Gases and their
Properties
Goals:
1. Use the gas law equations.
2. Apply the gas laws to stoichiometric calculations.
3. Describe the states of matter based on kineticmolecular theory.
4. Recognize why real gases do not behave like ideal
gases.
THREE STATES OF MATTER
General Properties of Gases
• There is a lot of “free”
space in a gas.
• Gases can be expanded
__________________.
• Gases occupy containers
uniformly and completely.
• Gases diffuse and mix
___________.
Properties of Gases
Gas properties can be
Model depends on—
•
•
•
•
V=
T=
n=
P=
modeled using math.
Pressure
• Pressure – force per unit area (force divided
by the area over which the force is exerted).
SI unit is the pascal (Pa)
Pressure =
Force
Area
SI units – Pascal (Pa)
Newton (N)
1 Pa = 1 N/m2
Square meter (m2)
Newton- the force that will give a 1-kg mass an
acceleration of 1 meter per second (m/s).
Barometer
• Barometer – device to measure atmospheric pressure. Invented in
1643 by Evangelista Torricelli. It is based on a column filled with
mercury (Hg).
• On average, at sea level, the column supported by the air
pressure is 760 mm Hg high – 1 atmosphere (atm).
1 atm = ______ mm Hg = _____ Torr
Why Hg and not H2O?
Pressure Units
1 atm = 760 mm Hg = 760 Torr
SI unit
1 atm = ________Pa (pascal) = ______ kPa (kilopascal)
Units used in weather reports
1 atm = 29.921 inHg (inches of mercury)
= 1013.25 mbar (millibars)
Units used by engineers
1 atm = 14.696 lb/in2 or psi (pounds per square inch)
Gas Laws
Gas law
Equation
Variables
Constant(s)
Boyle’s law
Charles’s law
Avogadro’s law
Combined gas law
Ideal gas law
P- pressure
V- volume
T- temperature
n- number of moles
R- universal gas constant
Boyle’s Law: P-V relationship
• Robert Boyle, 1662 : Boyle’s Law
– For a given amount of gas at a constant temperature,
the volume of the gas varies inversely with its
pressure.
Va1/P
V=a/P
VP = a
a- proportionality
constant
Boyle’s Law: P-V relationship
If V increases P must decrease, and viceversa.
V=a/P
P1
VP = a
P2
V1
V2
• A gas is enclosed in a 10.1 L tank at 1208 mmHg. Which of the following is a
reasonable value for the pressure when the gas is transferred to a 30.0 L
tank?
400 mmHg
3600 mmHg
Boyle’s Law
A bicycle pump is a good example of Boyle’s law.
As the volume of the air trapped in the pump is reduced,
its pressure goes up, and air is forced into the tire.
Boyle’s Law: P-V relationship
• Any units can be used for P and V (same units used
throughout the calculation).
• Same sample of a confined gas at constant T.
V1P1 = V2P2
• A sample of air occupies 73.3 mL at 98.7 atm and 0oC. What volume
will the air occupy at 4.02 atm and 0oC?
Boyle’s Law
Va1/P
Pa1/V
Pa1/V
P=a/V
VP = a
a- proportionality
constant = slope of the line
Charle’s Law: T-V relationship
• Jacques Charles, 1787 : Charles’s Law
– For a given amount of gas at a constant pressure, the volume
of the gas varies directly with its temperature.
– For each oC rise in T, V expands by 1/273 of its V at 0oC;
for each oC drop in T, V contracts by 1/273 of its V at 0oC.
- Volume of a fixed amount of a
gas at a constant P is directly
proportional to its Kelvin T.
V2
VaT
V = bT
V1
T1
-273.15oC
T2
Is the absolute 0 in Kelvin scale
V/T=b
b - proportionality
constant
Charle’s Law: T-V relationship
• If T increases, V must also increase; when T
decreases, V must also decrease.
• For the same sample of trapped gas at a constant
pressure.
• For all gas law calculations involving T, absolute T in
kelvins must be used.
V1
T1
=
V2
T2
0 oC
40 oC
Charle’s Law: T-V relationship
• A sample of oxygen gas occupies a volume of 2.10 L at
25oC. What volume will this sample occupy at 150oC?
(Assume no change in pressure.)
