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Period: ___________
Unit 2 Packet – Energy and States of Matter
Unit 2 Packet Contents Sheet (This Paper!)
Unit 2 Objectives
Notes: Kinetic Molecular Theory of Gases- 3 pgs
(with Behavior of Gases Reading, and Notes completed)
Pressure Conversions (DA Practice)
Unit 2 w/s # 2- Measuring Pressure
Unit 2 Worksheet # 1
Gas Laws- Graphing to Determine Relationships
Boyle’s Law Notes
Boyle’s Law Practice Problems
Diver’s Law Notes
Diver’s Law Practice Problems
Charles’ Law Notes
Charles’ Law Practice Problems
Gay-Lussac Law Notes
Gay-Lussac Law Practice Problems
Unit 2 w/s #3- PVTn Problems- 2 pgs
Unit 2 Review Guide- this isn’t all questions to answer- more of an
outline. You need to personally make sure you understand all the parts!
DO NOT, under any circumstances, throw this away!
This packet MUST be saved for the final exam.
Unit 2: Learning Goal:
Students understand how gasses behave and the relationship between
pressure, volume, number of particles, and temperature (P, V, n, & T).
Students are able to solve quantitative P, V, n, T problems.
Scale
Score Comment
Score 4 Students show mastery of score 3 without any errors plus:
Apply quantitative problem solving to real-world situations
Score 3 Without any major errors, students can:
Understand how gasses behave and the relationship
between pressure, volume, number of particles, and
temperature (P, V, n, & T). Students are able to solve
quantitative P, V, n, T problems.
Score 2 Without any major errors, students can:
Recognize how gasses behave and the relationship
between pressure, volume, number of particles, and
temperature (P, V, n, & T). Students are able to solve
quantitative P, V, n, T problems.
Score 1 With help from the teacher, students can:
Understand how gasses behave and the relationship
between pressure, volume, number of particles, and
temperature (P, V, n, & T). Students are able to solve
quantitative P, V, n, T problems.
Score 0 Even with the teachers help, students show no understanding of
how gasses behave and the relationship between P, V, n, & T.
Students are not able to solve quantitative P, V, n, T problems.
Chemistry – Unit 3 Energy and Kinetic Molecular Theory
In the 18th and 19th centuries scientists wrestled with identifying and describing
the nature of the “stuff” that produced change. One concept that became popular
for a while was that of “caloric” (what we now call heat).
“Caloric was originally conceived of as a quantity that would flow from a hotter
object to a cooler one that would warm up as a result. It answered the need for a
way for the cause of warming to get from here to there. Not only did caloric serve
as a cause for warming, it was also considered to be the cause for changes of
phase. Caloric enabled particles of a substance to move farther apart until the
attraction of the particles for each other became too weak to hold them together.
Although Lavoisier did not think that caloric necessarily was an actual
substance, in its storage and transfer it was like a substance.”
When scientists recognized that the “stuff” involved when forces were applied to
objects to lift them or change their speed was the same “stuff” that was involved
when the temperature of objects changed, they worked to develop a single energy
concept. “So when the energy concept was developed it was important to
distinguish it from caloric. In snuffing out the caloric concept, the clear picture
of energy storage and transfer that it fostered was unnecessarily lost, too.”
Even though we recognize that energy is not a physical substance, we choose to
use the substance metaphor to describe it.
We’ll use three principles to guide us in the development of the energy concept. 1. Energy can be viewed as a substance-like quantity that can be stored in a physical
system.
2. Energy can “flow” or be “transferred” from one system to another and so cause
changes.
3. Energy maintains its identity after being transferred.
If you are unsure what we mean by the use of a substance metaphor, consider
how we describe information. We say that it can be stored in books, on computer
hard drives or floppy disks or CD-ROMs. Information can be transferred from
place to place via cables or by wireless transmission techniques - in fact you just
did this when you accessed this lesson via the Internet, transferred it to your
computer and then (perhaps) printed it. But there is nothing substantial about
the information itself; you can’t touch it or measure its mass on a balance. The
third point is important to consider because many texts talk about energy
transformations as if somehow it is the energy that is changing rather than the
physical system that gains or loses it. Consider the information metaphor again:
even though we move information from place to place or store it in different
ways, nothing about the information itself has changed.
