of Gases
Rearranging the last equation
Starting with…
Ptotal = Pa + Pb
Mixtures of Gases
Pa =
Dalton’s Law
From the I.G.E.
Ptotal
n RT
= tot
V
na
Ptotal
ntot
The ratio of moles of “a” to the total moles is called the
n RT
Pa = a
V
mole fraction, χa.
The gases are at the same temperature and
volume, so…
Ptotal Pa
=
ntot
na
Mixtures of Gases
Pa = χ a Ptotal
These equations are also valid for more complicated
mixtures of gases.
Mixtures of Gases
9
When working with gas mixtures, the I.G.E. can still be
used but now n refers to the total number of moles.
Example : What’s the total pressure of 78 moles of N2, 21
moles of O2 and 1 mole of Ar, confined to a volume of
100.0L and a temperature of 300K ?
Mixtures of Gases
Mixtures of Gases
Collecting Gases
„
„
„
gases are often collected by having them
displace water from a container
the problem is that since water evaporates, there
is also water vapor in the collected gas
the partial pressure of the water vapor, called the
vapor pressure, depends only on the
temperature
‰
„
so you can use a table to find out the partial pressure of
the water vapor in the gas you collect
if you collect a gas sample with a total pressure
of 758.2 mmHg* at 25°C, the partial pressure of
the water vapor will be 23.78 mmHg – so the
partial pressure of the dry gas will be 734.4
mmHg
‰
Table 5.4*
Mixtures of Gases
Mixtures of Gases
10
Gases in Chemical Reactions
Given the following reaction ;
CO (g)
+
Cl2 (g)
catalyst
COCl2 (g)
Given the following reaction ;
What volume of CO is required to completely react with
25.0 L of Cl2 if both gases are initially at the same
temperature and pressure ?
Δ
NaN3 (s)
2 Na (l)
+
3 N2 (g)
How many grams of sodium azide (NaN3) are needed to
generate 50.0L of N2 at 25.0oC and 800 mmHg ?
What mass of CO is required to completely react with 25.0
L of Cl2 at a temperature of 300oC and a pressure of 1.50
atm ?
Gases in Chemical Reactions
Ideal vs. Real Gases
„
„
Effect of Molecular Volume
Real gases often do not behave like ideal
gases at high pressure or low temperature
Ideal gas laws assume
„
„
„
at low temperatures and high pressures these
assumptions are not valid
Real Gases
at high pressure, the amount of space
occupied by the molecules is a significant
amount of the total volume
the molecular volume makes the real volume
larger than the ideal gas law would predict
Real Gases
11
Effect of Molecular Interactions
„
van der Waals modified the ideal gas
equation to account for the molecular
volume
‰
b is called a van der Waals constant and is
different for every gas because their molecules
are different sizes
nRT
V=
+ nb
P
„
at low temperature, the attractions between the
molecules is significant
„
the intermolecular attractions makes the real pressure
less than the ideal gas law would predict
„
van der Waals modified the ideal gas equation to
account for the intermolecular attractions
‰
a is called a van der Waals constant and is different for
every gas because their molecules are different sizes
P=
Real Gases
nRT
⎛n⎞
− a⎜ ⎟
V
⎝V⎠
2
Real Gases
12