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Unit 1
Fundamental Concepts
Chemistry 020, R. R. Martin
1 Introduction
Q: What is chemistry?
A: The study of matter and its properties at the atomic
and molecular levels.
Matter is anything that has mass and occupies space.
It exists in three phases (= states):
solid: rigid shape and fixed volume
liquid: fixed volume but not rigid in shape
gas: neither fixed volume nor rigid shape
2 Properties of Substances
Physical properties: Can be observed without
changing the chemical identity of a substance
(i.e. without making or breaking covalent bonds)
Examples:
Melting point and boiling point. A substance that melts
at 0°C and boils at 100°C is most likely water.
Solubility - table salt (NaCl) is easily dissolved in
water, copper (Cu) is not.
1
Color: Substances are colored if they selectively
absorb certain wavelength regions of the visible
spectrum.
Chemical properties are observed when a substance
takes part in a chemical reaction. Mercury II oxide
decomposes to mercury (Hg) and oxygen when
heated to 600°C.
Physical and chemical properties can be used to
identify a substance.
We indicate the physical state of matter by following
its formula with one of these symbols:
(s)
solid
(l)
liquid
(g)
gaseous
H2O(l): liquid water
H2O(s): ice
H2O(g): water vapor
Element: A type of matter that cannot be broken
down into two or more pure substances. Alternatively:
A substance in which all atoms have the same atomic
number.
Every element is identified by its symbol, e.g.
C (carbon), Cu (copper), He (Helium), Hg (mercury)
2
3 Atoms
Atom: a neutral species consisting of
• Protons (particles carrying one positive charge (+1),
and a mass of ~1 amu [atomic mass units])
• Neutrons (neutral particles, mass ~1 amu)
Protons and neutrons form the atomic nucleus
• Electrons (e-, particles carrying one negative
charge (-1), their mass is small, ~1/2000 amu).
If you want, you can imagine that the electrons “orbit”
around the nucleus, like the planets around the sun.
Example - Helium atom: 2 protons, 2 electrons, 2
neutrons, mass ~ 4 amu
In an atom, the number of electrons is equal to the
number of protons, so that the overall charge is zero.
Positive and negative charges attract each other, that
is why electrons are “bound” to the nucleus.
(The nucleus is extremely small, most of the atom is “empty”. The
diameter of an atom is 10,000 times that of its nucleus).
The chemical properties of an atom are determined
by its electrons. BUT the number of electrons is
determined by the number of protons in the nucleus.
We can define the atomic number Z:
3
Z = number of protons
Remember the definition of element: “A substance in
which all atoms have the same atomic number”
Symbol
H
He
Li
Be
B
C
N
O
F
Ne
Element name
Hydrogen
Helium
Lithium
Beryllium
Boron
Carbon
Nitrogen
Oxygen
Fluorine
Neon
Z
1
2
3
4
5
6
7
8
9
10
Example: all carbon atoms have six protons and six
electrons
The mass number A of an atom is obtained by adding
up the number of protons and neutrons in the
nucleus.
A = number of protons + number of neutrons
4
We can thus describe the composition of the nucleus
by a nuclear symbol; it is written in the following way:
Mass Number
A
Z
Atomic Number
X
Element symbol
The number of neutrons is therefore given by A – Z.
Examples:
12
Carbon: 6
C
235
Uranium: 92
often called C-12
U
often called U-235
However, not all atoms of one element have the same mass. They can
differ in their number of neutrons.
Atoms that contain the same number of protons, but a different number
of neutrons are called isotopes.
5
Example: There are three isotopes of hydrogen
1
1
H ”protium” – zero neutrons usually what we mean when we say
hydrogen (of course it is most commonly found as the molecule H2)
(This is the most common isotope of hydrogen)
2
1
H
”deuterium” – one neutron
(Sometimes the symbol “D” is used instead)
3
1
H ”tritium” – two neutrons
(Sometimes the symbol “T” is used instead)
For the most part, isotopes of the same element have very similar
chemical properties because they have the same number of electrons.
Note: Some atoms are radioactive and decay to form different elements (transmutation)
14
6C
→ 7N14 + e-
6
The mass of atoms (and molecules) can be measured by mass spectrometry.
It shows that chlorine consists of two isotopes:
35
17
Cl
mass 34.97 amu, with 75.53% abundance
37
17
Cl
36.97 amu, with 24.47% abundance
(Note: these are atom %'s, not mass %'s)
The mass of an element is usually represented as the weighted average
of all its isotopes (i.e. in the periodic table, see below)
For Cl:
34.97 amu × 0.7553 + 36.97 amu × 0.2447 = 35.46 amu
Some elements have only one stable isotope, e.g. for
sodium
23
11
Na
is the only isotope.
