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The Mole Concept
Relative Mass
The relative mass of an object is the mass of that object as a
multiple of some other object’s mass.
In the example, the mass of 5 oranges equals the mass of 2
grapefruits.
The ratio (fraction) of the
heavier grapefruit to the
Lighter orange is 5 : 3 or
5 oranges = 1.67 oranges
3 grapefruits 1 grapefruit
The mass of a grapefruit
in terms of an orange is
a relative mass.
Finding the Mass of Atoms: Relative Masses
Since an atom is much too small to weigh on any balance,
scientists have decided to express their mass compared to
some atom that is arbitrarily assigned some mass number.
For example, a hydrogen atom has a mass of 1.67 E -24 g.
A oxygen atom has a mass of 2.66 E -23 g.
If hydrogen (the lighter atom) is assigned a mass of 1, then
the relative weight of the oxygen atom to the hydrogen
atom is:
2.66 E -23 g oxygen atom
= 15.9 O approx. = 16 O
1.67 E -24 g hydrogen atom
1 H
1 H
O:
H:
The Mass of Carbon Atoms Relative to Hydrogen
Hydrogen atoms are the lightest so a ratio is made of the
heavier carbon atom to the lighter hydrogen atom.
a carbon atom
= 2.0 E -23 g = 12
a hydrogen atom
1.67 E -24 g
1
A carbon atom is 12 times more massive (heavy) than a
hydrogen atom.
The weight of carbon as 12 is a weight relative to hydrogen
which is assigned a weight of 1.
C:
H:
Isotopes: Atoms of the Same Kind Differing in Mass
In nature atoms of one kind (like carbon atoms) are not
identical. Atoms of one kind can differ slightly in their
masses. Some carbon atoms have a relative mass of 12
(relative to hydrogen) while other carbon atoms have a
mass of 13 and still others have a mass of 14. Atoms of
the same kind that differ slightly in their masses are called
isotopes.
carbon isotopes:
carbon-12
carbon-13
carbon-14
Percentages of Carbon Isotopes
98.89 % of carbon atoms have a mass of 12. (relative to H)
1.11 % of carbon atoms have a mass of 13. (rel. to H)
.0000000001% of carbon atoms have a mass of 14. (rel. to H)
In a typical sample of carbon the average mass of an atom is
12(.9889) + 13(.0111) = 12.0111 = about 12 (relative to H)
Hydrogen Makes a Poor Standard
Hydrogen is the lightest element so it is convenient to assign
it a value of 1. However hydrogen is not common on earth,
it is explosive to work with, it is a gas at room temperature
– all properties that make it an inconvenient mass
standard.
The IUPAC world organization of chemists decided to make
the carbon-12 isotope (assigned a mass of 12u) the mass
standard to which the masses of all the atoms of the
various elements are compared. Carbon is a solid, fairly
unreactive and very common on earth. One u is an atomic
mass unit (sometimes designated as amu) and has a value
of 1.67 E -24 g.
A magnesium atom with a relative mass of 24u has a mass
that is twice that of carbon-12.
Gay-Lussac’s Law of Combining Gas Volumes
In 1802, Joseph Louis Gay-Lussac published his Law of
Combining Gas Volumes. This law says that the ratio
between the volumes of the reactant gases and the
products can be expressed in simple whole numbers.
When nitrogen gas and hydrogen gas react to form
ammonia gas, 3 volumes of hydrogen combine with 1
volume of nitrogen to form 2 volumes of ammonia.
Note ammonia has a
chemical formula of NH3
Another Example of Gay-Lussac’s Law
Two volumes of hydrogen gas react with 1 volume of oxygen
gas to produce 2 volumes of water gas (steam).
1 volume of hydrogen gas reacts with 1 volume of chlorine
gas to produce 2 volumes of hydrogen chloride gas.
Other Examples of Gay-Lussac’s Reacting Gas Law
Under one set of conditions of temperature and pressure,
2 L of nitrogen gas react with 1 L of oxygen gas to make 1
L of dinitrogen oxide gas (N2O)
Under another set of conditions of temperature and pressure,
1 L of nitrogen gas react with 1 L of oxygen gas to make 1 L
of nitrogen monoxide gas (NO)
Under yet another set of conditions of temperature and
pressure,
1 L of nitrogen gas react with 2 L of oxygen gas to make 1 L
of nitrogen dioxide gas (NO2)
John Dalton’s Atomic Theory
John Dalton, an English teacher, in 1803 read a paper in
which he proposed an atomic theory – that all substances are
composed of hard, indivisible particles called atoms. This
paper was published in 1805 and distributed to scientists
worldwide.
The Main Points of Dalton’s Atomic Theory
1. All matter is composed of atoms which are hard, indivisible
particles.
2. Atoms cannot be made or destroyed.
3. All atoms of the same element are identical.
Different elements have different types of atoms.
4. Chemical reactions occur when atoms are rearranged
Compounds are formed from atoms of the constituent
elements.
