NAME ______________________________NOTES: UNIT 1 (3): THE BASICS OF MATTER & ENERGY 1
Chemistry studies Matter and Energy … So, let’s ask a few important questions…
I) What is matter? *anything which possess mass and volume
A) Law of the Conservation of Mass, Energy & Charge:, (Major Reason #1)
In an isolated system  mass (energy, and charge) cannot be created or destroyed
by ordinary chemical means, however,
energy can be converted into various forms of energy and/or transferred
within the system.
For the first year student, it may be easier to conceptualize this using the dimension, of mass,
rather than energy or charge. This law can be stated in another way.
The total mass of the universe is constant within measurable limits; whenever matter undergoes a
change, the total mass of the products of the change is, within measurable limits, the same as the total
mass of the reactants. What mass you put in...You must get out. http://www.chem.wisc.edu/deptfiles/genchem/sstutorial/Text1/Tx14/tx14.html &
https://www.princeton.edu/~achaney/tmve/wiki100k/docs/Conservation_of_mass.html
Hence: For our work, assume mass, energy and charge are conserved in reaction chemistry.
Think about the LCME this way: You can't clean something without something else getting dirty
What mass you put in, ya gotta get out. It's that straight forward.
Here’s a metaphor for LCME and chemical reactions. Imagine each letter in each word is an element
* DIRTY + ROOM  DORMITORY
* THE MORSE CODE  HERE COME DOTS
* SNOOZE ALARMS  ALAS NO MORE ZS
B) LCM was first articulated well, by Antoine Laurent Lavoisier (and his wife, Marie-Anne).
In a closed system, the mass of the reacted contents equals the mass of the
contents of the system after the reaction is completed.
David's Portrait of Monsieur Lavoisier and His Wife
http://www.bc.edu/bc_org/avp/cas/his/CoreArt/art/neocl_dav_lavois.html
The Lavoisiers carefully massed the reactants (ingredients) and the products
of a chemical reaction. They showed that while the matter may change its
state (e.g. solid reactants may, via new bonds, become gaseous), the total
mass of the matter (products) in the reaction chamber, is the same at the end
as the mass of the matter at the beginning of the experiment. Much later,
(like 125 years later), this idea was expanded to incorporate energy, in terms
of an isolated system
81
1) An isolated system is often described as a set of apparatus &/or chemicals in which no new
mass or energy is allowed to enter, or to exit, once an experiment has been initiated, because
the system of chemicals is isolated from the surrounding environment. A closed system may
allow an energy transfer, but it does not allow a transfer of mass.
When massed before initiation, and after completion, the LCME states that there is no net
change in mass and/or energy content ... although energy may have been converted into
different forms and transferred from or to the matter of the system.
a) Here is a good place to mention: DI GAETANO'S RULE #1:
To most rules, there is at least one exception ...including Rule #1.
(...sometimes there are no exceptions!)
2) and, there are times when mass /energy are not conserved ... but that's with a nuclear
transformation
For example: Try on this cool fact: Via nuclear fusion, the Sun, converts its hydrogen fuel
to helium, and some of the hydrogen / helium matter is converted to energy. It is released
as "solar energy" (400 million, million, million, million watts of energy/minute are released
by the sun. Wonders of the Solar System: Empire of the Sun with Professor Brian Cox [Note: 1 watt = 59.9 joule/minute]
Take Home Message: The LCME is best applied to issues of reaction chemistry and does not apply at
all times to nuclear reactions, under all circumstances. There are nuclear
transmutations in which mass is converted to energy, & vice versa.
3) As well as being described as anything with mass and volume,
Matter has * extensive and intensive physical properties
An Extensive Property is
dependent upon "how much" of the
substance there is Or, it is one that
changes as the size of the sample changes
mass
volume
length
enthalpy (energy)
entropy (disorder)
number of molecules
weight
work or
(mass) (acceleration)
Area
An Intensive Property is
specific to the substance and is
INDEPENDENT of the system's size. An
intensive property scales with changes in,or
to the size of the system .
density
pressure
temperature (for a system in thermal equilibrium)
concentration (for a homogeneous solution)
malleability
melting point
color or odor
any constants pegged to “per gram” or any
molar values e.g. Molar enthalpy, Molar
entropy: These are pegged to a non-variable /
defined or constant mass such as a mole mass
82
Proof 1: Think of ice, but think of a massive, a titanic (?) iceberg, if you will ... and then think of an ice cube from your
freezer. Assume they are both pure water (ice) at -10ºC.
Both of the temperatures are identical ... hence temperature is intensive (it does not depend upon the size of the system)
But, now think about melting the two samples with a meeker burner ... Can you suggest the temperature at which each
sample of ice will melt? (Both will melt at 0 ºC … so melting point is intensive) … Now, think about the amount of
energy required to melt, each sample. Is the amount the same? ... No. Due to the greater mass of the iceberg we can
imagine it will take a phenomenally larger amount of energy to melt the iceberg to liquid water ... hence energy is
extensive (dependent on the size). Note that this energy is calculated by ΔH = mass(Hfusion) … a mass-dependent
equation.
iceberg
vs.
ice cube
http://www.hdwallpapersdepot.com/iceberg-wallpapers.html
Proof 2: Here’s another way to think of this: When you add two variables together and the result doubles then the
property that changed is extensive. Any property that remains the same, is an intensive property.