7
For carbon there are two:
12
6
C
13
~ 99% abundance, 6
C
~ 1% abundance
12
6
We define the mass of one C atom as exactly 12
amu (i.e. 12.0000000000000000000000000000 … amu)
8
EXAM QUESTION: Nov. 2004, Q1
Naturally-occurring magnesium consists of three
isotopes. Of the three, 24Mg, atomic mass 23.985
amu, is 79.0% abundant, and 26Mg, atomic mass
25.983 amu, is 11.0% abundant. The number of
neutrons in the nucleus of the third isotope is
A) 10
B) 12
C) 13
D) 15
E) 16
The periodic table gives an average atomic mass for Mg of 24.31
amu and atomic # = 12
Let the third isotope = xMg. Its abundance must be
1 - .79 -0.11 = 0.1
Now:
Average mass Mg = Fraction24Mg(mass 24Mg )
+ Fraction26Mg(mass 26Mg )
+ FractionxMg(mass xMg )
OR:
24.31 = .79 x 23.985 + 0.11 x 25.983 + 0.10(mass xMg )
mass xMg = 25.04 or 25Mg
25 = #of Protons + #of Neutrons = 12 + #of Neutrons
#of Neutrons = 13
9
4 Brief Introduction to the Periodic Table
The “official” Chem 020/023 periodic table is shown on the
next page. It will be provided to you for exams. Learn how to use it !!!
The horizontal rows in the table are called periods.
As we go through these periods, there is a certain periodicity that is similar for
most rows of the table.
First period:
Second period:
H
Li
Be B
C
N
O
F
He
Ne
The vertical columns are called groups (or “families”)
Elements in the groups 1,2,13,14,15,16,17,18 are
called main group elements.
This is a new nomenclature; 13 used to be 3, 14 used to be 4, etc.
Elements in group 1 are called alkali metals.
Elements in group 2 are called alkaline earth metals.
(owing to their tendency to form basic (=alkaline) hydroxides, i.e. Ca(OH)2)
Elements in groups 3 - 12 are called transition metals.
Elements in group 17 are called halogens.
All halogens form stable molecules consisting of 2 atoms (F2, Cl2)
Elements in group 18 are called noble gases. “Noble”
indicates that they are very unreactive.
They do not form stable molecules consisting of two atoms. He does exist, He2
does not exist. Ar does exist, Ar2 does not exist.
Elements 58-71 are called lanthanides, 90-103 are called actinides.
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Periodic Table of the Elements
1
18
1
H
1.008
2
13
14
15
16
17
2
He
4.003
3
Li
6.941
4
Be
9.012
5
B
10.81
6
C
12.01
7
N
14.01
8
O
16.00
9
F
19.00
10
Ne
20.18
11
Na
22.99
12
Mg
24.31
3
4
5
6
7
12
13
Al
26.98
14
Si
28.09
15
P
30.97
16
S
32.07
17
Cl
35.45
18
Ar
39.95
19
K
39.10
20
Ca
40.08
21
Sc
44.96
22
Ti
47.88
23
V
50.94
24
Cr
52.00
25
Mn
54.94
26
Fe
55.85
27
Co
58.93
28
Ni
58.69
29
Cu
63.55
30
Zn
65.39
31
Ga
69.72
32
Ge
72.61
33
As
74.92
34
Se
78.96
35
Br
79.90
36
Kr
83.80
37
Rb
85.47
38
Sr
87.62
39
Y
88.91
40
Zr
91.22
41
Nb
92.91
42
Mo
95.94
43
Tc
(98)
44
Ru
101.1
45
Rh
102.9
46
Pd
106.4
47
Ag
107.9
48
Cd
112.4
49
In
114.8
50
Sn
118.7
51
Sb
121.8
52
Te
127.6
53
I
126.9
54
Xe
131.3
55
Cs
132.9
56
Ba
137.3
57
La
138.9
72
Hf
178.5
73
Ta
180.9
74
W
183.9
75
Re
186.2
76
Os
190.2
77
Ir
192.2
78
Pt
195.1
79
Au
197.0
80
Hg
200.6
81
Tl
204.4
82
Pb
207.2
83
Bi
209.0
84
Po
(209)
85
At
(210)
86
Rn
(222)
87
Fr
(223)
88
Ra
(226)
89
Ac
(227)
104
Rf
(261)
105
Db
(262)
106
Sg
(266)
107
Bh
(262)
108
Hs
(265)
109
Mt
(266)
110
111
112
(269)
(272)
(277)
58
Ce
140.1
59
Pr
140.9
60
Nd
144.2
61
Pm
(145)
62
Sm
150.4
63
Eu
152.0
64
Gd
157.3
65
Tb
158.9
66
Dy
162.5
67
Ho
164.9
68
Er
167.3
69
Tm
168.9
70
Yb
173.0
71
Lu
175.0
90
Th
232.0
91
Pa
(231)
92
U
238.0
93
Np
(237)
94
Pu
(242)
95
Am
(243)
96
Cm
(247)
97
Bk
(247)
98
Cf
(251)
99
Es
(252)
100
Fm
(257)
101
Md
(258)
102
No
(259)
103
Lr
(260)
8
9
10
11
11
Elements in the same group tend to show very similar
chemical properties, e.g.
