Transcript Gases and Their Properties

Gases and Their Properties
Chapter 11
Gases
Some common elements and compounds exist in the gaseous
state under normal conditions of pressure and temperature.
Many common liquids can be vaporized.
Our gaseous atmosphere provides one means of transferring
energy and material throughout the globe.
Gas behavior is reasonably simple and they are well
understood. Simple mathematical models may be used.
11.1 Properties of Gases
Gas Pressure
Pressure is the force exerted by particles on an object divided
by the area upon which the force is exerted.
Gas pressure may be measured in millimeters of mercury
(mm Hg or torr), standard atmospheres (atm), the SI unit
pascal (Pa), or the bar.
1 atm = 760 mm Hg = 101.325 kPa = 1.01325 bar
Practice Problem
Convert 575 mm Hg into atmospheres and
kilopascals.
11.2 Gas Laws: Experimental Basis
 The volume of a fixed amount of gas at a given
temperature is inversely proportional to the
pressure of the gas is a statement of Boyle’s Law.
 Therefore, at constant temperature and number of
moles…
P1V1 = P2V2
Practice Problem
A sample of CO2 has a pressure of 55 mm Hg
in a volume of 125 mL. The sample is
compressed so that the new pressure of the gas
is 78 mm Hg. What is the new volume of the
gas, assuming constant temperature?
Gas Laws: Experimental Basis
 Charles’ Law: If a given quantity of gas is held at
constant pressure, its volume is directly proportional
to the Kelvin temperature.
V1/T1 = V2/T2
Remember that T must always be expressed in kelvins!
Practice Problem
 A balloon is inflated with helium to a volume of 45 L
at room temperature (25oC). If the balloon is cooled
to -10. oC, what is the new volume of the balloon?
Assume that the pressure does not change.
Gas Laws: Experimental Basis
 Boyle’s and Charles’ Laws may be combined into
one equation to give the general gas law or
combined gas law. It applies to situations in
which the amount of gas does not change.
(P1V1)/T1 = (P2V2)/T2
OR
P1V1T2 = P2V2T1
Practice Problem
You have a 22 L cylinder of helium at a
pressure of 150 atm and at 31 oC. How many
balloons can you fill, each with a volume of
5.0 L, on a day when the atmospheric pressure
is 755 mm Hg and the temperature is 22 oC?
Avogadro’s Hypothesis
Avogadro proposed that equal volumes of gases
under the same conditions of temperature
and pressure have equal numbers of
molecules.
Practice Problem
If 22.4 L of gaseous CH4 is burned, what volume of
O2 is required for complete combustion? What
volumes of CO2 and H2O are produced? Assume all
gases have the same temperature and pressure.
CH4 + 2O2  CO2 + 2H2O
11.3 Ideal Gas Law
 The four quantities that can be used to describe a gas
include pressure, volume, temperature, and amount.
 All three laws can be combined to determine a
universal gas constant, R, that can be used to
interrelate the properties of a gas.
PV = nRT
R = 0.082057 Latm/Kmol
Practice Problem
 The balloon used by Jacques Charles in his historic
flight in 1783 was filled with about 1300 mol of H2.
If the temperature of the gas was 23 oC, and its
pressure was 750 mm Hg, what was the volume of the
balloon?
Density of Gases
 Since n = mass/molar mass, then PV = (m/M)RT
 Since density is defined as d = m/V, we can rearrange the
ideal gas equation to say
D = (PM)/(RT)
Calculate the density of dry air at 15.0 oC and 1.00 atm if its
molar mass (average) is 28.96 g/mol.
Practice Problem
 A 0.105 g sample of a gaseous compound exerts a pressure
of 561 mm Hg in a volume of 125 mL at 23.0 oC. What is
its molar mass?
Homework
 After reading sections 11.1-11.3, you should be able to do
the following…
 P. 546 (12-30 even)
11.4 Gas Laws and Chemical Reactions
 Gaseous ammonia is synthesized by the following reaction
N2(g) + 3H2(g)  2NH3(g)
in the presence of an iron catalyst at 500 oC.