Imagine a cylinder with a moveable piston with 1 Liter of a gas at STP.
Now, to it, add another 1 liter sample of the same gas at STP.
Think: The volume doubles, the mass doubles. (Thus, each is extensive).
But, the new system will still be at standard temperature (0ºC) and standard pressure at
(101.3kPa), making temperature and pressure (in this case) intensive. The density of the gas is the same (volume scaled
with mass), thus density is an intensive property.
83
PRACTICE:
Think of two identical blocks of ice. Each block is its own system.
Each block is 50.0 grams and at −10 ºC.
system A
Okay, now, add the two blocks together
system B
Got it??
into a single system, (C). Compare C to A (or B)
1) Upon combination, what has happened to the temperature? Did it increase / decrease / remain the
same?
a. Thus, temperature is an * intensive
property
2) What has happened to the number of molecules of ice-water?
a. Thus, the number of molecules is an *extensive
Did it increase / decrease / rts?
property
3) What happens to the amount of energy (q) required to melt C into a liquid, compared to A?
a. Thus, the q (as in q = mcΔT) is an *extensive
property
4) What happens to the melting point of the ice systems as you compare C to A? _______________
a. Thus, melting point is an *intensive
property
5) What has happened to the mass of C relative to A? __________________
a. Thus, mass is an *extensive
property.
6) What has happened to the volume when comparing C to A? _________________
a. Thus, volume is an *extensive
property.
7) What has happened to the density of C relative to A? _________________
a. Thus, density is an *intensive
property
And, that last question raises a really interesting point ….Since the volume increased (or scaled) with the
new, larger mass, the ratio for density (M/V) is constant. Hence, volume changed in proportion with mass
(scales with mass) making the density an intensive property, or independent of the system's size.
Thus, (and here’s the interesting point….) when two extensive properties are divided by each other the
result is an intensive property
e.g ... Mass (extensive) = Density (intensive) I think that is sort of COOL! Ideas intermeshing…
Volume (extensive)
(Note: To check your answers, go online to my website http://scientiaestubique.weebly.com/ and highlight the * marked
areas. Change the font to black, and the answers will appear! Yeah, it’s magic.)
84
Check Your Understanding of the Conservation of Mass& Energy, and Intensive and Extensive
Properties. Answers are at the bottom of the next page
1) Use the table of masses
Masses of Components for a Sundae
Component
Mass
(grams/serving)
1 scoop Chocolate Ice Cream
72.3
1 scoop Vanilla Ice Cream
Hot Fudge
Banana
Whipped Cream
Cherry
71.5
37.0
122.0
2.1
6.7
Show your set up that determines the mass of a hot fudge banana split sundae made with: 2 scoops of vanilla
ice cream, 1 scoop of chocolate ice cream, 3 servings of hot fudge, 1 banana, 2 servings of whipped cream
and two cherries.
Math Set Up:
Total Mass of the Sundae = *2(71.5 grams)+ 1(72.3 grams) + 3(37.0 grams) + 1(122.0 grams) + 2(2.1 grams) + 2(6.7 grams)
ans: 465.9 grams
2) Given the balanced equation representing a reaction for the formation of water: 2 H2 + O2 → 2 H2O
What should be the total mass of water formed when 8 grams of hydrogen (H2) react completely
with 64 grams of oxygen (O2)?
and Think! What is the mass of H2 & O2 before they react completely?
Now, What does the Law of the Conservation of Mass, Energy & Charge say?
Okay ... answer the question....
The mass of water produced should be:
(1)
(2)
(3)
(4)
(5)
less than 18 grams
less than 64 grams, but I can't tell you exactly how much
72 grams
less than 72 grams, but I don't know how much exactly
more than 72 grams, but how much more, is unclear
85
3) A 157.48 gram block of iron, with a volume of 20.00 cm3 has a density of 7.874 grams/cm3, at STP.
Make a statement regarding the density of 60.00 cm3 block of a sample of the same iron at STP. Explain
your thinking. In your response, use either of the terms extensive property or intensive property, and be sure
to support your answer with some sort of "because" statement....
The density of a 60.00 cm3 block of iron ________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
For question 4, determine the “truth” or accuracy of the Assertion and then the accuracy of of the “Reason”.
Then, select a pair of terms from 1-5, which describes the validity of the assertion and the validity and
relationship of the reason.
ASSERTION
1)
2)
3)
4)
5)
REASON
True
True
True
False
False
True statement and it correctly explains / predicts the assertion
True statement but it does NOT correctly explain / predict the assertion
False
True
False
For example:
Mr. D. has brown eyes
because
Mr. D. wears glasses
The answer is "2". Both statements are true. However, the wearing of glasses is unrelated with eye color.