5. The relative masses of two atoms can be determined by using
experimental mass ratios of two elements in a compound and
by assuming that the simplest number ratio of 1 atom of one
kind : 1 atom of the other kind applies when there is just one
compound of the two elements. For example in the compound
of magnesium and oxygen the experimental mass ratio is 1.519
g Mg : 1 g O. If 1 atom of Mg is joined to 1 atom of O, then a Mg
atom is 1.519 times more massive than an O atom.
Dalton’s Theory Explained and Predicted Chemical Laws
Dalton’s Atomic Theory explained the Law of Definite
Composition because if atoms have definite masses and if
they always combine in a fixed number ratio in a compound,
then it follows that there will be a fixed mass ratio of one
element to another.
Ex. 1 Mg reacts with 1 O to form MgO The mass of each Mg
is 24.305 and the mass of each O is 15.9994 so the mass ratio
in the compound will be 1(24.305) : 1(15.9994) = 1.519 : 1
The mass ratio in the compound water is 1(15.994) O :
2(1.0079) H = 7.94 : 1
If there is more than one compound between two elements,
then the ratio by mass of one element to the second element
will be in a whole number ratio between the two compounds.
This is called the Law of Multiple Proportions.
Explaining Gay-Lussac’s Law: Avogadro
In 1811 an Italian chemist, Amadeo Avogadro, wrote a paper
making a bold assertion to explain Gay-Lussac’s Law.
Avogadro proposed that:
Equal volumes of gases at the same temperature and
pressure contain equal numbers of atoms. This statement
is referred to as Avogadro’s hypothesis. Today we use this
statement changing the last word atoms to particles.
How Avogadro’s Hypothesis Explained Gay-Lussac’s Law
John Dalton Objects to Avogadro’s Explanation
Dalton in his atomic theory stated that atoms can not be
divided. Avogadro’s hypothesis required that in many
reactions the reactant atoms must be severed in half to
maintain the equal number of particles principle. Dalton
strongly felt this was incorrect and in print lambasted
Avogadro and Gay-Lussac for their ideas and poor
experimental methods.
John Dalton
Amadeo Avogadro
Stanislao Cannizzaro
In 1860 the Italian Stanislao Cannizzaro harmonized the
indivisible atom idea of Dalton with Avogadro’s hypothesis
by recognizing the existence of molecules. Cannizzaro
also demonstrated how his ideas could be used
experimentally to determine the relative masses of atoms.
The Atomic Mass of an Element
The atomic mass of an element
is a weighted average of the
weights of the isotopes of that
element.
For example, chlorine has two
main isotopes, chlorine-35 (
75.77%) and chlorine-37
(24.23%). The weighted average
of these two is .7577(35u) +
.2423(37u) = 35.48u = about
35.5u
35.5 u of Cl and 35.5 g of Cl
35.5u of Cl is the mass of an average Cl atom (much too small
to be weighed on a balance)
35.5 g of Cl can be weighed on a balance. Chemists have
discovered that 35.5 g of Cl has 6.02 x 1023 atoms of Cl. This
number of atoms of Cl is referred to as one mole (mol) of Cl
or Avogadro’s number.
Mass Ratios of Single Atoms vs Equal Numbers of Atoms
The mass ratio of 1 hydrogen atom to 1 oxygen atom is
1u : 16u = 1 : 16
The mass ratio of 100 H atoms to 100 O atoms is
100u : 1600u = 1 : 16 also
The mass ratio of 2500 H atoms to 2500 O atoms is
2500u : 40 000u = 1 : 16 also
Thus the mass ratio of equal numbers of atoms of different
kinds is the same as the mass ratio of one atom of each kind.
What is True When Element Mass Ratios = Single Atom Mass
Ratios?
Example :
25 g of hydrogen atoms is compared to 400 g of oxygen
atoms. What must be true in terms of numbers of atoms?
Consider that 25g : 400g = 1 : 16
Comparing 35.5 g of Cl to 1 g of H
The mass ratio of 1 H atom to 1 Cl atom is 1u : 35.5u
35.5 g of Cl contains 6.02 x 1023 atoms
What must be true about 1g of H?
Expressing the Atomic Mass in g
Whenever an atom’s average mass is expressed in g, this
quantity has one mole or 6.02 x 1023 atoms in it.
Mg has an Atomic Mass of 24.305u so
24.305 g of Mg has ______________ atoms.
Pb has an Atomic Mass of 207.2 u so
207.2 g of Pb has _______________ atoms.
The Mole: Avogadro’s Number
The number 6.02 x 1023 is called the mole or Avogadro’s
number. This number was determined by chemists other
than Avogadro but they named this number in Avogadro’s
honour.
Determining the Mass of a Mole (mol) of a Compound
How much mass does one mol of H2O have?
One mol of H2O has
2 mol of H which has a mass of 2(1.008 g)
= 2.016 g
1 mol of O which has a mass of 1(15.9994 g) = 16.00 g
18.02 g
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