9 Chapter Gases
Lecture 20
(CHEM 1010) March 31
Agenda: Ideal Gas Law
Applying the Ideal Gas Law
Daltons Law of Partial Pressures
Kinetic Molecular Theory of Gases
Grahams Law (Diffusion and Effusion
world gas
Real
Ideal Gas Law
Pressure
1 atm = 760 mmHg = 1 torr = 101.325 kPa
Boyles Law
V inversely proportional to P
Charles Law
V directly proportional to T
Avogadros Law
Ideal Gas Law PV = nRT
R can be
V directly proportional to n
8.314 J/(K mol) or 8.314 kg m2/(s2 K mol)
0.08206 L atm/(K mol)
Problem 9.68 challenge
Pure oxygen gas was first prepared by heating mercury
(II) oxide, HgO:
2HgO(s) 2Hg (l) + O2(g)
What volume (in liters) of oxygen at STP is released by
heating 10.57 g of HgO?
Problem 9.69 challenge
How many grams of HgO would you need to heat if you
wanted to prepare 0.0155 mol of O2 according to
2HgO(s) 2Hg (l) + O2(g).
Gas Laws and Chemical Reactions
Challenge
9.12 5th
Propane gas (C3H8) is used as fuel in rural areas. How many
liters of CO2 are formed at STP by the complete combustion
of the propane in a container with a volume of 15.0L and a
pressure of 4.5 atm at 25C. The unbalance equation is
C3H8(g) + O2(g) CO2(g) + H2O(l)
Gas Laws and Chemical Reactions
Challenge
9.12 5th
Propane gas (C3H8) is used as fuel in rural areas. How many liters of CO2
are formed at STP by the complete combustion of the propane in a
container with a volume of 15.0L and a pressure of 4.5 atm at 25C. The
unbalance equation is
C3H8(g) + O2(g) CO2(g) + H2O(l)
Gas Laws and Chemical Reactions
Calculate the volume of oxygen in liters at 35C and 630.0 mmHg, that
could be obtained by heating 10.0 g of potassium chlorate (KClO3).
Step #2:
# mols O2 = 0.1223 mol of O2
V = ?, R = 0.0821 L atm K-1 mol-1
T = 35 + 273 = 308 K, P = 630 / 760 = 0.82895 atm
V = nRT/P
V = [(0.1223mol)(0.0821LatmK-1mol-1)(308K)]/0.82895atm
= 3.73L
= volume of O2 at 35 C & 630 torr (or 630 mm Hg)
Daltons Law of Partial Pressures
Many chemical problems involve mixtures of gases
and not pure gases.
In the case of gas mixtures the total gas pressure can
be related to the pressures of individual gas
components (partial pressures).
Daltons Law of Partial pressures states:
The total pressure of a mixture of gases is just the
sum of the pressures that each gas would exert if it
were present alone.
PT = P1 + P2 + P3 +
Daltons Law of Partial Pressures
It is possible given the mole fraction of a gaseous
component and the total pressure to determine the
individual partial pressures:
Pi = X iPT
The mole fraction of a component:
ni
X=
Mole fraction (Xi) = the i ratio of the number of moles of
nT
one component (ni) to the number of moles of all
components present (nT).
Applying Daltons Law of Partial Pressures
A sample of natural gas contains 8.24 moles of
methane (CH4), 0.421 mole of ethane (C2H6) and
0.116 mole of propane (C3H8). If the total pressure of
the gases is 1.37 atm, what are the partial pressures
of the gases?
Pi = X iPT
ni
Xi =
nT
Applying Daltons Law of Partial
Pressures
Partial Pressures Challenge
Applying Daltons Law of Partial Pressures
Q. 9-113 5th When 2.00 mol of NOCl (g) was heated to 225C in a 400.0
L steel reaction vessel, the NOCl partially decomposed according to the
equation
2 NOCl (g) 2 NO (g) + Cl2(g).
The pressure in the vessel after reaction is 0.246 atm.
(a) what is the partial pressure of each gas in the vessel after reaction?
(b) What percentage of the NOCl decomposed?
Kinetic Molecular Theory of Gases
The gas laws allow us to predict the behavior of
gases.
They do not explain what is happening at the
molecular level to cause this behavior.
Much of the physical properties displayed by gases
can be explained by examining the molecular motion
of individual molecules.
Molecular motion is a form of energy and can also be
defined as the capacity to do work:
energy = work done = force x distance
The energy of motion is known as Kinetic energy.
Kinetic Molecular Theory of Gases
Relating the physical properties of gasses to the motion
of gas molecules lead to a set of four generalizations
about the behavior of gasses.
These generalizations are known as the kinetic
molecular theory of gases (kinetic theory of gases).
1.
Gases consist of very small molecules (atoms).
2.
The combined volume of the atoms is negligible
compared with the empty space between them.
3.
Gas molecules or atoms have no attractive or
repulsive forces between them.
Kinetic Molecular Theory of Gases
Kinetic molecular theory of gasses continued:
4.