Assertion
*4
The density of a sample of water is
doubled by doubling the mass of water.
Reason
because
Density is an extensive property and must
change as the mass of the sample changes.
5) 20.00 grams of calcium metal has approximately 3.01 x 1023 atoms of calcium. A 40.00 gram sample of
calcium metal has approximately 6.02 x 1023 atoms of calcium. How does this information illustrate whether
the number of atoms is an intensive or extensive property?
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
6) Mass, as in the number of grams, is extensive. The change in energy, as measured by joules (J) is extensive.
The concept of specific heat, is the number of joules per gram, required to raise the temperature of that
gram, by 1 Kelvin. Is specific heat an extensive or intensive property? __________________
Defend your thinking: ________________________________________________________________
_________________________________________________________________________________
86
answers:
1) 2(71.5 grams) + 1(72.3 grams) + 3(37.0 grams) + 1(122.0 grams) + 2(2.1 grams) + 2(6.7 grams)
2) 3
3) .. is the same as the smaller block, because the density of a solid at a particular temperature is a constant (an intensive property) and does not rely upon the volume
(or the mass) of the solid. With the greater volume of 60 cm3 the mass has changed in proportion.
4) both statements are false … for very similar reasoning given in #3
5) The number of atoms is an extensive property. The number of atoms depends upon the “size” of the sample. In the example, a 40.00 gram sample has
more atoms (twice as many, really), than the 20.00 gram sample. The number of atoms, therefore is not a constant, for it changes as the amount of substance changes.
6) intensive … 2 reasons are correct: first, specific heat is J/g which represents the division of two extensive properties, thus producing an intensive property (Proof 2)
OR specific heat is J/g and that is Joules per 1 gram … thus the mass is non-variable and “pegged” or specific, thus independent of changing mass, for
the mass cannot be anything but 1 gram, hence specific heat is intensive.
C) Mass: the extensive property of an object that causes it to have weight in a gravitational field. Mass
is the measure of resistance of an object to a change in its state of motion (inertia). It is
A surprisingly
measured by the force required to give the object a specific acceleration … And on Earth,
tough term to
we use the force that gravity exerts, to measure mass.
define.
1) basic SI unit = kilograms
Note: 1 kg = 1,000 grams
e.g) 0.500 kg = 500. g
Calculate: How many grams are equivalent to 0.25 kg?
Calculate: How many kilograms are equal to 75 grams?
2) Weight: * pull of gravity on the mass
a) SI unit:
kg·m/s2 or Newton
English unit: pound (lb)
When we measure an object on a balance, we are measuring against a standard mass. And
while it isn’t surprising that mass and weight are used interchangeably –it is incorrect to
do so, really. You see, the concept of “weight” becomes important, only when the force
exerted by gravity is changed. Since that force is a constant from the balance to your desk
(unless your desk is at the top of Mt. Everest), the term weight is not wholly appropriate.
However, when the gravitational force changes, the weight of an object from one point to
another, can change, but its mass is essentially constant.
b) Think of a an astronaut weighing 120 lbs here on Earth. We all know that when she gets to the
Moon, she will experience a sense of weightlessness, to some degree. She can ...jump higher,
hit a golf ball farther.... So, what has happened? Did she lose mass? If so, which part of her
body did she have to cut off? WHAT!? Is there any another explanation?
Check out http://www.exploratorium.edu/ronh/weight/ for your weight on other planets!
87
D) Volume: the amount of physical space, the matter occupies
1) regular cube: Length x Width x Height
* e.g.
1 cm x 1 cm x 1 cm = 1 cm3 or 1 cc
2) Archimedes, King Hiero II of Syracuse, and Water displacement
3) 1 Liter = 1,000 mL = 1,000 cm3 (cubic centimeter or cc)
….And the on-call doctor yelled …. “Get me 10 cc's of epinephrine!”
https://naeophyx.wordpress.com/tag/archimedes
Demo Time!!! Maestro, A Little Music, Please....
cubic decimeter
http://www.chem.uiuc.edu/webFunChem/volume/volume3.htm
http://core.ecu.edu/chem/chemlab/equipment/egcylinder.htm
http://core.ecu.edu/chem/chemlab/equipment/evolumetricflask.htm
4) solids and liquids tend to have * constant volumes
a) If you transfer a solid object from one vessel to a different yet larger vessel,
the volume of the solid
*
remains the same
b) When you transfer 100 mL of water from a 400 mL beaker to a 1,000 mL beaker,
the volume of the water (liquid) * remains the same
5) gases have no constant volume. The volume of a gas may be reduced or expanded
dramatically, as the conditions of temperature and pressure change, (they may be
compressed or expanded, dramatically)
a) The volumes and pressures of gases are subject to change as pressure and
temperature change.
b) Can you come up with a few examples of when gases are compressed or allowed to
expand? Anyone? Anyone? … Bueller? … Bueller?