Charle’s Law
Charle’s Law
Practice
• What effect will the following changes have on the V
of a fixed amount of gas?
a. an increase in P at constant T
b. a decrease in T at constant P
c. a decrease in P coupled with an increase in T
• What effect will the following changes have on the P
of a fixed amount of gas?
a. an increase in T at constant V
b. a decrease in V at constant T
c. an increase in T coupled with a decrease in V
Avogadro’s Hypothesis
• Avogadro’s Hypothesis – equal number of molecules of
different gases compared at the same T and P occupy
equal V.
• Avogadro’s Law – at fixed T and P, the V of a gas is
directly proportional to the number of molecules of a gas
or to the number of moles of gas, n.
– If the number of moles of gas doubles, the volume doubles.
– If the mass of a gas doubles, the volume doubles.
Van
V = cn
Avogadro’s Hypothesis
The gases in this experiment are all
measured at the same T and P.
2 H2(g) + O2(g)
2 H2O(g)
Molar Volume
•
Molar Volume of a gas – is the volume occupied at
STP by 1 mol of any gas and it is 22.4 L .
Standard conditions of T and P (STP):
T = 0oC (273K)
P = 1 atm (760 Torr)
1 mol gas = 22.4 L (at STP)
Molar Volume
1 mol gas = 22.4 L (at STP)
1 mol of N2 = 28 g N2, will occupy 22.4 L at STP.
1 mol of CO2 = 44 g CO2, will occupy 22.4 L at STP.
Calculate the volume occupied by 4.11 g of methane
(CH4) gas at STP.
Strategy: Convert mass of gas to moles of gas and use the molar volume
relationship as conversion factor to find out the volume at STP.
Practice
• Solve the Charle’s Law for T2
Students should be familiar rearranging gas
laws equations and applying them in problems.
Gas Laws
Gas law
Equation
Boyle’s law
Charles’s law
Avogadro’s law
Variables
Constant(s)
P1V1 = P2V2
P, V
n, T
V1 / T1 = V2 / T2
V, T
n, P
V1 / n1 = V2 / n2
V, n
P, T
Combined gas law
Ideal gas law
P- pressure
V- volume
T- temperature
n- number of moles
R- universal gas constant
Combined Gas Law
V proportional to 1/P
V proportional to T
V proportional to n
V1
T1
V1P1 = V2P2
• Therefore, V prop. to nT/P
• A fixed amount of gas under a
set of initial conditions is
changed to a set of final
conditions.
V a nT
P
PV = constant
nT
V1P1
T1
=
V2P2
T2
PV = nRT
=
V2
T2
What volume will occupy a 5 mL bubble of air exhaled by
a deep-sea diver at 1.8 atm and at 5oC when it reaches
the surface of the sea, at 0.98 atm and at 25oC?
Ideal Gas Law
• For varying amounts of gas (number of moles, n).
• Units:
P in atmospheres (atm)
V in liters (L)
T in kelvins (K)
PV = nRT
• Universal gas constant, R
L atm
R = 0.0821 mol K
• Used to calculate any of the four quantities – P, V, n
or T if the other three are known.
How much N2 (in Kg) is req’d to fill a small room with a volume
of 960 cubic feet (27,000 L) to P = 745 mm Hg at 25 oC?
Gas Density
• Reported in g/L at STP.
• If you know the density, you can calculate the
molar volume.
1 mol gas = 22.4 L (at STP)
• From the molar volume of gas, you can calculate
the density of the gas using the molar mass.
Gas Density
• Density is proportional to
molecular mass.
Which balloon(s) is(are) filled with the higher density gas?
The density of air at 15 oC and 1.00 atm is
1.23 g/L. What is the molar mass of air?
Dalton’s Law
• Dalton’s experimental observation – adding H2O vapor
to a certain pressure to dry air, the P exerted by the
air would increase by an amount equal to the P of the
water vapor.
• Dalton’s conclusion – each gas in a mixture of gases
behaves independently, exerting its own pressure.
• Dalton’s Law – The total P of the mixture is equal to
the sum of the partial pressures exerted by separate
gases.
Ptotal = P1 + P2 + P3 + ….
Dalton’s Law
Vapor Pressure
• Vapor pressure – is the partial pressure exerted by
the molecules of a substance in the gas phase above
the liquid phase of the substance.
• Vapor pressure is T dependent (increasing T, increase
the vapor pressure).
For water:
T (oC)
0
10
20
30
40
50
60
70
80
90
100
Vapor pressure (mmHg)
5
9
18
32
55
93
149
234
355
526
760
Oxygen is collected over water at 20oC. The total P
inside the collection jar is 740 mmHg. What is the
pressure due to the oxygen alone?
