The Berkeley Review MCAT General Chemistry Part 2

324 Pages·2011·49.1 MB·English

by  The Berkeley Review

General
Chemistry
Part II
Sections VI-X
Section VI
Gases
Section VII
Phases & Phase Changes
Section VIII
Thermochemistry
Section IX
Kinetics
Section X
Electrochemistry
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Terminology and Concepts
a) Gas-Phase Definitions
b) Kinetic Molecular Theory of Gases
c) Boltzmann's Distribution
d) Ideal Oases
Section VI e) Real Oases
Gas Laws
Gases a) Applying Qas Laws
by Todd Bennett b) Avogadro's Law
c) Boyle's Law
d) Charles's Law
Gas mixture
O = Lighter gas Gas mixture,
I added evacuated? Gas System Properties
• ssHeavier gas
a) Partial Pressure
b) Manometers
Gas Notion
a) Qas Speed and Velocity
b) Diffusion
Gas mixture is richer Gas mixture is richer in c) Effusion and Infusion
in the heavier gas on the lighter gas on the d) Isotopic Enrichment
the left side of the tube right side of the tube
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Specializing in MCAT Preparation
Gases Section Goals
Know the definition of a gas and the terms associated with gases.
Youmust know what an ideal gas and a real gas are. Understand the following terms used to describe
a gas system: pressure, volume, concentration, density, temperature, moles, molecules, collision
frequency, ana mean free path.
Have a solid understanding of the kinetic theory of gases.
Be able to recite a viable description ofgases at themicroscopic level using thekinetic theory of
gases. Knowthat gasesmoveabout theirenvironment in a random fashion, and that they frequently
collide with other gas particles and the walls of the container. Know that the momentum of heavier
gases is greater than the momentum of lighter gases. Know that the velocities of each gas particle
sum to zero for a gas in a stationary, closed container.
Know the proper applications of the various gas laws.
Know hentouseAvogadro's, Boyle's, andCharles's laws from thevariables presented in thequestion.
Have an understanding of the experimental conditions required to use each law. Recognize the
shape of the graphs that show the relationships between the variables of each gas law.
Be able to distinguish between a real gas and an ideal gas.
An ideal gas is composed of molecules that occupy no volume and exhibit no intermolecular forces.
A real gas is just what the name implies, a gas made up of real molecules that do occupyvolume
and exhibit intermolecular forces. The pressure and volume ofareal gas are therefore different from
those of an ideal gas. The Vander Waalsequation (whichyou should understand but not memorize)
shows the relationship betweenideal variablesand real variables for a gas.
Be able to determine the partial pressure of a gas within a mixture.
The total pressure of a system is the sum of the individual pressures (partial pressures) of all of the
component gasparticles. Thepartial pressure duetoonecomponent in themixture canbedetermined
by multiplying the mole fraction of the component by the total pressure of the system. Youmust
be able to convert between different pressure units.
Understand the relationship between speed, mass, and temperature for a gas.
You must know the effectof a particle'smass on its velocity. Lightergases travel at a faster rate than
heavier gases. The velocityor a gas particleis inverselyproportional to the square root of its mass.
You mustknowtheeffect of temperature onvelocity. Athighertemperatures, gases travel at a faster
rate. The velocity of a gas particle is directly proportional to the square root of the temperature.
Understand the concepts of effusion and effusion rate, infusion, and diffusion.
e^
Effusion isthe process bywhich gas molecules pass from within a container to the outside through
pores in the container wall. The rate of effusion depends on the velocity of the gas molecules, the
number of pores in the material, and the size of the pore relative to the size of the molecule. When
gases enter a container through a pore, the process is referred to as infusion. When a gas particle
moves from a region of higher concentration to a lower concentration, the process is known as
diffusion.
General Chemistry Gases and Gas Laws Introduction
Gases and Gas Laws
The gas phase, from the macroscopic perspective, is defined as the state of a
closed system in which molecules have no definite shape and no definite volume.
From the microscopic perspective, the molecules are freely moving particles
traveling through space, where the kinetic energy associated with each particle is
greater than the potential energy of intermolecular forces. The gas phase is the
first of three phases of matter that we shall address. Gases differ from liquids in
that liquids have a definite volume, and the molecules in a liquid are in
continuous contact with neighboring molecules. Gases differ from solids in that
solids have a definite volume and definite shape, and the molecules in a solid
undergo no translational motion and are in continuous contact with neighboring
molecules. Of the three common phases of matter (solid, liquid, and gas), the gas
phase has the largest amount of kinetic energy and the greatest entropy. To
reach the gas phase, energy must be added to the molecules within a system that
is not already in the gas phase. It is essential to understand a gas from both the
macroscopic and microscopic perspectives.