* think: s.c.u.b.a., hot air ballooning, human breathing, ear's popping, home heating
systems, aerosol spray cans, butane lighters , phlebotomy etc...
88
BREAK DOWN INTO GROUPS OF TWO. Answer each question, by selecting or by providing the most
correct answer. Use your notes.
1) During all chemical reactions, mass, energy
and charge are
(1) absorbed
(2) formed
(3) conserved
(4) released
4) Given the balanced equation representing a
reaction: H+(aq) + OH-(aq) → H2O(l) + energy
In this reaction, there is conservation of
2) Given the balanced equation representing a
reaction:
(1) mass, only
(2) charge and energy only
(3) mass and charge, only
(4) charge, energy and mass
Mg(s) + Ni2+(aq) → Mg2+(aq) + Ni(s)
What must be the total electrons lost by Mg(s)
when 2 electrons are gained by Ni2+ ?
(1) 1
(2) 2
(3) 3
5) A 1.0 gram sample of which element will
uniformly fill a closed 2.0 Liter container
at STP?
(4) 4
3) Given the balanced equation representing
a reaction: C + O2 → CO2
(1) Helium(gas)
(3) Mercury(liquid)
(2) Lead(solid)
(4) Carbon(solid)
6) The gravitational force of Jupiter is approximately
What is the total mass of CO2 formed when
24 grams of carbon react completely with
64 grams of oxygen?
(1) 88 grams
(2) 40 grams
(3) 56 grams
(4) 92 grams
2.5 times greater than Earth’s. What effect would
the greater gravitational field have on someone’s
mass and on their weight?
_________________________________________
_________________________________________
Multiple Choice Answers: 1) 3
2) 2
3) 1
4) 4
_________________________________________
5) 1
_________________________________________
7) Which reaction is improbable, assuming the complete reaction of only the pure samples of the reactants, in a closed
system? Defend your thinking.
(1)
3 Fe + 4 H2O  4 H2 + Fe3O4 + 2 CaSO4
(2)
2 Al + 3 Fe(NO3)2 
2 Al(NO3) 3 + 3Fe
Defense: __________________________________________________________________________
___________________________________________________________________________________
8) Describe what you understand by the term: closed system: ______________________________________________
__________________________________________________________________________________________
89
What determines volume? Can an object have a greater mass than a second object AND YET
have the same volume?
Things that
make you go
HMM!
What’s your hypothesis? I think an object can / cannot have different masses
yet have a constant volume.
1) Grab a 400 mL beaker and fill it with about 200 mL of water.
2) Mark the level of water with some masking tape
a) Based on the beaker markings, what is the approximate volume? _________mL
(it should be close to 200mL)
3) Fill a film canister with 30 pennies. Cap the canister and carefully place it in the
water.
a) What has happened to the water level? _______________
b) What is the volume of the canister filled with pennies? _________mL
Mark the new level with another piece of tape.
4) Carefully remove the canister. Replace any lost water to the beaker, using your
tape marking as a guide.
5) Remove 15 pennies from the canister, so as to reduce the overall mass by half.
a) PREDICT: How much do you think the water level will change once you put
the canister back into the beaker?
_____________________________________________________________________________________________________
6) Replace the cap and put the canister back into the beaker of water.
a) What has happened to the water level? __________________
b) What is the volume of the canister with ½ the number of pennies? ____mL
Which statement do your results support?
___ a) The volume of water an object displaces depends only on the dimensions of the object and
NOT on the mass of the object.
___ b) The volume of water an object displaces depends on BOTH the dimensions of the object
an the mass of the object.
Question: In your opinion then, what is more responsible for the displacement of the water…??
___a) the volume (dimensions) of the sealed canister
___b) the mass of the pennies in the canister
90
c) Scientists adopted a standard used to compare and contrast
gas samples, because the volume and pressure of a gases
can be changed.
Pushing down the
plunger increases
pressure
STP: Standard Temperature and Pressure (Table A)
Standard
Temperature
Standard Pressure
You must know 2 values, in 2
different systems of measurement
You must know 2 values, in 2
different systems of measurement
0 C = 273 K
1 atm = 101.3 kPa
Note: Standard Temperature
and Room Temperature are
different. Room temperture
ranges from 20ºC to 23ºC
Note: There are other, older
equivalent values with which
I want you to be familiar
760 torr = 760 mmHg
d) Let's look at the Kelvin Temperature Scale:
i) Absolute Zero = 0 K or  -273ºC
The temperature of an object depends on how fast the atoms / molecules or
ions which make up the object can shake, or oscillate. As an object is
cooled, the oscillations of its atoms / molecules / ions slow down. For
example, as water cools, the slowing oscillations of the molecules allow
the water to freeze into ice. In all materials, a point is eventually reached at
which all oscillations are the slowest they can possibly be. The
temperature which corresponds to this point is called absolute zero. Note
that the oscillations never come to a complete stop, even at absolute zero.
http://www.pa.msu.edu/sciencet/ask_st/012992.html
For an interesting romp through the issues of temperature, check out
PBS's NOVA website: http://www.pbs.org/wgbh/nova/zero/ . You can
investigate some interesting issues such as: Is there an absolute hot????
