The Law of Combining Volumes of Gases: When two gases react, the volumes
that combine are in a ratio of small whole numbers. The ratio of the volume of
each product, if a gas, is also in the ratio of small whole numbers.
Example:
1 Liter of hydrogen + 1 Liter of chlorine = 2 Liters of Hydrogen Chloride
2 Liters of hydrogen + 1 Liter of oxygen = 2 Liters of Water
3 Liters of hydrogen + 1 Liter of nitrogen = 2 Liters of Ammonia
Mass is always conserved; but the volume of a gas is not.
Avogadro’s Hypothesis: Equal volumes of different gases contain the same
number of particles. The particles of a gas may be atoms or molecules. One
liter of hydrogen = one liter of chlorine = one liter of hydrogen chloride in terms
of particles (read atoms or molecules)
Avogadro’s Law and the reaction of hydrogen and oxygen to
produce water
2 liters of hydrogen + 1 Liter of oxygen -> 2 Liters of water
Dalton: H + O -> HO
Simplicity of atoms
Avogadro: 2 H2 + O2 -> 2 H2O
Equal volumes equal particles
Both equations are balanced. Which is correct (if either?)
Dalton’s hypothesis provided no link between the relationships
between the volumes of the reactants and products.
Avogadro’s hypothesis provided a direct link between the
relationships between the volumes of the reactants and products.
(1) Avogadro’s Number (N0) is defined a the number
of atoms in exactly 12 g (0.012 kg) of 12C
(2) Experimentally, N0 is found to be equal to 6.02 x
1023
(3) The mass (expressed in grams) of Avogadro’s
number of atoms of an element is equal to the relative
atomic mass of that element
(4) A mole of a substance equals the amount of that
substance that contains Avogadro’s number of atoms
(element) or molecules (compound)
Lorenzo Romano Amedeo Carlo Avogadro,
conte di Quaregna e di Cerreto (1776 - 1856)
Avogadro’s number is 6.02 x 1023 (unlisted)
*An Avogadro's number of standard soft drink cans
would cover the surface of the earth to a depth of over
200 miles.
•If you had Avogadro's number of unpopped popcorn
kernels, and spread them across the United States of
America, the country would be covered in popcorn to
a depth of over 9 miles.
*
If we were able to count atoms at the rate of
10 million per second, it would take about 2 billion
years to count the atoms in one mole.
Avogadro’s interpretation of gas reactions:
H2
1L
+
Cl2
1L
->
2 HCl
2L
2 H2
2L
+
O2
1L
->
2 H2O
2L
3 H2
3L
+
N2
1L
->
2 NH3
2L
Dalton’s interpretation of reactions:
H
+
Cl
->
HCl
H
+
O
->
HO
H
+
N
->
HN
Conceptual basis of Avogadro’s Hypothesis
The particles of any gas all occupy the same space at a given
temperature and pressure, independent of the composition of the
gas. Thus, a given number or “particles” (atoms or molecules) of a
gas will occupy the same space of same volume.
One liter of hydrogen gas, contains the same number of hydrogen
“particles” as the number of oxygen “particles” in one liter of
oxygen gas or the numbe of nitrogen “particles” in one liter of
nitrogen gas.
Consider the experiment:
1 L of hydrogen + 1 L of chloring -> 2 L of hydrogen chloride
Consider the interpretations:
H
+
Cl
->
2 HCl Impossible!
H2
+
Cl2
->
2 HCl Possible
Dalton
Avogadro
Amazing consequence of Avogadro’s
hypothesis
The molar volume of a gas is the volume of
one mole of the gas (at standard temperature
and pressure). This molar volume near room
temperature and atmospheric pressure is 22.4 L
The weight of 22.4 L of any gas is the
molecular weight the gas!
“In 1757, being at sea in a fleet of 6 sail bound against Louisburg,
I observed the wakes of two of the ships to be remarkably smooth,
while all the others were ruffled by the wind, which blew fresh.
Being puzzled with the differing appearance, I at last pointed it out
to our captain, and asked him the meaning of it? "The cooks,"
says he, "have, I suppose, been just emptying greasy water through
the scuppers, which has greased the sides of those ships a little,"
and this answer he gave me with an air of some little contempt as
to a person ignorant of what everybody else knew. It occurred to me
the learned are apt to slight too much the knowledge of the ancients
and the vulgar.