Energy Storage and Transfer At this point, let us consider another metaphor to describe energy storage and
transfer – that of money. We store money in accounts at the bank or credit
union. We can have checking accounts, various savings accounts, certificates of
deposit, etc. These accounts store money. There is nothing different about the
money in checking and savings accounts. This money can be transferred back
and forth in the bank without changing the nature of the money or the total
quantity of money that resides in the collection of accounts that is attached to
your name; let’s call this the system for convenience.
The same is true of energy. It is stored in objects and in the arrangement of
objects in a physical system. We use different “accounts” to help us keep track of
energy as its transfer causes change in the objects or in their arrangement. As
with money, nothing about the energy itself has changed. Let’s consider the
accounts we will use in this course.
1. Thermal energy, Eth – is the energy stored by moving particles. The quantity of
thermal energy stored by a collection of particles is related to both their mass and
velocity. You instinctively recognize this as you would rather catch barehanded
baseballs thrown by your instructor than ones thrown by a major league pitcher.
Similarly, you wouldn’t be hurt if you were pelted by ping-pong balls, but would
suffer if you were showered with golf balls.
2. Phase energy, Eph – is the energy stored in the system due to the arrangement of
particles that exert attractions on one another. Attractions result in a decrease in
the energy of a system of particles. As particles become more tightly bound, their
Eph is lowered. Solids possess the lowest phase energy; liquids possess more, since
the particles in a liquid are freer to move than those in a solid; and a gas possesses
the greatest amount of Eph since the particles in a gas have completely broken free
from one another. Eph is the energy account involved when phase changes occur.
3. Chemical energy, Ech- is the energy due to attractions of atoms within molecules.
These attractions are described as chemical bonds because they are directed between
specific atoms in the molecule.
There are also three ways that energy is transferred between system and
surroundings. While most texts refer to them as nouns (work, heat and
radiation) we prefer to describe the ways as gerunds to emphasize that they are
processes rather than real things apart from energy. They are working (W),
heating (Q) and radiating (R). It is very important to recognize that such energy
transfers affect both the system and the surroundings. Energy doesn’t
mysteriously appear or get lost.
1. Working (usually referred to as work by the physicists although it is not something
different from energy) is the way in which energy is transferred between
macroscopic (large enough to be seen) objects that exerts forces on one another. It is
OK to calculate how much “work” one object does on another so long as you do not
think that work is something an object stores.
2. Heating (referred to as heat by the chemists) is the way in which energy is
transferred by the collisions of countless microscopic objects. Energy is always
transferred from the “hotter” object (one in which the molecules have greater Eth) to
a colder one (one in which the molecules have lower Eth). If all the molecules have
the same mass, then the “hotter” ones are moving faster than the “colder” ones. It’s
OK to say that you heat an object – just not that the object stores heat.
3. Radiating is the process in which energy is transferred by the absorption or emission
of photons (particles of light). A light bulb filament can be heated to the point that it
glows; this is the emission of photons that carry energy away from the filament. You
can be warmed by light from the sun as the photons transfer energy to you.
The relationship between energy storage and transfer is given by the 1st Law of
Thermodynamics, ∆E= W + Q + R. This is shown by the system schema below:
It shows that energy transferring into and out of the system affects the nature of
the energy storage in the system. The 1st Law of Thermodynamics and the Law
of Conservation of Energy state that the algebraic sum of these energy changes
and transfers must add up to zero, accounting for all changes relative to the
system.
Kinetic Molecular Theory (KMT) This is one of the really important theories in chemistry. It accounts for the
behavior of substances during all sorts of physical change. There are three key
points: 1. Matter is made of tiny particles that are in constant random motion.
2. These particles exert long-range attractions and short-range repulsions on one
another. Attractions bring about a reduction in the energy state (Eph ) of the
system; repulsions bring about an increase in the energy.
3. A hotter sample is one whose molecules are moving (on average) faster than the
molecules in a colder sample.