And you can figure out how a refrigerator works .... It's not bad!
ii) Conversion: K = C + 273
(see Table T of your Reference Charts)
10C = * 283
Kelvin
25C = * 298
173 K = * -100
ºC
500 K = * 227
Kelvin
ºC
91
iii) Origin of the Kelvin Temperature Scale (Named after Lord Kelvin: (William Thomson 1824-1907)
Imagine a 1 Liter container of gas with a moveable piston, so that as the gas
can expand or decrease in volume, while pressure is kept constant.
With such a piston, and a trapped gas, Kelvin noticed that for every 1C change in
temperature (up or down) the volume changed (up or down) by 1/273 (really 1/273.16)
of the original 1 Liter volume.
Volume = 1 Liter
100ºC
0ºC
At 0C
increase temp to 100C
Volume = 1 + 100
273
0ºC
-100ºC
decrease temperature to -100C
Volume = 1 – 100
273
0ºC
-273 C
decrease temperature by 273C, to -273 C
Volume = 1 - 273 = 0 L
273
92
I often say that when you can measure what you are speaking about, and express it in numbers,
you know something about it; but when you cannot measure it, when you cannot express it in
numbers, your knowledge is of a meager and unsatisfactory kind.
Lord Kelvin (William Thomson, 1st Baron) (1824-1907) In: Popular Lectures and Addresses, London, 1889
Okay, so, let’s run the numbers…
1) When the Celsius temperature doubles from 20 ºC to 40ºC does the Kelvin temperature double? * NO
2) To what temperature must a system at 20ºC be raised in order to have effectively "doubled the
Kelvin temperature?
* Since 20°C = 293K ... the temperature must be raised to 586 K OR 313°C
3) What is the Kelvin temperature equivalent to the normal boiling point of water? *373 K
4) What is the Kelvin temperature equivalent to the freezing point / melting point of water? *273K
5) When 1 Liter of gas is cooled from 273K to 272K you would expect a change in volume by *1/273 of a L
6) Challenge: The pressure of a fixed amount of gas kept at constant volume (as in a sealed vessel)
varies proportionally with its absolute (the Kelvin) temperature. Assume 300. L of a gas
sealed in a steel can at with a pressure of 1.5 atm at -20.℃. To what Kelvin temperature
must the gas be heated, in order to exert a pressure of 3.0 atm? What is the temperature
in Celsius?
93
e) Let's shift to what we mean by the phrase: Standard Pressure
Consider this: We live at the bottom of an ocean of air...
http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_09.html
A column of air 1.00 m2 in cross-sectional
area extending from the earth’s surface
through the upper atmosphere has a mass
of about 10,300 kg, producing an
atmospheric pressure of approximately
101.3kPa (also called, 1 atmosphere or 1 atm)
http://tonydude.net/NaturalScience100/Topics/2Earth/3atmosphere.html
94
Now... How does pressure change when we leave our ocean of air, and
dive into our ocean of water???
Surface Air Pressure = 1 atmosphere (1 atm) or 101.3 kPa
10 meters underwater = 2 atmospheres
(or 202.6 kPa)
Think about the math …. Assuming:
Pressure = Force = mass (acceleration)
Area
Area
As we go deeper below the surface of the
ocean, there is an ever increasing mass of
water above our “area”. Couple this
increasing mass of water, to the mass of the
gaseous atmosphere it is not too surprising
to conclude that the pressure is increasing!
Personally, I am still in wonderment, that any
cellular creatures can live and thrive 2,100
meters (and more) below the surface of the ocean
at the level of the hydrothermal vents! e.g. frilled
shark, giant tube worms, vampire squid, pacific
viperfish.... How does that work??? Really … I don’t
get it…
20 meters = 3 atm (or 303.9 kPa)
underwater
30 meters = 4 atm (or 404.12 kPa)
95
The Concept of Density
 READ THIS  Read the following portions of an article written by Dr. S. J. Hawkes of Oregon State
University. The article is written for teachers ... so it may sound a bit odd to your ear ... being
that you are the student ... yet I want you to try to concentrate on his main point. Many can do
the math of density (quantitative as in, quantity or math), but fewer seem to be able to
grasp the qualitative (as in quality or character) issues of density. The article appeared in the
Journal of Chemical Education, Jan 04 p 14-5 HIGHTLIGHT IMPORTANT IDEAS!!!
