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UNIT 1 : STOICHIOMETRY.
Introduction.
Matter to represent anything that has mass and occupies space. Chemicals are examples of
matter. Chemistry is the study of matter, its properties, and the changes it undergoes.
There are two major branches: pure and applied chemistry. Pure chemistry deals with
describing known substances and discovering new compounds. Applied chemistry is the search
for uses for chemical substances. New chemicals are being discovered or produced every day.
Isotopes and Atomic Mass .
Investigations conducted as long ago as the late 1700's revealed that atoms of different elements
have different masses. Dalton included this idea in his atomic theory in 1804. What he didn't
know at the time was that two atoms of the same element may also have different masses. That's
because he didn't know about subatomic particles. Today, we know that the number of protons
and neutrons in an atom determines the mass of an atom. Remember the terms like electron (e ),
proton (p+), and neutron (n) — (see the chart below); however, there are a number of other terms
used to describe the atom.
Summary of subatomic particles of the atom.
Particle
proton
neutron
electron
Location
nucleus
nucleus
outside nucleus
Relative Charge
1+
0
1-
Relative Mass
1836.12
1838.65
1
It is important that you be familiar with the following key terms.
1.
Atomic Number (Nuclear Charge) : The atomic number of an element is equal to the
number of protons in an atom. Atomic number is also called nuclear charge because it is
based on the number of protons (positively charged particles) in the nucleus. For
example, all atoms of carbon have six protons, so the atomic number (or nuclear charge)
of carbon is six. Atomic numbers are whole numbers.
2.
Mass Number : The mass number of an atom is equal to the sum of its protons and
neutrons. For example, an atom of helium has two protons and two neutrons, so its mass
number is four. Mass numbers are also whole numbers. Sometimes the mass number of
an atom is included in its name; for example, helium - 4.
3.
Isotopes : It is possible for atoms of the same element to have different numbers of
neutrons. These atoms are termed isotopes. For example, if a carbon atom has six
neutrons and another has eight neutrons, then they are isotopes of carbon. (The prefix isomeans the same.)
Example : Two isotopes of carbon. Carbon - 12 is stable but carbon - 14 is radioactive.
Isotope Name
Isotope Notation
Carbon - 12
12
6
mass number
Isotope Name
C
atomic number
Isotope Notation
Carbon - 14
14
6
mass number
C
atomic number
Average Atomic Mass :
When you look up the atomic mass of an element in the periodic table, you will find that its
value usually has 2 decimal places; (C is 12.01 amu). The reason for this is that most naturally
occurring elements have more than one isotope. This means that when we measure the atomic
mass of an element, we must take into account the average mass of the naturally occurring
isotopes. The natural relative abundances of the isotopes are usually expressed as percentages.
Example :
Copper, a metal known since ancient times, is used in electrical cables and
pennies. The atomic masses of its two stable isotopes, copper- 63 (69.09%) and
copper- 65 (30.91%), are 62.93 amu and 64.9278 amu, respectively. Calculate the
average atomic mass of copper.
Solution :
Average Atomic Mass for Cu = (0.6909)(62.93 amu) + (0.3091)(64.9278 amu) = 63.55 amu
Sample Problem :
The atomic masses of the two stable isotopes of boron, boron-10 (19.78%) and boron-11
(80.22%), are 10.0129 amu and 11.0093 amu, respectively. Calculate the average atomic mass of
boron.
The Mole (Avogadro's Number).
The word “mole” comes from the Latin “moles”, meaning a mass or pile of something. A mole
is a number, 6.022137 x 1023 to be exact. It is sometimes called Avogadro’s number in honour
of Amedeo Avogadro.(See handout). The mole is a useful amount in chemistry because the basic
unit of matter (the atom) is so very, very, very, very, small. Most people have a hard time
imagining how big a number like 6.022137 x 1023 really is. Atoms are so small that it takes an
incredibly huge number of them to make up a visible amount. For example, a mole of regular
marbles spread over the Earth’s surface would cover it to a depth of 80 km. When dealing with
large numbers of atoms on a consistent basis can get to be tiresome after a while. That's where
the mole comes in.
A mole is the number of carbon-12 atoms in exactly 12 grams of carbon-12. This number was
determined by dividing the mass of a single carbon-12 atom into a 12 g mass of carbon-12. Since
the mass of a single carbon-12 atom is tiny (1.99 x 10-23 g), the value of a mole comes out to be a
huge number. Remember that the mole is not an exact number and current estimates place its
value at 6.022137 x 1023. The greater precision (number of decimal places) in the current value is
a function of the greater precision of the devices currently used to measure the mass. We use the
value of 6.02 x 1023 particles (atoms, ions or molecules) in all our calculations for this course;
(see the chart that follows). At this point, the most important thing to remember about the mole is
that it represents a big number - a very, very, very big number. Chemists use it in the same sort
of way that a egg farmer uses the dozen.