1 G. Swackhamer, Cognitive Resources for Understanding Energy, 2003, p 6
1 G. Swackhamer, p 7
Behavior of Gases and a few words about Pressure
Ideally, nearly all substances exhibit similar behavior in the gas phase due to the large relative
distances and negligible interaction between the particles. This results in predictable
relationships between the variables that describe gas behavior: pressure (P), volume (V),
temperature (T), and quantity of gas (n).
Pressure:
Pressure is defined as force/unit area. In a filled balloon pressure is created by the collisions of
molecules with the walls of the balloon. The more air there is in the balloon, the more
collisions against the walls of the balloon, and the higher the pressure inside. Atmospheric
pressure or air pressure is caused by the collision of atmospheric gas particles with the earth.
There are many ways to measure pressure and it is often necessary to convert from one way to
another (using dimensional analysis). Examples of different pressure measurements are:
Pressure Unit Abbreviation Definition Equivalence
to 1 atm
Atmosphere atm 1 atm is the pressure
of the atmosphere
at sea level at 0ºC
Millimeters of
mercury (Hg)
Torr
mmHg
torr
1 mmHg (1 torr) is
the pressure that
supports a column
of mercury 1mm
high at 0ºC
760 mmHg = 1 atm
760 torr = 1 atm
Pascals Pa 1 Pa is the force of 1
Newton/m2
Pascals use metric
prefixes
101325 Pa = 1 atm
101.325 kPa = 1 atm
Pounds per square
inch psi 1 psi is the force of
1 pound (lb)/in2
14.7 psi = 1 atm
1atm = 760 mmHg = 760 torr = 101325 Pa = 14.7 psi
It is important that you recognize that when you see the above abbreviations pressure (P) is what
is being discussed.
Remember: to convert from one pressure unit to another use dimensional analysis.
Kinetic Molecular Theory of Gases (KMT- Gas Behavior) and Pressure Kinetic Molecular Theory
of Gases (KMT)
(Pg 383 in the Zumdahl
textbook)
Variables that describe gas
behavior….
(Behavior of Gases
Reading)
Variable Abbreviation Unit(s)
Pressure
V
Particles, atoms, etc.
The variable…. Pressure!
Definition:
Ways to measure pressure:
Pressure Unit: Abbreviation:
Atmosphere
mmHg
1 atm = _____ mmHg = ______torr = ______ Pa = ______ psi
Sample Problem: How many atm are in 950 mmHg? Use Dimensional Analysis,
Show work!!
Pressure Conversions
Use dimensional analysis to solve the following pressure conversions:
1. 1 atm to mmHg
2. 795 mmHg to torr
3. 795 mmHg to atm
4. 795 mmHg to Pa
5. 795 mmHg to psi
6. 105600 Pa to kPa
7. 105600 Pa to atm
8. 105800 Pa to mmHg
9. 105800 Pa to torr
10. 105800 Pa to psi
11. 25.2 psi to atm
12. 730 mmHg to atm
13. 800 torr to atm
14. 101700 Pa to atm
Name
Date Pd
Unit 2 Worksheet 2 - Measuring Pressure
Problems 1 and 2. Calculate the pressure of the gas in the flask connected to the
manometer.
3. What do we mean by atmospheric pressure? What causes this pressure?
4. How do we measure atmospheric pressure? Is atmospheric pressure the same
everywhere on the surface of the earth?
5. Why is the fluid in a barometer mercury, rather than water or another liquid?
6. Explain why you cannot use a pump like the
one at the right to lift water up to the 3rd
floor of an apartment complex.
7. One standard atmosphere of pressure (SP) is equivalent to mmHg.
8. Convert pressure measurements from one system of units to another in the
following problems.
1 atmosphere = 760 mmHg = 14.7 psi (pounds per square inch)
a. 320 mmHg x = atm
b. 30.0 psi x = mmHg
c. The barometric pressure in Breckenridge, Colorado (elevation 9600 feet) is
580 mm Hg. How many atmospheres is this?
Name
Date Pd
Unit 2 Worksheet 1
1. You decide to boil water to cook noodles. You place the pan of water on the stove
and turn on the burner.
a. How does the behavior of the water molecules change as the pan of water is
heated?
b. What about your answer to (a) would change if there were more water in the
pan?
