Gases
http://www.chem.leeds.ac.uk/delights/animations/balloons.html
Gas Characteristics
• Based on the Gases lab, what are some
of the characteristics of gases?
The three states of matter.
The Structure of a Gas
• Gases are composed of particles
•
•
that are flying around very fast
in their container(s)
The particles in straight lines
until they encounter either the
container wall or another
particle, then they bounce off
If you were able to take a
snapshot of the particles in a
gas, you would find that there is
a lot of empty space in there
Gases Pushing
• Gas molecules are constantly in motion
• As they move and strike a surface, they
•
push on that surface
 push = force
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 = force per unit area
5
Gas Variables
• Volume (V) - mL, L, kL…
• Temperature (T) – oC measured in lab
but K (kelvin) for calculations
• Number of particles (n) – moles
• Pressure (P) – mmHg, psi…(more to
come)
The Pressure of a Gas
• Gas pressure is a 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
number of gas particles in a
given volume
volume of the container
average speed of the gas
particles
Measuring Air Pressure
• We measure air
•
•
pressure with a
barometer
Column of mercury
supported by air
pressure
Force of the air on
the surface of the
mercury counter
balances the force of
gravity on the column
of mercury
gravity
Manometer
for this sample, the gas has a
larger pressure than the
atmosphere, so
Common Units of Pressure
Converting Units of Pressure
PROBLEM:
A geochemist heats a limestone (CaCO3) sample and collects
the CO2 released in an evacuated flask attached to a closedend manometer. After the system comes to room
temperature, Dh = 291.4 mm Hg. Calculate the CO2 pressure
in atmospheres, and kilopascals.
Construct conversion factors to find the other units of pressure.
SOLUTION: 291.4 torr
1 atm
760 torr
= 0.3834 atm
0.3834 atm 101.325 kPa
1 atm
= 38.85 kPa
Gas Variable Relationships
• To investigate the relationship between
2 gas variables we need to hold the
other 2 constant.
• Constant P - same # of collisions/unit
area
• Constant V - rigid container
• Constant T – thermostat control
• Constant n – keep container sealed
Gas Variable Relationships
•
•
•
•
P and V
T and V
P and T
n and V
n, T = constant
n, P = constant
n , V = constant
T, P = constant
A molecular description of Boyle’s Law – the relationship
between P and V
The relationship between the volume and pressure of a gas.
PV
1 1 = P2V2
Boyle’s Law
Boyle’s Law Problems
• What is the volume of gas sample at
750 mmHg if its volume is 4.55 L at 900
mmHg?
• A sample of helium has a volume of 560
mL at standard pressure. What is the
pressure if the volume increases to 890
mL?
A molecular description of Charles’s Law – relationship between
temperature and volume
The relationship between the
volume and temperature of a
gas.
Charles’s Law
V2
T2
=
V1
T1
Charles’s Law
Jacques Charles (1746–1823)
• Volume is directly proportional to
temperature
constant P and amount of gas
graph of V vs. T is straight line
• As T increases, V also increases
• Kelvin T = Celsius T + 273
• V = constant x T
if T measured in Kelvin
Charles’ Law Problems
• What is the volume of a gas at 75oC if
its volume is 780 mL at 25oC?
• What temperature is required to change
the volume of a gas to 35 L if its volume
is 25 L at 10oC?
Boyle’s Law
1
V a
VxP
= constant
Charles’s Law
V = constant / P
P and n are fixed
V a T
V
= constant
T
Amontons’s Law
V a
V = constant x T
V and n are fixed
P a T
(Gay-Lusaac’s Law)
P
= constant
T
Combined gas law
n and T are fixed
P
T
P
P = constant x T
V = constant x
PV
P2V2
1 1
=
T1
T2
T
PV
P
T
= constant
Combined Gas Law Problems
• What is the volume of a gas at 60oC and
850 mmHg if its volume is 350 L at
STP?
• A gas has a volume of 765 mL at 40oC
and 1.25 atm. What is the temperature
if the sample has a volume of 900 mL
with a pressure of 900 mmHg?
An experiment to study the relationship between the
volume and amount of a gas.
V a n or V = constant x n
Equal volumes of gas under the same conditions contain equal number of
particles. If two gases are at the same conditions you can use volumes in
stoichiometric calculations in place of moles.
IDEAL GAS LAW
fixed n and T
Boyle’s Law
V=
constant
P
fixed n and P
fixed P and T
Charles’s Law
Avogadro’s Law
V=
constant X T
V=
constant X n
PV = nRT
R=
PV
nT
=
1atm x 22.414L
1mol x 273.15K
=
0.0821atm*L
mol*K
R is the universal gas constant
Standard Conditions
• Because the volume of a gas varies with
pressure and temperature, chemists have
agreed on a set of conditions to report our
measurements so that comparison is easy –
we call these standard conditions
– STP
• Standard pressure = 1 atm
• Standard temperature = 273 K (0 °C)
Standard molar volume.