Macroscopic View ofa Gas: A gas assumes the shape and volume of its container.
Gases are compressible and must be contained on all sides to hold them in place.
Gases are described by the macroscopic variables pressure, concentration,
temperature, and volume. Chemists treat gases as if they are composed of inert
spheres that occupyno molecular volume. This is a basicassumption of the ideal
gas law. Most calculations involving gases are based on the ideal gas equation
(PV = nRT). There are two common types of calculation questions about gases
that you may encounter on the MCAT 1) the before-and-after questions about the
effect of changes on a gas system and 2) the straightforward type using PV =
nRT. Calculation questions requiring you to find a precise value are few, but
conceptual relationships can be determined from calculations as well. The first
style of question is better understood as an application of one of the gas laws
(Avogadro's, Boyle's or Charles's laws). For instance, if the temperature increases
in a sealed, rigid container,what changes? This is another way of asking how a
change in temperature affects the pressure of a gas, assuming constant volume
and moles. Rather than memorize gas laws, know qualitativelyhow one variable
in the ideal gas equation affects another.
Microscopic View ofa Gas: Gases consist of individual molecules or atoms that are
randomlymoving about the space within a container. Theparticles are in contact
onlyduring collisions. Thisconcept is knownas the kinetic theory ofgases. Gases
can be described by the microscopic variables of collision frequency, mean free
path,and meanvelocity. Thefact that microscopic behavior involves interactions
between gas particles implies that the molecules do in fact occupy a small
volume and they are capableof exhibiting intermolecular forces (bothattractive
and repulsive). The strength of these forces varies with distance. Gases existas
real gases, which are approximatedas obeying idealbehavior when they do not
interact. Ideal gas behavior is best simulated at low pressure (fewer collisions
between molecules and minimal forces between molecules) and high
temperature (at high temperature, molecules have the energy to overcome
intermolecular forces). Under these conditions, the forces acting between gas
molecules becomenegligible. This is the basis of the kinetic theory of gases.
The behavior of a gas is predictable in terms of the variables that describe the gas
system. We use the ideal gas law to predict the effectsof changes on gas systems.
Although there are no ideal gases, the approximation is still rather close.
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Gener&l CtieilllStry Gases and Gas Laws Terminology and Concepts
Gas Phase Definitions
The terms used to describe a gas can be broken down into categories of
macroscopic and microscopic. We can consider either the system as a whole
(macroscopic perspective), or the individual particles that constitute the system
(microscopic perspective). Each of the macroscopic properties has a microscopic
equivalent. Table 6.1 lists the macroscopic and corresponding microscopic
properties that describe the state of a gas system.
Macroscopic Measurements Microscopic Measurements
Pressure (P; standard unit is arm.) Collision frequency and collision force
Volume (V; standard unit is liters) Mean free path
Moles (n; standard unit is moles) Molecules
Temperature (T;standard unit is K) Average kinetic energy
Table 6.1
It is imperative to have a well-developed glossary in your memory by the time
you take the MCAT. Organize the terms in a manner such that one definition
helps you to recall additional definitions. The definitions of selected terms from
Table 6.1 are:
Gas Pressure: Gas pressure is defined as the force per unit area exerted by a
gas through collisions against a defined area of the container wall. As the
gas molecules collide more frequently with the container walls or increase
their force during collisions with the walls, the gas pressure increases. The
gas pressure depends on the number of gas particles, the volume of the
container, and the temperature of the gas system. The standard unit for
pressure is atmospheres.
Collision Frequency: The collision frequency is defined as the rate at which
molecules in the gas system collide with each other and with the wall of the
container. The collision frequency can be increased in one of three ways:
increasing the temperature (energy of the gas system), increasing the
concentration of gas particles, or reducing the mean free path. All of these
changes result in an increase in the number of collisions experienced by a
molecule within the system in a given period of time.
Collision Force: The collision force is defined as the force exerted by a gas
particle during a collisionbetween it and the container wall. It is an impulse,
so both greater momentum and a shorter time of contact increase the force of
impact. The collision force can be increased by increasing the temperature
(energy of the gas system), because greater temperature imparts greater
velocity, and thus greater momentum, to each particle.
Volume: The volume of a gas is defined as the region within the walls of a
container. The actual volume that a gas molecule can occupy (the real
volume) is the volume of the container minus the volume of the other gas
molecules, because no two gas molecules can occupy the same volume at the
same time. The volume of a gas in an open environment is undefined,
because the container holding the gas is also undefined. The standard unit of
volume is liters.
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General Chemistry Gases and Gas Laws Terminology and Concepts
Concentration: The concentration of a gas is the number of gas particles per
unit volume in a container. A gas is assumed to be homogeneous, so a
sample from anywhere in the container may be used to determine the gas
concentration. As more molecules of gas are added to a system, or as the
volume of the container is decreased, the gas becomes more concentrated.