2. What property of matter best describes the way a typical alcohol thermometer
works? Explain (in terms of energy transfer) why the alcohol level in the
thermometer rises (or falls) when you place the thermometer in contact with
both warmer (or colder) objects.
3. Does the concept of temperature apply to a single molecule? Explain.
4. If you feel feverish, why can't you take your own temperature with your hand?
5. Your older brother announces that the lid to a jar of pickles from the refrigerator
is “impossible” to loosen. You take the jar, hold the lid under the hot water from
your sink’s faucet for a few seconds, and calmly open the jar. Your brother,
when faced with this blow to his pride, claims that he loosened it for you. What
knowledge of materials have you applied in this situation that really explains
how you were able to open the lid?
6. Describe how Anders Celsius devised the temperature scale that bears his name.
7. Which would feel warmer to the touch - a bucket of water at 50˚C or a bathtub
filled with water at 25˚C? Which of these contains more energy? Account for
any differences in your answers to these questions.
Gas Laws- Graphing to Determine Relationship between
Variables
Independent Variable
Axis on Graph
Dependent Variable
Axis on Graph
As x increases, y ______________
As x increases, y ______________
As x increases, y ______________
Graphical Methods- Summary
A graph is one of the most effective representations of the relationship between two variables.
The independent variable (one controlled by the experimenter) is usually placed on the x-axis.
The dependent variable (one that responds to changes in the interpret a graphical relationship
and express it in a written statement and by means of an algebraic expression.
Graph Shape Written
Relationship
Modification
required to
linearize graph
Algebraic
representation
As x . There is no
relationship between
the variables
None y = b, or
y is constant
As x increases, y
increases
proportionally. Y is
directly proportional
to x.
None y = mx + b
As x increases, y
decreases. Y is
inversely proportional
to x.
Graph y vs 1/x, or
y vs x-1
y = m(1/x) + b
Y is proportional to
the square of x
Graph y vs x2 y = mx
2 + b
The square of y is
proportional to x
Graph y2 vs x y
2 = mx + b
When you state the relationship, tell how y depends on x (e.g., as x increases, y …)
Boyles’ Law: The relationship between _________
and ______________.
Variables / Units
Held Constant
Relationship (direct
or inverse)
Relationship in
words
P _________
As ________________goes ______,
____________goes __________.
Pressure Units
Reminder…
Graph of
Relationship
Particle Diagram
Boyles’ Law
Practice Problem
A sample of oxygen gas occupies a volume of 250. mL at 740 torr pressure. What volume will it occupy at
800torr pressure?
P T V n
Initial
Final
Effect
Boyle’s Law Practice Problems Name:______________________________
Date:_________________ Period: _______
Solve each of the following problems using Boyle’s Law. Show all work and put a box around
your answer to receive full credit.
1. If 9.5 atms of pressure were increased to 25 atms of pressure, what would be the final volume
of a gas that originally occupied a space of 95 L?
2. If 760. mmHg of pressure were decreased to 458 mmHg, what would be the original volume
of a gas that ended up occupying a space of 1072 mL?
3. If the volume of a gas expanded from 958 mL to 1548 mL, what was the initial pressure
applied to it if the final pressure is 96.5 pounds per square inch?
4. If the volume of a gas contracted from 648 mL to 0.15 L, what was its final pressure if it
started at a pressure of 485 kPa?
5. If 95 lbs/in2 of pressure changed to 958.7 kPa, what would b the final volume of a gas that
originally occupied a space of 736.45 mL?
Diver’s Law: The relationship between _________
and ______________.
Variables / Units
Held Constant
Relationship (direct
or inverse)
Relationship in
words
P ________
As ________________goes ______,
____________goes __________.
1 mole is…
Graph of
Relationship
Particle Diagram
Diver’s Practice
Problem
If .105 moles of helium gas exerts a pressure of 1.5 atm,
what pressure would 0.337 moles
exert.
P T V n
Initial
Final
Effect
Diver’s Law Practice Problems Name:______________________________
Date:_________________ Period: _______
Solve each of the following problems using Diver’s Law. Show all work and put a box around
your answer to receive full credit.