Assume that 355 L of H2 gas at 25 oC and 542 mm Hg is
combined with excess N2 gas. What amount (mol) of NH3
gas can be produced? If this amount of NH3 gas is stored
in a 125 L tank at 25.0 oC, what is the pressure of the gas?
11.5 Gas Mixtures and Partial Pressures
 The pressure of each gas in a mixture of gases (such as our
atmosphere) is the partial pressure.
 Dalton’s Law of Partial Pressures states that a mixture of
gases is the sum of the partial pressures of the different
gases in the mixture.
Ptotal = P1 + P2 + P3 +…
Ptotal = ntotal(RT/V)
Partial Pressures of Gases
 A mole fraction, X, is defined as the number of moles of a
substance divided by the total number of moles of all
substances present.
 PA = XA(Ptotal)
Practice Problem
 15.0 g of halothane (C2HBrClF3) is mixed with 23.5 g of
oxygen gas. If the mixture is placed in a 5.00 L tank at 25.0
oC, what is the total pressure (mm Hg) of the gas mixture
in the tank? What are the partial pressures (mm Hg) of the
gases?
11.6 Kinetic-Molecular Theory of Gases
 The kinetic-molecular theory is a description of the
behavior of gases at the molecular level.
 Gases consist of particles whose separation is much greater
than the size of the particles themselves.
 The particles of a gas are in continual, random, and rapid
motion. As they move, they collide with one another and
the walls of their container.
 The average kinetic energy of gas particles is proportional
to the gas temperature. All gases, regardless of their
molecular mass, have the same average kinetic energy at
the same temperature.
Kinetic-Molecular Theory
 Kinetic energy of a gas particle of mass m may be
calculated by
KE = ½ (mass)(speed)2 = ½ mu2
where u is the speed of that molecule.
 Average kinetic energy depends only upon Kelvin
temperature. Therefore, average kinetic energy for a gas
sample is equal to one half the mass times the average of
the mean square speed.
Kinetic-Molecular Theory
 Since average kinetic energy is proportional to
temperature, then ½ mu2 must also be proportional to
temperature. Therefore the square root of the mean square
speed, the temperature, and the molar mass are related.
√u2 = √(3RT)/M
where R is 8.3145 J/Kmol
and 1 J = 1 kg(m2/s2)
All gases have the same average kinetic energy at the same
temperature.
Practice Problem
 Calculate the rms speed of helium atoms and N2 molecules
at 25 oC.
Homework
 After reading sections 11.4 – 11.6, you should be able to do
the following…
p. 547 (31-36 all, 38-44 even)
11.7 Diffusion and Effusion
 The mixing of molecules of two or more gases due to their
motion is called diffusion. Ex: pizza, bleach
 The movement of gas through a tiny hole in a container is
called effusion.
 Graham’s Law states that the rate of effusion of a gas is
inversely proportional to the square root of its molar mass.
Rate1/Rate2 = √(M2/M1)
Common Misconception!
 A gas with a lower molar mass does not effuse more
quickly because it is smaller, it does so because it is
moving more quickly and would have more collisions.
This would increase the probability that it would effuse
through a tiny hole!
Practice Problem
 A sample of pure methane, CH4, is found to effuse through
a porous barrier in 1.50 min. Under the same conditions,
an equal number of molecules of an unknown gas effuses
through the barrier in 4.73 min. What is the molar mass of
the unknown gas?
11.9 Nonideal behavior: Real Gases
 Most gases behave ideally at low pressures and high
temperatures.
 Assumptions are not always valid. Sometimes atoms or
molecules stick to each other and may be liquified.
Volume available to gas molecules may be small.
 The van der Waals equation adjusts for nonideal behavior
van der Waals Equation
(P + a[n/v]2)(V-bn) = nRT
where “a” and “b” are experimentally determined constants
 the pressure correction term accounts of intermolecular
forces, and the volume correction term accounts for
molecular volume
Practice Problem
 Using both the ideal gas law and the van der Waals
equation, calculate the pressure expected for 10.0 mol of
helium gas in a 1.00 L container at 25 oC. For helium,
a=0.034 (atmL2/mol2) and b=0.0237 L/mol.
Homework
 After reading sections 11.7 – 11.10, you should be able to
do the following…
 P. 548 (48-52)