“Noble Gases” (group 18): He, Ne and Ar do not react with
any other substances.
Li, Na, K all react violently with water according to
2 Na + 2 H2O Æ 2 NaOH + H2
+ HEAT
Metals and Nonmetals
The diagonal line starting at B and ending at Po separates
the metals from the nonmetals.
Metals are on the left; nonmetals are on the right.
Metals are “shiny“ solids that conduct electric current (very
low resistance); they also conduct heat very well.
Nonmetallic solids tend not to conduct electric current
(exception: carbon as graphite). Many nonmetals are
gases (of course gases do not conduct electric current).
The elements very close to the diagonal line are difficult to
classify
B
Si
Ge
As
Sb
Te
Boron
silicon
germanium arsenic
antimony
tellurium
They have electric conductivities between those of metals
and nonmetals and are often called metalloids. Especially Si, Ge
and As are used as semiconductors.
12
5 Molecules
It is rare to find isolated atoms in nature, only the noble gases He,
Ne, Ar, …. consist of individual, nonreactive molecules.
Most atoms tend to combine with one another in various ways.
Molecules are neutral particles, consisting of two or more atoms.
The atoms are held together by strong forces called covalent
bonds.
In a covalent bond, two atoms share a pair of electrons, details later.
Molecules can be very small, such as H2 (2 amu); or they can be huge, like
proteins (> 10,000 amu)
The protein cytochrome c consists of thousands of atoms, all linked by covalent
bonds. Its mass is 12,360 amu
13
Molecular substances are often represented as molecular formulas.
Examples: H2O water, NH3 ammonia, CH4 methane
Structural formulas are more informative, because they
show the bonding pattern within the molecule.
Examples:
Lines in these structures represent covalent bonds.
14
Simplest (= “empirical”) formula gives the simplest whole-number ratio of
the atoms in a compound
The compounds with the molecular formula: which gives the actual number of
atoms in a molecule of the substance, the molecular formulae: C2H4 and C3H6
both have the same simplest formula:
CH2
C6H12O6 (glucose) simplifies to:
CH2O
For water and many other small molecules, the molecular formula and the
simplest formula are identical.
15
6 Ions
When an atom loses or gains electrons it becomes an ion. Generally, metals
tend to lose electrons.
Examples: Sodium (Na) and calcium (Ca) are metals
Na Æ Na+ + eCa Æ Ca2+ + 2e-
Positively charged ions are called cations.
Nonmetals tend to gain electrons
Cl + e- Æ ClNegatively charged ions are called anions.
The ions dealt with so far are monoatomic (or “simple”)
ions. In contrast, polyatomic (or “complex”) ions are like a
molecule, several atoms joined by covalent bonds, but
there is an overall charge.
Examples: OH-, NH4+
16
When ions are formed, the number of protons in the nuclei
does not change.
Some common polyatomic ions
Note that:
• NH4+ is the only common polyatomic cation, most
others are derived from individual metal atoms: Na+,
Ca2+, …
• Most polyatomic anions contain oxygen “oxoanions”
-1
Hydroxide, OHNitrate, NO3Chlorate, ClO3Perchlorate, ClO4Cyanide, CNAcetate, C2H3O2Permanganate,
MnO4Hydrogen
carbonate
HCO3Dihydrogen
phosphate H2PO4-
-2
Carbonate, CO32Sulfate, SO42Chromate, CrO42Dichromate,
Cr2O72Hydrogen
phosphate HPO42-
-3
Phosphate, PO43-
17
Ions that are equally charged repel each other due to
electrostatic interactions.
Oppositely charged ions attract each other, this is referred
to as ionic bond.
A bulk sample of matter is electrically neutral, ionic
compounds always contain anions and cations, so that the
overall charge is zero.
Table salt has the overall composition NaCl, it consists of
Na+ and Cl- ions that forms a continuous network (crystal
lattice).
There are no individual “Na-Cl molecules”.
18
7 Units
Chemistry deals with qualitative questions
• How do we prepare X?
• What happens when X reacts with Y?
• How can we convert X into Z?
• How can we separate X and W?
… and with quantitative questions.
• What is the bond length in the molecule X-Y?
• How much X reacts with 1 g of Y?
• How fast does X react with Y?
• How much energy is released in the reaction?
Quantitative measurements need units.
Chemistry (and other Sciences) uses almost exclusively
S.I. units (Systeme International, a.k.a. metric, “mks-system”, for
meter, kilogram, second): All of the units of a particular quantity are
related to one another by factors of 10. It is often advantageous to
convert all quantities to SI units, before starting a calculation.