1. If 3.94 atms of pressure were increased to 11.62 atms, what would be the final quantity of a
gas that originally had 1.92 x 1020
molecules?
2. If 820. mmHg of pressure were decreased to 692.5 mmHg, what would be the initial quantity
of a gas that measured 2.2 moles after the change?
3. If 938 torr of pressure changed to 213060 Pa, what would be the final quantity of a gas that
was originally .56 moles?
4. If the amount of a gas lowered from 2.00 moles to 3.91 x 1023
atoms, what was its final
pressure if it started at STP?
5. If the amount of a gas rose from 4.16 x 1023
molecules to 1.6 moles, what was the initial
pressure applied to it if the final pressure is 792.3 torr?
Charles’ Law: The relationship between _________
and ______________.
Variables / Units
Held Constant
Relationship (direct
or inverse)
Relationship in
words
V ________
As ________________goes ______,
____________goes __________.
Kelvin is…
Graph of
Relationship
Particle Diagram
Charles’ Law
Practice Problem
The volume of a sample of gas is 2.50L at 45K. What is
the volume when it is heated to 125K at a constant
pressure?
P T V n
Initial
Final
Effect
Charles’ Law Practice Problems Name:______________________________
Date:_________________ Period: _______
Solve each of the following problems using Charles’ Law. Show all work and put a box around
your answer to receive full credit.
6. If 135 mL of a gas were expanded to take up 258 mL, what would be the final temperature of
a gas that originally measured a 300. K?
7. If 359 mL of a gas were contracted to only 268 mL, what would be the initial temperature of
a gas that measured 422 K after the change?
8. If a gas occupying a space of 526 mL changed to 1.1 L, what would be the final temperature
of a gas that was originally at standard temperature?
9. If the temperature of a gas lowered from 526 K to 98.25 °C, what was its final volume if it
started at 16.3 mL?
10. If the temperature of a gas rose from standard temperature to 48.1 °C, what was the initial
volume occupied if the final space was 0.680 mL?
Gay-Lussac’s Law: The relationship between
_________ and ______________.
Variables / Units
Held Constant
Relationship (direct
or inverse)
Relationship in
words
P ________
As ________________goes ______,
____________goes __________.
Graph of
Relationship
Particle Diagram
Gay-Lussac Practice
Problem
A collapsible cylinder contains a gas at 765mmHg
pressure. As external force causes the cylinder to
collapse, the pressure reaches 966mmHg. The final
temperature in the cylinder is 86.2o C. What was the
original temperature of the gas in the cylinder before it
collapsed?
P T V n
Initial
Final
Effect
Gay-Lussac’s Law Practice Problems Name:______________________________
Date:_________________ Period: _______
Solve each of the following problems using Gay-Lussac’s Law. Show all work and put a box
around your answer to receive full credit.
11. If 6.24 atms of pressure were increased to 23 atms of pressure, what would be the final
temperature of a gas that originally measured a comfortable 295 K?
12. If 780. mmHg of pressure were decreased to 528 mmHg, what would be the initial
temperature of a gas that measured 456 K after the change?
13. If 36 lbs/in2 of pressure changed to 861.6 kPa, what would be the final temperature of a gas
that was originally -113 °C?
14. If the temperature of a gas lowered to 50 °C, what was its final pressure if it started at STP
(standard temperature and pressure)?
15. If the temperature of a gas rose from standard temperature to 35 °C, what was the initial
pressure applied to it if the final pressure is 72.5 pounds per square inch?
Name
Date Pd
Unit 2 Worksheet 3 – PVTn Problems
On each of the problems below, start with the given P, V, T, or n; then make a
decision as to how a change in P, V, T, or n will affect the starting quantity, and
then multiply by the appropriate factor. Draw particle diagrams of the initial and
final conditions.
1. A sample of gas occupies 150 mL at 25 ˚C. What is its volume when the
temperature is increased to 50˚C? (P and n = constant)
P T V n
Initial
Final
Effect
2. The pressure in a bicycle tire is 105 psi at 25˚C in Fresno. You take the bicycle
up to Huntington, where the temperature is – 5˚C. What is the pressure in the
tire?