Avogadro’s Number, 6.02 x 1023
Element
Ionic Compound
Molecular Compound
name
carbon, C
sodium chloride, NaCl
water, H2O
mass
12.01 g
58.44 g
18.02 g
number
6.02 x 1023
atoms
6.02 x 1023 formula units of NaCl
6.02 x 1023 Na+ ions
6.02 x 1023 Cl- ions
6.02 x 1023 molecules of H2O
6.02 x 1023 O atoms
2 (6.02 x 1023) H atoms
Sample Problem :
A)
How many particles are there in a mole?
B)
How many atoms of sodium are there in one mole?
C)
What is the mass of one mole of sodium atoms?
The Molar Mass of a Compound.
As you know, few elements exist as pure substances in nature — most of them are found in
compounds. Although the periodic table provides you with the molar masses of the elements, it
does not provide you with the molar masses of compounds. To find the molar mass of a
compound, you have to write the chemical formula, list the number of atoms of each element,
and multiply this number by the molar mass of the element.
Example : Calculate the molar mass of water.
To do this, write the chemical formula: H2O. List the number of atoms of each element in the
compound: 2 H and 1 O. Multiply each number by the molar mass of the element and add the
products. The molar mass of H2O is 18.02 g/mol.
▸
You will be using the molar mass of water frequently, so it is a good idea to
memorize it as 18.02 g/mol.
When calculating the molar mass of a compound, it is important to remember what each
numerical subscript is indicating. Numbers to the lower right of an element symbol indicate the
number of "atoms" of that element in the compound. Numbers outside the parentheses are used
to balance a chemical formula. To determine the number of "atoms" in a formula, you multiply
terms inside the parentheses by the ones outside the parentheses.
Consider the formula:
There are:
(NH4)3PO4.
3 x 1 nitrogen atoms (a total of 3 N),
3 x 4 hydrogen atoms (a total of 12 H),
1 phosphorus atom,
4 oxygen atoms.
In chemistry, the conversion factor in mole calculations is molar mass (the mass of one mole).
This value has been calculated for each element and is usually included in a periodic table. In the
Nelson Chemistry periodic table of the elements, the molar mass value is located in the top right
hand corner of an element's cell. The value 55.85 g/mol means that a mole of iron atoms (atoms)
has a mass of 55.85 grams. See the diagram below.
Look at the following example :
Calculate the molar mass of barium hydroxide octahydrate.
SOLUTION :
Begin by writing the chemical formula for barium hydroxide octahydrate.
▸
Barium forms a 2+ ion because it is a Group 2 element ; Ba2+.
▸
Hydroxide is a polyatomic ion with a 1- charge ; OH -.
▸
Octahydrate means 8 H2O.
It takes two hydroxide ions to balance the charge on one barium ion, so the chemical formula is
Ba(OH)2· 8 H2 O .
Count and list the atoms/ions of each element, but treat water as a unit.
▸
1 Ba
▸
2O
▸
2H
▸
8 H2O
Next, look-up the molar mass of each item in the list and multiply. (Remember the molar mass of
water is 18.02 g/mol.)
Answer :
The molar mass of barium hydroxide octahydrate is 315.51 g/mol.
As you get comfortable with molar mass calculations, you can combine the steps into a single
line like this:
(1 Ba x 137.33) + (2 O x 16.00) + (2 H x 1.01) + (8 H2O x 18.02) = 315.51 g/mol
Always show the unit for molar mass (g/mol) in your final answer.
Note that in this course, molar mass values (calculated or listed in tables) ALWAYS show
precision to two decimal places.
Summary :
Here is a summary of the steps to complete in molar mass calculations.
1.
Write the chemical formula for the compound.
2.
List the number of particles of each element in the compound.
3.
Multiply each number in the list by the molar mass.
4.
Add the products. ALL molar mass values must show precision to TWO decimal
places in this course.
5.
Communicate your answer.
Sample Problem :
Calculate the molar mass for each compound.
A)
NaHCO3
E)
FeSO4·* 3H2O
B)
Sr(NO3)2
F)
lead(II) acetate
C)
Al2(SO4)3
G)
magnesium chloride
D)
CuSO4