SI units
meter
cubic meter
kilogram
Kelvin
second
mole
(m)
(m3)
(kg)
(K)
(s)
(mol)
for length
for volume
for mass
for temperature = oC + 273.14
for time
for amount of substance
19
Metric Prefixes
Factor
103
10-1
10-2
10-3
10-6
10-9
10-12
Prefix
kilo
deci
centi
milli
micro
nano
pico
Abbreviation
K
D
C
M
μ
N
P
Mass (symbol: m)
kg kilogram (defined) 1 kg is roughly the mass of 1 L of water
g gram
10-3 kg 1 g is roughly the mass of 1 mL of water
mg milligram
10-3 g = 10-6 kg
µg microgram 10-6 g = 10-9 kg
Length (symbol: l)
m meter (defined)
km kilometer
103 m
cm centimeter 10-2 m
mm millimeter
10-3 m
µm micrometer 10-6 m
nm nanometer 10-9 m
pm picometer
10-12 m
The wavelength of light is measured in nm. Blue light ~ 400 nm, red light ~ 700 nm.
Another unit that is sometimes used is the Ångstrom (Å) 1 Å = 10-10 m. The length of a
chemical bond is on the order of 1 Å.
20
Time (symbol: t)
s
second (same prefixes as above...)
Volume (symbol: V)
L
liter
1 L = 10-3 m3 = 103 mL
mL milliliter
1 mL = 1 cm3 = 10-3 dm3 = 10-3 L = 10-6 m3
It is helpful to visualize these volumes as little cubes.
Remember that liters are NOT an S.I. unit.
Many important units have more than one dimension, that
is, they involve the product or ratio of two or more
fundamental units.
Example:
Density d
Density = mass / volume.
Always watch the units used!
60 ml of benzene, C6H6(l), weigh 52.71g.
density of benzene in g/ml?
What is the
Density = mass / volume = 52.71g/60ml = 0.8785g/ml
21
The metal rhenium has a density of 20.53 g/ml at room
temperature. What is the weight (mass) of 1.5 liters of
rhenium?
Note 1.5 l = 1500 ml
Density = Mass/Volume = 20.53g/ml = mass/1500ml
Mass = 307950 g = 307.950 kg
22
Conversion of units:
Example: convert a volume of 543 cm3 to liters
XL
1L
~
~
543 cm3
1000 cm3
(you can read “~” as “corresponds to”)
Therefore:
x L 543 cm 3
=
1 L 1000 cm 3
543 cm3
cross-multiply: x L = 1000 cm3 × 1 L = 0.543 L
The Mole
The mole is just a number. It is just one word we use to
represent a certain number of things. We use it because it
is handy. It is easier than actually saying the number
itself.
One dozen eggs (12 eggs)
One mole of atoms (6.02 ×1023 atoms)
One mole of pennies (6.02 ×1023 pennies)
= 6.02 ×1021 $
Total cash in the world = approx 2 x1017 $
23
One mole contains 6.02 ×1023 items. 6.02 ×1023 is called
“Avogadro’s Number” (NA) (three significant figures)
NA has the unit mol-1
We abbreviate one mole as “1 mol”
How many moles of atoms are in one mole of He?
6.02 ×1023
How many moles of atoms are on one mole of CH4 ?
One mole contains CH4 6.02 ×1023 molecules
But one mole CH4 contains 5 moles of atoms
# 0f atoms = 5 x 6.02 ×1023 = 3.01 x 1024
24
Q. Why do we use this strange number, 6.02 x 1023 ?
Essentially because individual atoms are not very heavy…
we need a large number of atoms to achieve weights we
can handle easily.
Individual atom weights are expressed in amu. Let’s try
expressing 1 amu in grams:
We know
6.02 x 1023 atoms of the most abundant isotope of carbon
weigh 12.0g
Therefore 1 C-12 atom weighs 12.0g/6.02 x 1023atoms
= 1.99 x 10-23 g/atom
but 1 C-12 atom weighs 12 amu
or 1 amu = 1.99 x 10-23 gatom-1/12amuatom-1
= 1.66 x 10-24g/amu
25
The molar mass (MM) is the mass of one mole of
substance. MM has units of g/mol
C-12 has a molar mass of 12 g/mol
The atomic mass of He is 4.003 amu.
1 mol of He atoms (6.02 ×1023 atoms) weighs 4.003 g
The molar mass of He is 4.003 g/mol
The atomic mass of S is 32.07 amu.