Gas molecules are in constant random motion
and often collide. All collisions between gas
molecules are perfectly elastic (no overall energy
loss).
6.
The average Kinetic Energy of the gas molecules
is proportional to the temperature in Kelvin.
The molecular Kinetic theory of gasses allows us to
explain a number of macroscopic properties in
molecular terms.
Kinetic Molecular Theory of Gases
Gas pressure (Boyles Law):
Caused by the collision between molecules and the
walls of their container.
Magnitude of gas pressure depends on:
The frequency of collision per unit area.
How hard the molecules strike the walls.
Gas temperature (Charles Law):
A measure of the average kinetic energy of the gas
molecules.
More energetic random motion = higher temperature.
Kinetic Molecular Theory of Gases
Compressibility of Gases (Avogadros Law):
Molecules in the gas phase are widely separated
(assumption #1).
Therefore gases are more easily compressed to
occupy less volume than a liquid or solid.
Kinetic Energy Relationships
Relationship between T and kinetic energy (EK)
total kinetic energy for a mole of gas particles
3RT/2
kinetic energy per particle (includes NA)
3RT/2NA
What is the average speed of a gas particle?
EK = 3RT/2NA = mu2
m is the mass of the particle and u is the average
speed
solving for u = 3RT/M (where M is the molar mass)
Kinetic Energy Relationships
u = 3RT/M
molar
mass
average
speed
Kinetic Energy Challenge
Calculate the average speed of a nitrogen molecule (in
meters per second) on a hot day in summer (T = 37C)
and on a cold day in winter. (T = 25C).
Given: MN2 = 28.01 g/ mol, K = C + 273.15, R = 8.314 kg m2 K-1 mol-1
s-2
u = 3RT/M
Grahams Law Diffusion and Effusion of
Gases
Diffusion is the mixing of
gas molecules by random
motion with frequent
molecular collisions.
Effusion is the escape of
a gas through a pinhole
into a vacuum without
molecular collisions with
other gas molecules.
Grahams Law
T influences EK of gas (but not chemical composition)
All gases at the same T will have the same EK
mu2 = 3RT/2NA
( mu2)gas 1 = ( mu2)gas 2
(uga1)2/(ugas2)2 = m2/m1
for all gases
For diffusion , there are more complex interactions
occurring (we are not in a vaccum ie for effusion) but
Grahams law is a good approximation for the mixing of the
gases
Effusion challenge
9.20 b
5th
Which gas in the following pair diffuses more rapidly
and what are the relative rates of diffusion?
(b) N2 and acetylene (C2H2)
Ugas1/ugas2 = m2/m1
N = 14.01 amu
C = 12.01 amu
H= 1.01 amu
The Behavior of Real Gases:
Volume issue
The volume of a real gas is larger
than predicted by the ideal gas law.
The Behavior of Real Gases:
Attraction issue
Attractive forces between particles become
more important at higher pressures.
Intermolecular forces start to become very important
when molecules are about 10 molecular diameters
apart or less.
The Behavior of Real Gases
van der Waals equation
Correction for
intermolecular
attractions.
an2
P+
V2
V - n b = nRT
Correction for
molecular
volume.
van der Waals Equation Challenge
9.22 5th
Assume that you have 0.500 mol of N2 in a volume of
0.600L at 300K. Calculate the pressure in atm using
both the ideal gas law and the van der Waals equation.
For N2 a = 1.35 (L2atm)/mol2 and b = 0.0387 L/mol
PV = nRT
an2
P+
V2
V - n b = nRT
Chapter 9 Appendix
Kinetic Molecular Theory of Gases
Boyles Law:
Pressure results from the impact of gas molecules
on the walls of a container.
The collision rate is a reflection of the number of
molecules of gas per unit volume (number density).
Decreasing the volume increases the number
density and the collision rate.
Therefore pressure will be inversely proportional to
volume (Boyles Law).
1
V when n and T are constant
P
Kinetic Molecular Theory of Gases
Charles Law:
The average kinetic energy of gas molecules is
proportional to its temperature (assumption #5).
Raising the temperature of a gas will raise the
average kinetic energy of a gas.
As a result molecules in the gas will collide with the
container walls more frequently and harder and the
pressure will increase.
In order to maintain a constant pressure the volume
of the gas must increase proportionally with
temperature (Charles Law).
Kinetic Molecular Theory of Gases
Avogadros Law:
At constant T and P adding more particles will result
in an increase in volume.
If volume did not increase the number of collisions of
gas particles with the walls of the container would
increase (increasing P).
To avoid this increase, the volume increases.
Kinetic Molecular Theory of Gases
Daltons Law of Partial Pressures:
Gas molecules do not attract or repel one another
(assumption #4).
If this is true then the pressure caused by one type
of gas molecule will not be affected by the presence
of another type of gas molecule.
So the pressure of each gas present can be
calculated separately and the total pressure is the
sum of these individual pressures (Daltons Law of
Partial Pressures).