N
eanderthals knew no math yet knew that rock has a higher density than wood, and used that
knowledge to their advantage. Too many students believe that density is the result of the arithmetic
operation of dividing mass by volume. This makes density an abstraction and prevents them from
realizing, among other things, that compressing something must increase the density. They have not
absorbed the concept that “density” refers to the “denseness” (compated-ness) with which mass is
packed. End-of-chapter questions about density are almost exclusively exercises using the
equation: D = M
V
Many students who can use this equation without any difficulty find questions that test the concept of density to
be difficult or even unfair. They do not perceive a meaning to the numerical value of a compound’s density. Yet
as an aspect of chemistry, the qualitative concept of density is at least as important as its calculation or
measurement. We need to teach the following principles and to help students to perceive that the first one
implies all the others:
• First one: Density is a measure of the compactedness with which mass is packed.
• The more closely atoms are packed the higher will be the density. This has a tremendous influence
as well on electrical conductivity ... because electrons will be closer to each other.
• Other things being equal, compounds of atoms with greater atomic mass are denser.
• Compression increases density.
• Density of an object does not depend on its size or shape. As the mass of a substance increases,
the volume it occupies tends to increase proportionally.
• “Heavier” as applied to a substance is synonymous with “greater density” when compared to a
different substance of equal volume.
Students who can reason with ratios, which regretfully is less than half of all students, will perceive that all the
above follow from d=m/V. Most will not perceive this, and will see no connection between m/V and the concept
of density as denseness.
**************************************************
96
E) Density = Mass
Volume
1) a derived unit: (a unit not measured directly but is the result of a mathematical equation)
a) Water: Density = 1.00 g/mL (or 1.00 g/cm3) at 4.00C
b) a cm3 is a cubic centimeter: This unit is often used when describing the volume of a
solid (L x W x H) or most simply in the case of a cube:
1 cm x 1 cm x 1 cm = a volume of 1 cm3
i) other volume units: m3, mL, L
Did You Know…?
c) at ~ 4.00 C, 1 mL of water = 1 cm3 = 1 gram in mass
2) The density of an object is a ratio of its mass to its volume.
a) The density of a substance does NOT change, just because the mass of the
substance changes.
b) As the mass increases, the volume increases, proportionally that is... as the mass of
a substance increases, the volume increases making it a direct (a proportional)
relationship.
Volume as a function of Mass
inverse relationship
volume (cm3)
mass (grams)
Since they change proportionately, the density of a substance is * a constant (intensive)
at a specified temperature and pressure (these can affect density)
c) The density of an object does not depend upon its size or shape...
d) The density of a solid can change with temperature, but not pressure (a little lie)
The density of a liquid can change with temperature and pressure (but we ignore this)
i) as mass increases, * the volume increases proportionally.
or: mass  volume
e) What about the density of a gas?
(hint: take a look at the diagrams of the pistons at the top of p. 88)
_____________________________________________________________
97
3) Go to Table S of your NYS Expanded reference tables.
a) What is the density of aluminum? ______________
b) What is the density of neon? _____________
c) Based upon the density equation and the values from your charts, a 25.0 gram sample
of which element has the smallest volume?
i) carbon
Things that
make you go
HMM!
ii) titanium
iii) zinc
iv) gold
Is this a math problem or a theory problem?
What do/does each choice have in common?
What concept links mass and volume?
d) At STP, a 7.49-gram sample of an element has a volume of 1.65 cubic centimeters.
The sample is most likely
i) Ta
4) Chemistry connection to:
ii) Ti
iii) Te
iv) Tc
Environmental Science, Earth Science and Biology.
Density and Water....
a) Liquid water is the densest at approximately 3.98 ºC.
(close enough to say 4 ºC)
At this temperature, water has a density of 1.00 grams/mL
Below this temperature, and above this temperature, a sample of H2O has a
density less than 1.00 g/mL
b) By the way.... Does anyone know...
i) the percentage of the Earth's surface that is made of water? * 71
ii) the percentage of that amount that is drinkable (potable)water? * 3
iii) the percentage of that amount, that is actually available? * 1
%
%
%
98
PRACTICE:
1) Consider two cubes of pure iron
Barbara has 20 cm3 of iron and Meghan has 60 cm3 of iron. Which statement is FALSE?
___ Meghan’s sample has 3 times the density of Barb's sample.
___ Meghan's sample has 3 times the volume of Barb’s sample.
___ Meghan's sample has 3 times the mass of Barb's sample.
Defend your reasoning _________________________________________________________
2) Consider the following: Alicia has a pure silver coin with a volume of 120.24 mL.
What value do you need to know in order to calculate the mass of the coin? ___________
In which table of your reference charts can you find this value? __________
3) The density of water is greatest at 3.98C with a value of 1.00 g/cm3.
When any mass of pure water freezes, the sample's volume will expand by 9.10%. Assuming a
10.0 gram sample of water and its frozen form, ice, calculate the density of the ice.
Hint: Given the information, you should be able to determine the volume of the water sample. You should then be able to determine the volume of the ice.