1 mol of S atoms (6.02 ×1023 atoms) weighs 32.07 g
The molar mass of S is 32.07 g/mol
This also works for compounds:
Water:
The atomic mass of hydrogen is 1.01 amu
The atomic mass of oxygen is 16.00 amu
One molecule of water has two hydrogen atoms and one
oxygen atom, the mass of one water molecule is therefore
2 x 1.01 + 16.00 = 18.02 amu
1 mol of water molecules weighs
The molar mass of water is
18.02 g
18.02
g/mol
26
Mole – Gram Conversions
Use the equation
m = MM × n
m:
MM:
n:
mass [g]
molar mass [g/mol]
number of moles [mol]
Example: What is the mass of 0.0753 mol of CO2 ?
mass = 44g/mol × 0.0753 mol = 3.31g
Always include units in your calculations !!!
It’s easier to check your result (and memorize equations) when you know what the units
are.
27
EXAM QUESTION: Nov. 2004, Q2
How many atoms of Os (atomic number 76) are there in
1.0 × 10-3 g of OsO4 ?
A)
B)
C)
D)
E)
6.0 × 1023
2.4 × 1024
2.4 × 1018
9.5 × 1018
3.0 × 1024
Molar Mass OsO4 = 190.2g + (4 x 16g) = 254.2g
# of moles OsO4 = Mass/molar mass = (1.0 x 10-3
g)/(254.2g/mol)
= 3.93 x 10-6 g/mol
# of atoms Os = 6.03 x 1023 atoms/mol x 3.93 x 10-6 g/mol
= 2.4 x 1018
28
8 Mass Relations in Chemical Formulas
The composition of a compound is often specified by
citing the mass percents of the elements present.
Let’s take a 100 g sample of water. What is the mass in
grams of each element?
Let’s first figure out how many moles of water we are
dealing with:
m = MM × n
100g = 18.02 g/mol x n
n= # of moles water = 5.55
Therefore there are 2 x 5.55 moles of H atoms
and 5.55 moles of O atoms in 100 g of H2O.
2 x 5.55 moles of H atoms weigh 2 x 5.55 x 1.01 = 11.21 g
5.55 moles of O atoms weigh 5.55 x 16 = 88.80g
Therefore the mass composition of water is
H = (11.21/100) x 100 = 11.21 %
O = (88.80/100) x 100 = 88.80 %
NOTE: These are mass % !!!
29
The composition of H2O in mole % is
Mole % H = (Moles H)/(total moles) = [Moles H/(Moles H +
Moles O)] x 100
Mole % H = ( 2 x 5.55)/(2 x 5.55 + 5.55)] x 100 =66.7
Mole % 0 = ( 5.55)/(2 x 5.55 + 5.55)] x 100 = 33.3
30
The percent composition of a compound is often obtained
as the result of a chemical analysis. This can be used to
obtain the simplest ( empirical ) formula of the compound.
EXAM QUESTION: Nov. 2004, Q4
A compound containing manganese, chlorine and oxygen
contains 39.7% by mass of Mn and 25.6% by mass of Cl.
The empirical formula of this compound is
A)
B)
C)
D)
E)
MnOCl
MnOCl2
MnO2Cl
MnO3Cl
MnO3Cl2
We want the simplest ratio of the moles of each element in the compound.
If we assume 100 g of compound then the weight of Mn = 39.7g , the weight of Cl =
25.6 and the weight of O = 100 - 39.7 – 25.6 = 34.7g
Then:
Moles Mn = 39.7g/(54.94g/mol) = 0.72
Moles Cl = 25.6g/(35.45g/mol) = 0.72
Moles O = 34.7g/(16g/mol) = 2.17
Dividing by the lowest # of moles yields the ratio:
Mn 1 Cl 1 O 3
The empirical formula is: MnClO3
31
9 Mass Relations in Reactions
Chemical reactions are of the form
Reactants Æ Products
There are several distinct types of reaction, these include:
1. Acid/base reactions (will be studied in detail later).
2. Precipitation reactions (when a solid is produced by
reaction of two or more components in solution).
3. Oxidation/reduction reactions (will also be studied
later in detail).
4. Combustion reactions in which a compound reacts
with oxygen to produce the most stable oxidation
products. (the exception is in nitrogen containing
compounds where N2 is produced).
It would be better to write “Reactants
→
←
Products” to emphasize that chemical reactions
always represent an equilibrium, but for now we don’t have to worry about that.
Often you will have to perform calculations involving
chemical equations. Always use a balanced equation!
H2 + O2 Æ H2O is not balanced
2 H2 + O2 Æ 2 H2O is balanced (atom and charge balance!)
32
Use the symbols g, l, s to designate the physical state of
reactants and products. “aq” is used for species dissolved
in water (= aqueous solution), especially ions.
You also have to “know” what happens during the
reaction, e.g. when you burn hydrogen, a lot of heat is
generated, and thus the water is “g”, not “l”.
2 H2(g) + O2(g) Æ 2 H2O(g)
Table salt is dissolved in water:
NaCl(s) Æ Na+(aq) + Cl-(aq)
33
The “rocket fuel” used by NASA is a mixture of two liquids:
Hydrazine (N2H4) and dinitrogen tetraoxide (N2O4)
The products of the reaction are gaseous nitrogen and
water vapor.