This means that as a gas is compressed, it becomesmore concentrated.
Mean Free Path: The mean free path is defined as the average distance a
particle cantravel before colliding withanother particle. Although it isn't the
samething, it can be thought of as the average distance between gas particles
at any given time. It is the microscopic equivalent of concentration. If the
concentration of a gas remains constant, then the average distance between
any two particles within the container also remains constant.
Temperature: Temperature is a measure of the total kinetic energy of a
system. The greater theenergy ofeach particle in thesystem, thegreater the
total energy of the system, and thus the greater the temperature of the
system. Temperature can be measured in degrees Celsius or Kelvin,
although Kelvin is the bettermeasurement to usewhenworking with gases.
Average Kinetic Energy: The average kinetic energy ofa system refers to the
meanenergy ofa particle in that system. Astheenergy ofeach particle in the
system increases, the average kinetic energy of thesystem increases, thereby
resulting in an increased temperature.
Example 6.1
Which statement below accurately describes the relationship between
temperature and energy?
A. Temperature quantifies the energy of a system.
B. Energyquantifies the temperature of a system.
C. Temperature is independent of energy.
D. Temperature is variable, while energy is constant.
Solution
Temperature is a measurement of the average kinetic energy ofa system. The
best answer is choice A. A thermometer is used to determine the temperature of
a system. The way a thermometer works isbased onthe kinetic theory ofgases.
The thermometer is an evacuated closed column that is partially filled with a
pure liquid, preferably oflow volatility (such asmercury). Gases collide with the
outside of the evacuated glass casing that contains the non-volatile liquid. The
energy from these collisions is transferred through the glass walls and into the
liquid. A sufficient number ofcollisions can increase the vibrational energy of
the liquid in the container and force the liquid to expand, thereby causing the
height of thecolumn ofliquid to rise. This implies that the density ofa liquid is
inversely proportional to its temperature, because as the temperature rises, the
volume of a liquid increases (the liquid is expanding). Because the density of
water does not change uniformly (it increases from 0°C to 4°C and then decreases
from 4°C to 100°C), it cannot be used in thermometers. In addition, the range of
temperatures over which water exists as a liquid is toosmall. The liquid chosen
to fill a thermometer must have a large temperature range between its freezing
point and boiling point. In most thermometers, the liquid used is mercury. In
other thermometers, a non-volatile alcohol tinted with a red dye is used.
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Oeneral C^tieilllStry Gases and Gas Laws Terminology and Concepts
Kinetic Molecular Theory of Gases
The kineticmoleculartheory of gases takes a microscopic view of the component
molecules (or atoms) that make up a gas. Four assumptions associated with this
theory with which we shall concern ourselves are the following:
1. Particles are so small compared to the distances between particles (inter-
nuclear distances) that their volumes are negligible (assumed to be zero).
2. Particles move in straight lines. The direction of a particle's motion is
changed only by its collision with either another molecule or the walls of the
container. The collisions are said to be elastic (no energy is dissipated), and
momentum is conserved.
3. Particles are in constant random translational motion. Gas pressure is caused
by collisions of the particles against the walls of the container.
4. Gas molecules exhibit no intermolecular forces. This is to say that the
particles neither attract nor repel one another.
Figure 6-1 shows the random pathway of one single gas particle over time,
according to the rules of the kinetic molecular theory of gases. If the kinetic
energy of the particle increases, the particle's speed increases, so it collides more
frequently with the wall. Because it is moving faster, it collides with greater
momentum, so impulse increases. The result on the macroscopic level is that the
force per unit area exerted against the walls increase, meaning pressure is
greater. The kinetic theory of gases explains macroscopic observations using
principles derived from a microscopicmodel.
The particle moves until it collides with
the wall. In a real system, the particle
would also collide with other particles
present in the container.
Figure 6-1
When there are many gas particles in the container, collisions between particles
become more common than collisions with the wall. However, the presence of
more particles in the container also results in a greater number of collisions with
the walls, so the pressure of the system increases as particles are added to the
system. When there are particles of different masses in a mixed gas, heavier
particles move more slowly, hence they exhibit lower collision frequencies.
However, because they have a greater mass and only slightly reduced speed,
they collide with greater force (momentum).
As a general rule, lightergas molecules have greater average speeds (and greater
collision frequencies) than heavier ones, but less momentum (and thus less
collision force). Because pressure depends on both collision frequency and
collision force, gas particles of different masses exert the same pressure. On the
macroscopic level, this means that pressure is the same under identical
conditions for all ideal gases, independent of their molecular mass. A good
example is to compare helium and nitrogen. The reason they have the same
pressure at the same temperature is because they have the same kinetic energy
(mv2 term). The molecule with greater mass has less speed. The average speed
is inversely proportional to the square root of the mass.