* You must realize that you have a mass [10.0 grams of water] and a density of water [1.00g/mL]
❶ solve for the volume of liquid water D = M where: 1.00 g/mL = 10.0 grams
V
Vwater
so Vwater = ______mL
Once you have the volume of the water, you know that as it freezes that volume of water will increase by 9.10%
Thus you must ❷ find the volume of ice. To do this you must find the change in volume and then add it to the original
volume of the water you calculated in ❶.
That is:
The original Volume of water + the change in the volume = volume of the ice
So, you need to figure out what is 9.10% of the Volume of water … Take that answer and add it to the Volume of water,
this gives you the volume of ice …. OR you could look at it like this:
[(Vwater )(0.0910) + Vwater] = Vice
Once you have the volume of the ice … you can ❸ recalculate the density of the ice, using the mass (it never changed) …
and the new volume of the ice …. It should work out to be close to 0.9166 g/mL or 0.9166 g/cm3
a) Were you to drop an ice cube into a glass of room temperature water, based upon
your life experience, would the ice cube sink or float? _____________
b) Based upon your calculation to 3) should the ice cube sink or float? ___________
99
4) Nathan determines the volume of a small piece of silver using water displacement. The graduates are
shown. The density of silver is 10.500 g/cm3. Calculate the mass of silver.
5) Some elements exist with modifications to the arrangement and bonding of their atoms. They are
called allotropes of each other. For instance, O2(g) and O3(g), called ozone are allotropes of each other.
Diamond and graphite (as in your pencil or tennis racket) are both allotropes the element carbon. The
density of carbon in the form of diamond is 3.52 g/cm3. Graphite has density of 2.67 g/cm3. What
does it tell you about the arrangement of carbon atoms in diamond vs graphite?
____________________________________________________________________________
____________________________________________________________________________
a) Assume 5.00 grams samples of each carbon allotrope. Which one would have the
greater volume? ____________________ Defend your reasoning _________
__________________________________________________________________
6) Which member of the following pairs has the greater density? (Circle one member of each pair
as the answer) One pair is a trick ... in one of the pairs both examples have the same density ... can you
figure it out and why?
set 1) H2O(l) or
H2O(s)
set 2) helium
or
air
set 3) olive oil
or
H2O(l)
set 4) 115 L of CO2(g) at STP
or 1 L of CO2(g) at STP
Defend your thinking for the "trick pair": Be sure to have a “because” statement that cites data, a specific theory from your notes,
cites an equation or uses an appropriate metaphor.
___________________________________________________________________________
__________________________________________________________________________
100
7) Consider separate samples of 3.0 cm3 of gold, lead, iron and aluminum.
Which of the following is false?
1)
2)
3)
4)
The gold has the greatest volume.
The aluminum has the smallest mass.
All of the samples have different masses
The silver has a mass of 32 grams.
8) Which of the following would float on pure water at a temperature of 3.98℃?
1)
2)
3)
4)
A substance with a mass of 1.38 g. and a volume of 1.33 mL
A substance with a mass of 534.23 grams and a volume of 522.3 mL
A substance with a mass of 22.64 g and a volume of 3.35 mL
A substance with a mass of 418.23 g and a volume of 436.2 mL
9) Use the following diagram and your grasp of the course work to complete the question.
The ruler is in centimeters.
From: http://www.syvum.com/cgi/online/serve.cgi/members/gillilandd/quizzes/density.tdf
What is the approximate mass of the iron cube?
1)
2)
3)
4)
2.8 grams
4.0 grams
3.7 grams
5.4 gram
10) As the pressure on a gas is increased, the volume of the gas decreases inversely. Double
the pressure, and cut the volume to ½ of the original volume. What change occurs to the
density of the gas?
Ans: 1) the first statement is false 2) density would help ... look up on your reference table 3) 0.917 g/cm3, float ....float,
4) 38.85 g
5) The atoms of carbon in graphite are not as tightly packed (or are arranged with a greater occupied volume) that the atoms of carbon in a diamond.
5a) Graphite … defense: look at the math of D = M/V or use the concept that the atoms of graphite are not as tightly packed as those of diamond.
6) 1) H2O(l) 2) air 3) H2O(l) 4) trick pair … the density of a substance is an intensive property at the same temperature and pressure. 7) 1 8) 4
9) 2, using a density of 7.834 g/cm3 10) It doubles, for it changes directly with changes in pressure … As the volume decreases the density must
increase.
101
Question 11 uses two unfamiliar terms. They are 1 mole and 1 mole mass. These terms are closely related. You
do not need to really grasp what they are ...yet! Simply know that they are a standard measurement of the mass
of a substance in grams.
11) More Practice: The table below gives the molar mass and density of a number of gases at STP.
Gas
oxygen
Density and Mass
Mass of 1 mole (g) Density (g/L) at STP
32.0
1.43
(dioxygen gas)
carbon dioxide
ethane
hydrogen
44.0
30.0
2.0
1.96
1.34
0.089
64.1
17.0
38.0
2.86
0.759
1.70
(dihydrogen gas)
sulfur dioxide
ammonia
fluorine
(difluorine gas)
a) Plot the above data with density as a function of mole mass. Plot the points, and
please identify each set of coordinates by drawing a circle around the darkened
point of intersection. eg) 
 Title the graph appropriately using the axes in the names & label each axis in pen.