A lot of thermal energy is generated during the reaction. The gas molecules are
expelled from the rocket engine with an extremely high velocity; that is what makes the
rocket “fly”.
How do we balance a chemical equation like this?
1. Write down the “skeleton” equation:
N2H4 + N2O4 ÆN2 + H2O
2. Indicate the physical states of reactants and products
N2H4(l) + N2O4(l) ÆN2(g) + H2O(g)
3. Balance the reaction by finding the right coefficients
(Essentially by trial and error, more systematic methods
for balancing oxidation/reduction equations)
2 N2H4(l) + N2O4(l) Æ3 N2(g) + 4 H2O(g)
The coefficients in this equation represent the number of
molecules (also the number of moles!) that react with each
other.
Other possible solutions are:
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4 N2H4(l) + 2 N2O4(l) Æ6 N2(g) + 8 H2O(g)
or
N2H4(l) + ½ N2O4(l) Æ3/2 N2(g) + 2 H2O(g)
Usually we go for the smallest whole-number coefficients.
The relationships between amounts of reactants and
products (in moles and grams) are called stoichiometry.
35
The following is a “combustion question” Stoich-1, Q#7
(similar to many exam questions !!!). “Combustion” means “burning in excess oxygen”.
All C is turned into CO2, all H is turned into H2O.
A compound contains C, H, and O only. When a sample of
mass 0.246 g is burned in excess oxygen, 0.600 g of CO2
and 0.080 g of water are produced.
a) Calculate the empirical formula
b) Given that the molar mass is about 160 g/mol, what is
the molecular formula?
The reaction is:
CxHyOx + AO2 → xCO2 + (y/2) H2O
Notice: The moles CO2 produced = moles C in the reactant =
(mass CO2 produced)/molar mass CO2
= 0.6/44 = 0.036
Or mass C in the reactant = moles x molar mass = 12 x 0.036 =
.1636 g
And
2 x Moles H2O produced = Moles H in the reactant
Moles H2O produced = mass/molar mass = 0.08/18 = 0.0044
Moles H in reactant = 2 x 0.004 = 0.0088
Mass H in reactant = moles H x molar mass = 0.0088 x 1.01=
0.009
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And now % C in the reactant = (mass C/mass reactant) x 100 =
(0.1636/0.246) x 100 = 66.5
% H = (mass H/mass reactant) x 100 = (0.009/0.246) x 100 =
3.66
% O = 100 -%C -%H = 100 -66.5 – 3.66 = 29.84
Now we can proceed by assuming 100g of reactant:
Then Mass C = 66.5, moles C = 66.4/12 = 5.53
Mass H = 3.66, moles H = 3.66/1.01 = 3.66
Mass O = 29.84, moles O = 29.84/16 = 1.865
Dividing by the lowest yields: C = 2.96 , H = 1.96 , O = 1
OR C = 3 H =2 O = 1
The empirical formula then is C3H2O
The molar mass of the empirical formula is 3 X 12 + 2 x 1.01 + 1 x
16 = 54
Estimated molar mass is 160
The molecular formula must contain 160/54 = 2.96 = 3 empirical
formulae
The molecular formula is: C9H6O3
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10 Solute Concentrations, Molarity
Most chemical reactions that you will encounter occur in
solution.
The concentration of a solution is expressed in terms of its
concentration, another term for this is molarity.
molarity = moles of solute / liters of solution
The molarity (=concentration) has units of moles per liter
(unit M).
1 M = 1 mol L-1
A 6 M solution of NaOH has 6 moles of NaOH per liter of
liquid.
[ ]s are often used in this context.
[NaOH] means “the concentration of NaOH”
In this example, [NaOH] = 6 M. We say “the solution is 6
molar”.
Solutions can be concentrated (high conc.), e.g. 6 M
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NaOH, or dilute (low conc.), e.g. 10-3M NaOH = 3 mM
NaOH.
Here is how you prepare a 0.1 M solution:
Calculating with concentrations
You have a bottle labeled “concentrated HCl”. It has [HCl]
= 12.0 M.
How many moles are there in 25.0 mL?
Molarity = Moles/Volume (in liters)
Moles = Molarity x volume (in liters)
= 12moles/liter X 0.025 liters = 0.3
What volume of the 12 M solution must be taken to
contain 1.00 mol HCl?
Molarity = Moles/Volume (in liters)
Moles = Molarity x volume (in liters)
1.00 = 12 moles/liter x Volume
Volume = .083 liters = 83 ml
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Any substance which is IONIC in solid is IONIC in
aqueous solution (i.e. positive and negative ions separate
from one another).
e.g. KCl (s)
Æ
K+(aq) + Cl-(aq)
A crystal of KCl contains K+ cations and Cl- anions.