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General Chemistry Gases and Gas Laws Terminology and Concepts
Example 6.2
In a rigid, closed container, how does an increase in temperature affect the gas
particles in the system?
A. The mean free path increases.
B. The collision force decreases.
C. The collision frequency increases.
D. The particle momentum decreases.
Solution
The fact that the container is rigid means that the volume does not change.
Because it is a closed system, the moles of gas do not change (matter can neither
enter nor exita closed system). The concentration remains constant, so the mean
free path does not change. This eliminates choice A. The mean free path is the
average distance a particle travels between collisions. It canalso be thoughtofas
the average distance betweenparticles at any given instant. Because the volume
of the container does not change, and the moles of gas do not change, the
concentration (density of gas) does not change. This means that the particles are
the samedistance apart, so the mean free path does not change. According to the
equation PV = nRT, if the temperature of the system increases while volume and
moles remain constant, the pressure must increase. This means that collision
force, collision frequency, or both must have increased. As temperature
increases, the velocity of the particles increases (the kinetic energy increases in
terms of velocity). With an increase in velocity, the particles travel the distance
between collisions at a greater rate, so they collide more frequently. Because the
particles have greater velocity, they have greater momentum, so the collision
force increases. The result is that the collision force and collision frequency both
increase, so choice B is eliminated and choice C is the best answer. At greater
velocity, the particles have greater momentum, so choice D iseliminated.
Boltzmann's Distribution
Ina gas system, notall particles have the same kinetic energy. There is instead a
random distribution of energies, known as Boltzmann's distribution. Figure 6-2
shows a Boltzmann's distribution of kinetic energy for the particles in a gas
system at two different temperatures (total energies). The mean kinetic energy
does notcorrespond to the apex of thecurve, but to a point slightly to the rightof
the apex. This is because the energy distribution graph is skewed to the right.
As temperature increases, each particle gains kinetic energy, shifting the
distribution to the right. In Figure6-2, T2 is greater thanTi.
Kinetic energy
Figure 6-2
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General ChemiStry Gases and Gas Laws Terminology and Concepts
Ideal Gases
An ideal gas is a theoretical gas which obeys the following three conditions:
1. The molecules exhibit no intermolecular forces.
2. The molecules occupyno microscopic volume (are point masses).
3. All collisions are perfectly elastic.
Because the constraints of the ideal gas cannot be met by real molecules, an ideal
gas is strictly theoretical. Gases are closest to ideal at high temperature (having
more kinetic energy to overcome intermolecular forces), low pressure
(interacting minimally with one another), and when the system is composed of
small, inert particles. The most ideal gas is helium (which has the smallest
particles of any substance known and which exhibits negligible intermolecular
forces). Toverify these conditions, consider a phase diagram. When pressure is
small and temperature is large, the state of matter is gaseous, far from the other
phases in the phase diagram.
The ideal gas law was the result of empirical observations, such as noting that
the volume ofa gas is inversely proportional to its pressure, volume is directly
proportional to temperature, and volume is directly proportional to moles. From
these relationships, Equation 6.1 (a composite formula) was derived.
V oc (6.1)
p
Equation 6.1 canbeconverted intoEquation 6.2 by introducing a constant.
V = k— (6.2)
P
Equation 6.2 can then be rearranged to yield: PV = k-n-T, which in essence is
Equation 6.3, where the constant is R (the ideal gas constant), rather than k (a
generic constant). Ideal gases obeyEquation 6.3, the idealgas equation.
PV = nRT (6.3)
where P is pressure, Vis volume, n is moles, T is temperature, and R is the ideal
gas constant of 0.0821 Latm.-mole^IC1.
In the best ofall possible worlds, all gases would be ideal. But real gases make
up 100% of all gases, so there are no ideal gases. However, while there are no
ideal gases, we can make calculations for gases that are ideal and then adjust for
our errors. Theidealgas law produces answersclose enough to the exact values
for real gases that we can use it in everyday practice. Deviations from ideality
are approximated, and rough corrections are made to determine the conditions
for a real gas. For example, asvolume decreases, gases behave less ideally. This
isbecause theactual size of themolecules does not change, so the percent of the
volume occupied by the molecules increases. The molecules interact more and
are limited in the free space they can occupy.
Ideal gas problems are straightforward, plug-and-chug in their purest form.
Ideal gas questions also encompass the before-and-after case questions
associated with gas laws. As you approach these problems, isolate the value that
you are looking for and solve for it in terms of the other variables. Be sure to use
thecorrect units. It iseasy to forget to use kelvins. What you must do is observe
what remainsconstant when you consider a system.
PV = nRT /. R =PV, soMi =Ml
nT niTi n2T2
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