This art of smoothing the waves with oil is an instance of both!
-Benjamin Franklin,
Philosophical Transactions of the Royal Society of London, 1776
Clapham Pond
"...at Clapham I observed a large pond very rough with the wind. I fetched a cruet of oil and
dropt a little of it on the water. The oil, though not more than a teaspoonful, produced an
instant calm over a space of several yards square, and then spread amazingly till it filled a
quarter of the pond, perhaps half an acre, as smooth as a looking glass. .... If a drop of oil
is put on a polished marble table, or on a looking-glass that lies horizontally, the drop
remains in place, spreading very little. But when put on water it spreads instantly many feet
around, becoming so thin as to produce the prismatic colors, for a considerable space, and
beyond them so much thinner as to be invisible, except in its effect of
smoothing the waves."
---Benjamin Franklin, letter to William Brownrigg, November 7, 1773.
Drop hits water.
H 2O H 2O H 2O
H 2O
Drop spreads on
water.
H 2O H 2O H 2O
H 2O
Monolayer forms
on water.
H 2O H 2O H 2O
H 2O
This incredibly simple experiment provides a means of
understanding fundamental facts about molecules and the
forces between them. It even leads to a means of
determining molecular size and shape!
For example, if the teaspoon were 2 cc of oil and the area of
a half an acre is approximately 2000 m2, the film thickness
(volume/area) would be ca 10-7 cm (1 nanometer, 10 Å),
which is right on the molecular dimensions of an "olive oil"
molecule!!! This is clearly within the experimental
uncertainty of measuring acreage!
Chapter 2 Stoichiometry
Learning Goals:
(1)
How to translate the coefficients of the atoms involved in
balanced chemical equations into moles of elements and
compounds and how to translate moles into mass of elements
and compounds.
(2)
For gases, how to translate the coefficients of the atoms
involved in balanced chemical equations into moles of elements
and compounds and how to translate moles into volumes of
elements and compounds which are gases.
(3)
How to determine the limiting reagent in a reaction from
the balanced chemical equation and the available masses of the
reagents.
Empirical Formulas and Molecular Formulas
(1) Empirical formula: a formula which displays the simplest ratios of
the number of atoms of different elements that make up a substance
(2) Molecular formula: a formula which displays the exact number
and kinds of atoms that are present in one molecule. The molecular
formula is the compositional structure of a molecule
(3) Lewis structure: a structure which displays how the atoms of a
molecule are connected. The Lewis structure is the constitutional
structure of a molecule
(4) Molecular structure: a three dimensional representation of how the
atoms of a molecular are arranged in space. The molecular structure
displays the configurational structure of atoms about each other in
space.
Percentage atomic composition from empirical or molecular
formulas
Empirical or molecular formula -> % composition of elements
Example: H2O
Need: relative masses of H and O
From periodic table: H = 1.00, O = 16.0
One mole of H2O consists of 2 moles of H atoms and one mole of O
atoms. 2 moles of H atoms have a mass of 2 g and 1 mole of O atoms
have a mass of 16.
The mass of one mole of water is 18 g. The percent of H in water is
2/18 x 100 = 11%; the percent of O in water is 16/18 = 89 % O.
Section 2.2:
Using balanced chemical equations
Hydrocarbon
+ Oxygen
->
Carbon dioxide + Water
What is the balanced chemical equation for complete combustion of C4H10?
? C4H10 +
? O2
->
? CO2
+
? H2O
Answer (by inspection and molecular weights of reactants and products):
One mol of C4H10 = 58.12 g; one mol of O2 = 32.00 g; one mol of CO2 = 44.01 g; one
mol of H2O = 18.01 g.
2 C4H10 +
13 O2
116.2 g C4H10 + 416.0 g O2
->
8 CO2
+
->
352.1 g CO2 + 180.1 g H2O
2 mol of C4H10 13 mol of O2
8 mol CO2
Example of the law of mass balance.
116.2 g + 416.0 g =
352.1 g + 180.1 g
REACTANTS
PRODUCTS
=
10 H2O
10 mol H2O
532.2 g
SAME MASS