Some covalent substances give ions in solution:
(e.g. acids, see chapter 3)
e.g. HCl (g)
Æ
H+(aq) + Cl-(aq)
Water is generally the best solvent for ionic substances,
i.e. ionic substances are most soluble in water.
Give the concentration, in mol/L, of each ion in
0.080 M K2SO4
K2SO4(s) + H2O(l) → 2K+(aq) + SO42-(aq)
[K+(aq) ] = 2 x 0.080 = 0.160, [SO42-(aq)] = 0.080
Substances that exist completely as anions/cations in
solution are called strong electrolytes. Solutions of these
substances conduct electric current.
40
Weak electrolytes are only partially ionized, e.g. acetic
acid CH3COOH Æ CH3COO-(aq) + H+(aq)
~99%
~1%
Charges of some “transition metal cations” commonly
found in aqueous solution:
11 Limiting Reactant and Yield of a Reaction
A cheese sandwich consists of 1 bun and 1 slice of
cheese.
You have 100 buns, and 32 slices of cheese. How many
cheese sandwiches can you make???
Cheese is the limiting reactant, buns are the excess
reactant.
1 mol of oxygen is mixed with 1 mol of hydrogen, ignition
of this mixture leads to the formation of water.
What is the limiting reactant?
What is the excess reactant?
2H2 + O2
→
2H2O
Clearly one mole of oxygen requires two moles of
hydrogen for complete reaction. Hydrogen is the limiting
reagent, oxygen is in excess.
After reaction ½ mole of oxygen will be left open.
41
Reactants are not always mixed exactly in their
stoichiometric proportions. Often you will have to decide
which is the limiting reactant.
The final amount of limiting reactant is always ZERO.
42
EXAM QUESTION: Nov. 2004, Q7
Insoluble Ag2CrO4 is formed from AgNO3(aq) and
Na2CrO4(aq) according to the equation
2 AgNO3 + Na2CrO4 Æ Ag2CrO4(s) + 2 NaNO3
When 50.0 mL of 0.100 M AgNO3(aq) are mixed with
100.0 mL of 0.0200 M Na2CrO4(aq), the maximum mass,
in grams, of Ag2CrO4(s) that can be produced is
A)
B)
C)
D)
E)
0.567
1.66
0.448
0.332
0.664
Moles AgNO3 = MV = 0.1 x .050 = 0.005
Moles Na2CrO4 = MV = 0.02 x 0.1 = .002
Now if we have 0.002 moles of Na2CrO4, 0.004 moles of AgNO3
will be required for complete reaction.
We have 0.005 moles AgNO3 , therefore Na2CrO4 is the limiting
reagent and 0.002 moles of Ag2CrO4 will be produced.
Mass Ag2CrO4 produced = moles x MM
= 0.002 x (2 x 107.9 + 52 + 4 x 16) = 0.664g
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12 Yield
Suppose you carry out a chemical reaction. Based on the
reactant amounts used, and on the equation of the
reaction you expect 10 g of product. However, due to
experimental imperfections only 9 g are obtained.
(Some material was “lost” during handling …)
This means you only obtained 9/10 = 0.9 (= 90%) of the
expected product. We say that the yield of the reaction is
0.9 (or 90%).
In general:
mass obtained
Yield =
maximum mass expected
which is the same as
Yield =
moles obtained
maximum number of moles expected
(usually expressed in %)
Example: 4 mol of H2 and 2 mol of O2 are mixed and
ignited. 1.3 mol H2O are found as reaction product. What
is the yield?
44
2H2 + O2
→
2H2O
2 moles O2 would react with 4 moles H2 to yield 4 moles
H2O (note the stoichiometry is exact in this case).
We get only 1.3 moles H2O
Yield = actual / expected = 1.3/4 = .325
or 32.5%
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Percentage Purity Calculations
Sometimes a chemical substance is not pure (e.g. gold in
a rock sample). For an impure compound, we define the
Percent Purity =
mass of pure compound present
× 100%
mass of total compound present
This may also be expressed on a molar basis (but that’s uncommon).
Example
A sample of concentrated nitric acid contains 70.0% HNO3
by mass (the remainder being water). The density of this
solution is 1.41 g cm-1. What volume of solution will
contain 2.50 mol of nitric acid?