The Density of a Gas from the Ideal Gas Law
density = m/V
where m = mass
n = m/MM
PV = nRT
PV = (m/MM)RT
m/V = MM x P/ RT
•The density of a gas is directly proportional to its molar mass.
•The density of a gas is inversely proportional to the temperature.
Molar mass of a gas
PV = nRT
m
PV =
RT
MM
m RT
MM =
PV
Mixtures of Gases
• When gases are mixed together, their molecules behave
independent of each other
– all the gases in the mixture have the same volume
• all completely fill the container  each gas’s volume = the
volume of the container
– all gases in the mixture are at the same temperature
• therefore they have the same average kinetic energy
• Therefore, in certain applications, the mixture can be
thought of as one gas
– even though air is a mixture, we can measure the pressure,
volume, and temperature of air as if it were a pure
substance
– we can calculate the total moles of molecules in an air
sample, knowing P, V, and T, even though they are different
molecules
Mixtures of Gases
•Gases mix homogeneously in any proportions.
•Each gas in a mixture behaves as if it were the
only gas present.
Dalton’s Law of Partial Pressures
Ptotal = P1 + P2 + P3 + ...
Why do we need to know this?
A molecular description of Dalton’s law of partial pressures.
Exchange of O2 and CO2
depends on their partial
pressure differences
across membranes.
Collecting Gas by Water
Displacement
Vapor Pressure of Water
Summary of the stoichiometric relationships among the
amount (mol,n) of gaseous reactant or product and the gas
variables pressure (P), volume (V), and temperature (T).
P,V,T
of gas A
ideal
gas
law
amount
(mol)
amount
(mol)
P,V,T
of gas A
of gas B
of gas B
molar ratio from
balanced equation
ideal
gas
law
Stoichiometric Gas Problem
• How many L of CO2 gas at 25oC and 880
mmHg are formed when 15.9 g of
gasoline (C8H18) are combusted?
• How many L of O2 at 20oC and 0.95 atm
are required to generate 250 mL of CO2
at 1.05 atm and 40oC when gasoline
burns?
Kinetic Molecular Theory
(KMT) of Gases
• KMT is a model to explain the behavior
of gaseous particles and is based on
extensive observations of the behavior
of gases.
• If a gas follows all the postulates of the
the KMT it is said to be an ideal gas.
Postulates of the KMT
• Particles are in constant, random,
straight line motion. Collisions with
walls of their container generate
pressure.
• The actual volume of gas particles is
negligible. Particles are far apart. The
volume of a gas is effectively the
volume the particles occupy, not their
particle volume.
Postulates of the KMT
• Gas particles do not attract or repel.
• The average kinetic energy of a
collection of gas particles is directly
proportional to the Kelvin temperature
of the gas.
Diffusion of a gas particle through a
space filled with other particles.
distribution of molecular speeds
mean free path
collision
frequency
Gas Effusion
Movement of a gas through a small opening
What factors affect the effusion of a gas?
Distribution of molecular speeds at three temperatures.
Relationship between molar mass and molecular speed.
Graham’s Law of Effusion
The rate of effusion of a gas is inversely related to the square root of its
molar mass.
1
rate of effusion a
√MM
Ideal vs Real Gases
• How do gas volumes respond under a range of
conditions (such as changing pressures and
temperatures)?
• If a gas is ideal, the graph of PV/RT vs P for
one mole of gas will have a slope of 1.
• http://intro.chem.okstate.edu/1314F97/Chap
ter10/RealGas.html
Deviations from Ideality
• For an ideal gas:
•
PV = nRT or V = nRT/P
• When you actually measure gas
volume at high pressures and low
temperatures, the Vexperimental often
does not match Vtheoretical
Deviations from Ideality
• Why doesn’t Vexp = Vtheor ?
• If Vexp > Vtheor:
• Some gas particles do repel each
other so volume is greater than
predicted.
• Gas particles do have a volume so
volume cannot be reduced beyond a
certain point.
Deviations from Ideality
• Why doesn’t Vexp = Vtheor ?
• If Vexp < Vtheor:
• Some gas particles do attract each
other so volume is reduced more than
expected.
Corrections for Deviations
from Ideality
• Johannes van der Waals modified the ideal
gas law to account for deviations.
•
P
x V = nRT
• [Pexp + a(n/V)2] x (V-nb) = nRT
[Pexp + a(n/V)2] corrects for attractive or
repulsive forces (“a” depends on the
particle)
• V-nb corrects for particle volume (“b” is a
measure of particle volume)
•
Selected Values for a and b for the van der Waals
Equation
Gas
Formula
a [(L2 · atm)/mole2]
b [L/mole]
Helium
He
0.03412
0.02370
Hydrogen
H2
0.2444
0.02661
Nitrogen
N2
1.390
0.03913
Oxygen
O2
1.360
0.03183
Carbon dioxide
CO2
3.592
0.04267
Acetylene
C2H2
4.390
0.05136
Chlorine
Cl2
6.493
0.05622
n - Butane
C4H10
14.47
0.1226
n - Octane
C8H18
37.32
0.2368