(V and n = constant)
P T V n
Initial
Final
Effect
3. What would be the new pressure if 250 cm3 of gas at standard pressure is
compressed to a volume of 150 cm3 ? ( = constant)
P T V n
Initial
Final
Effect
4. What would be the new volume if 250 cm3 of gas at 25˚C and 730 mm pressure
were changed to standard conditions of temperature and pressure? ( =
constant)
5. Sam’s bike tire contains 15 units of air particles and has a volume of 160mL.
Under these conditions the pressure reads 13 psi. The tire develops a leak.
Now it contains 10 units of air and has contracted to a volume of 150mL). What
would the tire pressure be now?
6. A closed flask of air (0.250L) contains 5.0 “puffs” of particles. The pressure probe
on the flask reads 93 kPa. A student uses a syringe to add an additional 3.0
“puffs” of air through the stopper. Find the new pressure inside the flask.
7. A 350 mL sample of gas has a temperature of 30˚C and a pressure of 1.20 atm.
What temperature would needed for the same amount of gas to fit into a 250 mL
flask at standard pressure?
P T V n
Initial
Final
Effect
P T V n
Initial
Final
Effect
P T V n
Initial
Final
Effect
P T V n
Initial
Final
Effect
8. A 475 cm3 sample of gas at standard temperature and pressure is allowed to
expand until it occupies a volume of 600. cm3. What temperature would be
needed to return the gas to standard pressure?
9. The diagram below left shows a box containing gas molecules at 25˚C and 1 atm
pressure. The piston is free to move.
In the box at right, sketch the arrangement of molecules and the position of the
piston at standard temperature and pressure. Does the volume decrease
significantly? Why or why not?
P T V n
Initial
Final
Effect
Chemistry – Unit 2 Review
To prepare to do well on the Unit 2 test, you should assemble your packet to
review, as well as your lab book, preferably in a small group where you can draw
from each other’s understanding. Here are the key points you should know.
These are not a set of questions to work out, more of an outline- make sure you
understand all aspects!
Energy Think of energy as a quantity that is always involved when there is a change in
the state of matter. When a substance gets hotter or colder or changes phase,
energy is either transferred into or out of the system. One way energy is stored
in a system is kinetic energy (due to the motion of the particles). As particles
move faster, their kinetic energy increases. As the particles move faster, they
tend to move farther apart from one another. Temperature is a measure of the
kinetic energy of the system.
1. Explain why the alcohol level in a thermometer rises when it is placed in a
warmer fluid. (4-step process)
2. Explain why the alcohol level in a thermometer falls when it is placed in a cooler
fluid. (4-step process)
3. Explain how the Celsius scale was devised and why it is not appropriate to use it
when describing the behavior of gases. (review ws 1, PVTn lab)
Kinetic Molecular Theory This theory describes all matter as being composed of tiny particles in endless
random motion. In a solid, the particles vibrate, but are locked into an orderly
array. In a liquid, the particles are still touching but are free to move around
past one another. In a gas, the particles are moving very rapidly and are widely
separated. Using a series of particle diagrams, represent samples of a solid,
liquid, cold gas and hot gas.
Gas behavior Gas pressure is a measure of the collisions of the molecules with the sides of the
container. A barometer is used to measure atmospheric pressure; a manometer
is used to measure the pressure in a container. (review ws 3)
The 4 variables P, V, n, and T are interrelated. Any factor that affects the
number of collisions has effect on the pressure. You should be able to:
4. Predict the effect of changing P, V, n, or T on all of the other variables.
Remember: P α1/ V P αn T αV P αT
5. Explain (in terms of the collisions of particles) why the change has the effect you
predicted.
6. Explain why one must use the absolute temperature scale to solve gas problems.
7. Use factors to calculate the new P, V, n, or T (review ws 3). Make a decision as
to how the change affects the variable you are looking for.
8. Suppose that you lowered the temperature of a gas from 100˚C to 50 ˚C. By
what factor do you change the volume of the gas?
9. Suppose that 25.0 mL of a gas at 725 mm Hg and 20˚C is converted to standard
pressure and temperature. What would be the new volume?
10. Find your copy of The Model so Far and note what modifications in our
particle model of matter we have made in this unit.