% HNO3 = [ (Mass HNO3 )/ (Mass Solution) ] x 100 = 70
0.7 x Mass solution = mass HNO3
2.5 moles HNO3 weight 1 + 14 + 3 x 16 = 63g = mass HNO3
0.7 x Mass solution = 63g
Mass solution = 90 g
Now we want the volume of the solution and:
Density = Mass solution/volume = 1.41 g cm-1
= 90g/volume
volume = 90g/1.41 g cm-1 = 63.83 cm-1
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Some Solubility Rules You should Know
Solubility of Ionic Solids in Water
Soluble Compounds
Exceptions
Nitrates (NO3-)
None
Li+ , Na+ , K+ , NH4+
None
Halides (Cl-, Br-, I-)
Ag+, (Hg2)2+, Pb2+
Sulfates (SO42-)
Ca2+, Sr2+, Ba2+, Pb2+
Insoluble Compounds
Exceptions
Sulfides (S2-)
Groups 1 and 2 and NH4+
Carbonates (CO32-)
Group 1 and NH4+
Phosphates (PO43-)
Group 1 and NH4+
Hydroxides (OH-)
Group 1, Ba2+ and NH4+
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13 Uncertainties in Measurements, Significant Figures
Chemistry is based on experiments, experiments are
based on measurements, the result of a measurement
carries a certain degree of uncertainty.
Although there are some exact numbers in chemistry (e.g.
there are exactly two hydrogen atoms in a H2 molecule), most experimental
results contain some amount of error or uncertainty. This
is unavoidable in most cases.
Difference between accuracy and precision:
Accuracy - how closely does the measured value agree
with the "true" value?
Precision - how well do repeated measurements of the
same thing agree with each other?
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The uncertainty of a measurement has to reported,
together with the actual result.
Example: “5 mL” of liquid are removed from a beaker by
three different methods that have a different accurracy.
The actual results are:
- 5 mL ± 1 mL
- 5 mL ± 0.1 mL
- 5 mL ± 0.01 mL
We will drop the ± sign and simply write
5 mL, 5.0mL, 5.00 mL
In doing this, it is understood that there is an uncertainty of
no more than one unit in the last digit
(i.e. 1 mL, 0.1 mL, 0.01 mL, respectively).
There is one significant figure in 5 mL, two in 5.0 mL, and
three in 5.00 mL.
Example: Three persons weigh the same object. They
report:
(a) 15.02 g
(b) 15.0 g
(c) 0.001502 kg
There are
4 significant figures in (a)
3
(b)
4
(c)
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Zeros are not significant when used to fix the position of
the decimal point (leading zeros”, as in [c]). BUT trailing zeros are
significant (as in [b]).
The last digit to be shown should be the first “doubtful
digit”. When we say “1.005 g”, it is implied that the real
value is probably between 1.004 and 1.006 g.
The number of a piece of rock is given as “500 g”. This
statement can be ambiguous. Is it 500 g ± 1 g (three
significant figures) ??? 500 g ± 10 g (two significant
figures) ??? (anything is possible)
Usually it is better to use exponential notation to make
clear what is meant:
5.00 × 102 g (three significant figures)
5.0 × 102 g (two significant figures)
5 × 102 g
(one significant figure)
Note that for exact numbers the concept of significant
figures is not required (there is no uncertainty).
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Number of significant figures in combined expressions
Carrying significant figures through calculations is discussed in the Lab Manual (pages
17-19), but this is a more sophisticated treatment than we need to use. Instead we will
use the method given MH5, (pages 17-21).
When measured quantities are multiplied or divided, the
number of significant figures in the result is the same as
that in the quantity with the smallest number of significant
figures.
Example: a plane travels about 5.6 × 103 km in 8.50 hours.
What is the average velocity ?
By using your calculator, you will find that
velocity = distance / time = 658.82353 km/h
Are all these figures meaningful? There are 2 significant
figures in the numerator, and 3 in the denominator. The
result has 2 significant figures.
It should be reported as speed = 6.6 × 102 km/h.
When you discard insignificant figures, the result has to be rounded off or rounded up.
In a calculation, do not do any rounding until you obtain the final result.
Note: Your calculator will give as many figures as it has
room to display, but usually they are not all significant.
Another problem with calculators is that they usually omit
trailing zeros to the right of the decimal place, which, as
we discussed, are significant. Never copy numbers from
your calculator without thinking about them !!!!
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When measured quantities are added or subtracted, the
number of significant decimal places of the result is the
same as that in the quantity with the smallest number of
decimal places
i.e. in this case you should pay attention to the position of the decimal place
Example: Let’s find the total mass of a solution containing
10.21 g of instant coffee
0.2 g
of sugar
256 g of water
Your calculator reports 266.41 g, but this should be
reported as 266 g.
Because “256” has zero significant decimal places, the result also has zero significant
decimal places (but three significant figures in total).
Exact numbers don't count when determining the number
of significant figures in the result of a calculation.
Examples:
One standardized paper weight has mass of 25.0 g. What
would be the mass of two of these paper weights?
An inch is defined as 2.54 cm. How many inches are
there in 1.2345 cm?
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Combined Calculations
Combined operations are carried out step by step carry extra digits till
the end:
(41.23 x 4.184 x 18.3) + (28 x 18.3)
= 3.156 x 103 + 5.18 x 102
= 3.156 x 103 + 0.518 x 103
= 3.67 x 103
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