 Draw a "best fit line" through the points in pencil.
b) Using the graph, what is the mass of 1 mole of an unknown gas at STP with a
density of 1.10 g/L? ____________
c) Calculate the per cent error (use your reference charts to find the equation) between
your answer obtained from reading the graph, in b) and an accepted value of 26.2g.
Equation:
Substitution
Answer: _________________
d) The density of air at STP is 1.29 g/L. Three balloons filled with sulfur dioxide, carbon
dioxide, and hydrogen are released into the Earth’s atmosphere (air). Using data found
in the above table, predict if the balloon will float upward or will sink in air.
The sulfur dioxide balloon will _____________________________________
The carbon dioxide balloon will _____________________________________
The hydrogen balloon will _________________________________________
Answer 11) sink, sink, float
102
Title
Density as a function of Mole Mass
103
NAME ____________________________________________ TRY THIS! DENSITY AND PROPERTIES
Directions: Use your grasp of physical chemistry and your ability to use evidence to complete each of the
following questions.
___1) Which of the following is NOT a physical property?
1) liquid nitrogen (N2(l)) boils at -196°C
2) sugar dissolves in water
3) gold melts at 1064°C
4) gasoline burns in air
5) a compound of copper is blue
In order to determine the answer, what is the critical question you wish to ask / or what is the critical
piece of information you wish to know?
_____________________________________________________________________
___2) A piece of polypropylene rope (used by water skiers) floats on water, whereas a terephthalate polymer
from a soda bottle sinks in water. Using the polymers and water, order the three materials, from least
dense to most dense.
____________________________________________________________________________
least dense
most dense
What knowledge/information do you possess that allows you to answer the question, successfully?
________________________________________________________________________________
3) According to Mark Winter, at http://www.webelements.com/mercury/
Mercury is the only common metal liquid at ordinary temperatures. Mercury is sometimes
called quicksilver. It rarely occurs free in nature and is found mainly in cinnabar ore (HgS)
in Spain and Italy. It is a heavy, silvery-white liquid metal. It is a rather poor conductor of
thermal energy as compared with other metals but is a fair conductor of electricity. It alloys
easily with many metals, such as gold, silver, and tin. These alloys are called amalgams.
Which of the following is an extensive property of a sample of mercury?
1)
2)
3)
4)
shiny surface
melts at 234.22 K
has a density of 13.6 g/cm3
has a volume of 27.1 cm3
In order to determine the answer, what is the critical question you wish to ask / or what is the critical
piece of information you wish to know?
_____________________________________________________________________
104
For questions 4) - 6) Use the following passage, and your grasp of chemistry.
Turquoise is a semi-precious gemstone (and one of the birthstones for December!). A particular piece of
turquoise is a 2.5 grams blue-green solid, with a density of 2.65 g/cm3.
4) Calculate the volume of the piece of turquoise. Record the volume, with an appropriate unit. Show your
work. Watch your sig figs.
_______________
5) Identify the information for the piece of turquoise which are qualitative and those which are quantitative.
qualitative: __________________________________________________________
quanitative: __________________________________________________________
6) Identify the information for the piece of turquoise which are extensive and those which are intensive.
extensive: ___________________________________________________________
intensive: ____________________________________________________________
7) Identify the following as either physical changes or chemical reactions
a) ____________________ the desalination of sea water into pure water and salt
b) ____________________ the production of SO2(g) from the combustion of coal
c) ___________________ the tarnishing of silver metal, with the formation of AgS(s)
d) ___________________ dry ice (CO2(s)) subliming to CO2(g)
e) ___________________ the decrease in the density of a sample of mercury as it is heated from
-100K to 288 K
f) ____________________ KNO3(s) dissolving in water
In order to determine the answer, what is the critical question you wish to ask / or what is the critical
piece of information you wish to know?
_____________________________________________________________________
Answers:
1) 4 The critical question I want to ask is which of these situations, is a chemical reaction or which verb suggests that there the situation results in
new bonds (new compounds) being made?
2) polypropylene rope, water, terephthalate polymer … the floating and/or sinking in water as an indication of relative density compared with that of
water.
3) 4 I want to ask which of the choices represents a dimension or calculation which changes as the amount of matter changes...because that would
be an extensive property.
4) 6.6 cm3
5) semi-precious gemstone (maybe) … blue-green color, solid ….. mass of 2.5 grams, density of 2.65 g/cm3
6) mass of 2.5 grams, (you could include, as well, the volume calculated in question 4) …… density of 2.65 g/cm3 , blue-green color
7) a) physical change b) chemical reaction c) chemical reaction d) physical change e) physical change
f) physical change
/ Is there a change in the bonding? / Are new bonds being made ?
105