Partial Pressures and Respiration
• Exchange of gases (CO2 and O2) between:
alveoli and blood capillaries;
arteriole and extracellular fluid;
extracellular fluid and cells occurs by
diffusion.
• Gases go from higher partial pressure to
lower partial pressure.
• Diffusion – the flow of a substance from a
region of higher concentration to a region
of lower concentration.
• CO2 is the trigger; if too high we take a
breath, if too low, there is no breathing.
Gases and Stoichiometry
2 H2O2(liq) ---> 2 H2O(g) + O2(g)
1.1 g of H2O2 decompose in a flask with a volume of 2.50 L.
What is the pressure of O2 at 25 oC? Of H2O?
2 H2O2(liq) ---> 2 H2O(g) + O2(g)
Decompose 1.1 g of H2O2 in a flask with a volume of 2.50
L. What is the pressure of O2 at 25 oC? Of H2O?
Kinetic-Molecular Theory
Theory used to explain gas laws. KMT
assumptions are
• Gases consist of _____________________
__________________________.
• P arises from _______________________.
• No __________ or __________ forces
between molecules. Collisions elastic.
• Volume of molecules is ____________.
Kinetic-Molecular Theory
Because we assume molecules are in motion,
they have a kinetic energy.
KE = (1/2)(mass)(speed)2
At the same T, all gases have the same
average KE.
As T goes up for a gas, KE also
increases — and so does speed.
Kinetic-Molecular Theory
At the same T, all gases have the same average KE.
As T goes up, KE also increases — and so does speed.
Maxwell’s equation
u2
3RT
M
root mean square speed
where u is the speed and M is the molar mass.
– speed INCREASES with T
– speed DECREASES with M
Speed’s Distribution
• Boltzmann plots
• Named for Ludwig
Boltzmann doubted
the existence of
atoms.
• This played a role
in his suicide in
1906.
Velocity of Gas Molecules
Molecules of a given gas have a range of
speeds.
Average velocity
decreases with
increasing mass.
Gas Diffusion and Effusion
DIFFUSION is the gradual mixing of molecules
of different gases.
EFFUSION is the movement of molecules
through a small hole into an empty container.
Gas Effusion
Molecules effuse thru holes in a
rubber balloon, for example, at
a rate (= moles/time) that is
• proportional to T
• inversely proportional to M.
Therefore, He effuses more
rapidly than O2 at same T.
Graham’s Law
Rate for A
Rate for B
M of B
M of A
• Rate of effusion is inversely
proportional to its molar
mass.
– HCl and NH3 diffuse from
opposite ends of tube.
– Gases meet to form NH4Cl
– HCl heavier than NH3
– Therefore, NH4Cl forms closer
to HCl end of tube.
Kinetic-Molecular Theory
Model used to explain de behavior of gases. Postulates:
1. All matter is composed of tiny, discrete particles called molecules (N2, Ar).
2. The molecules are in rapid, constant motion and move in straight lines (strike
the walls of the container, exert pressure).
3. The molecules of a gas are small compared with the distances between them
(low density, compressibility).
4. There is little attraction between molecules of a gas.
5. Molecules collide with one another, and energy is conserved in these
collisions (elastic- the sum of the kinetic energies before and after collision
is equal).
6. Temperature is a measure of the average kinetic energy of the gas
molecules (on average, the particles of a cold sample move more slowly than
the particles of a hot sample).
Deviations from Ideal Gas Law
• Real molecules have volume.
• There are
intermolecular forces.
– Otherwise a gas could not become a liquid.
Account for volume of molecules and
intermolecular forces with VAN DER
WAALS’s EQUATION.
Van Der Waals’s Equation
P V = n R T
Measured V = V(ideal)
Measured P
(
P
2
n a
+ ----2
V
)
V
-
nb
nRT
vol. correction
intermol. forces
Cl2 gas has a = 6.49, b = 0.0562
For 8.0 mol Cl2 in a 4.0 L tank at 27 oC.
P (ideal) = nRT/V = 49.3 atm
P (van der Waals) = 29.5 atm
Deviations from Ideal Gas Law
• PV = nRT
• PV = constant
y = mx + b
m = slope
correction to Volume
m = -1.5
Vc = V – m
Vc = 20 + 1.5 =
21.5 mL
PV
P
Remember
• Go over all the contents of your textbook.
• Practice with examples and with problems at
the end of the chapter.
• Practice with OWL tutor.
• Work on your OWL assignment for Chapter
12.
• Practice with the quiz on CD of Chemistry
Now.