Fundamental Chemical Laws and Dalton

1
Fundamental Chemical Lawsand Daltons Atomic
Theory and Cannizzaros Contribution
Lecture 4

• Chemistry 142 A
• James B. Callis, Instructor
• Winter Quarter, 2006

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Some Definitions

• Matter- The stuff of the universe. That which
  occupies space.
• Substance - A material that cannot be separated
  by physical means into two or more materials with
  different properties.
• Element - A substance that that cannot be
  decomposed into simpler substances by chemical
  means.
• Compound A substance containing two or more
  chemical elements.

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Three Laws that Led to the Atomic Theory

• Law of Mass Conservation The total mass of
  substances does not change during a chemical
  reaction (Lavoisier).
• Law of Definite (or Constant) Composition No
  matter what its source, a particular chemical
  compound is composed of the same elements in the
  same parts (fractions) by mass (Proust).
• The Law of Multiple Proportions When two
  elements form a series of compounds, the masses
  of one element that combine with a fixed mass of
  the other element are in the ratio of small
  integers to each other (Dalton).

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Conservation of Mass

• Matter is neither created nor destroyed in a
  chemical reaction.
• In every chemical operation an equal quantity of
  matter exists before and after the operation.
• Mass is conserved in a chemical reaction.
• Moreover, in chemical change, the mass of the
  elements is conserved, element by element.
• Development of this law was made possible by the
  analytical balance.

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Problem 4-1 Definite Composition
Chemical analysis of a 9.07 g sample of calcium
phosphate shows that it contains 3.52 g of Ca.
How much Ca could be obtained from a 1.000 kg
sample? Mass fraction Ca Mass Ca in 1.000
kg
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Problem4-2 Law of Multiple Proportions
If elements A and B react to form two
compounds, the different masses of B that combine
with a fixed mass of A can be expressed as a
ratio of small whole numbers.
Example Nitrogen Oxides I II
Cmpd Mass N Mass O Mass Ratio O/N Ratio of Ratios
I 46.68 53.32
II 30.45 69.55
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Daltons Atomic Theory

• Matter is composed of indivisible atoms.
• All atoms of a given chemical element are
  identical in mass and in all other properties.
• Different chemical elements are composed of
  different atoms of different masses.
• Atoms are indestructible. They retain their
  identities in a chemical reaction.
• A compound forms from its elements through the
  combination of atoms of unlike elements in small
  whole number ratios.

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Compounds and Molecules
The composition of a compound is shown by its
chemical formula. The symbol "CO2" for the
substance carbon dioxide indicates that it
contains two atoms of oxygen for every atom of
carbon. In most cases, the chemical formula also
defines a molecule. Here, the atoms in the
formula are linked together by attractive forces
strong enough to keep the group together for a
reasonable period of time.
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The Theorys First Challenge The Relative Masses
of Atoms

• Dalton incorrectly assigned a mass of 8 to
  elemental oxygen because he thought that
  elemental hydrogen was monatomic (mass 1). He
  concluded that the formula of water was HO.
• Gay-Lussac found that 2 volumes of hydrogen and 1
  volume of oxygen combined to form 2 volumes of
  water. This implied that the formula of water was
  H2O.

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However, another of Gay-Lussacs results was
confusing 2 L of water vapor were produced for
every 2 L of hydrogen gas that reacted. Here are
the expected and actual results

• Expected Results
• If water is HO 1 L hydrogen gas 1 L oxygen gas
  -gt 1 L water vapor
• If water is H2O 2 L hydrogen gas 1 L oxygen
  gas -gt 1 L water vapor
• Actual Result
• 2 L hydrogen gas 1 L oxygen gas -gt 2 L water
  vapor
• Implication If is assumed that oxygen is
  monatomic, the oxygen must split in half!!?

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Gay Lussacs Law of Combining Volumes
The volumes of two reacting gases (at the same
temperature and pressure) are in the ratio of
simple integers. Moreover, the ratio of the
volume of each product gas to the volume of
either reacting gas is the ratio of simple
integers.
Avogadros Hypothesis
Equal volumes of different gases (at the same
temperature and pressure contain equal numbers of
particles.
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Cannizzaros Contribution

• Cannizzaro analyzed many gaseous compounds and
  showed that their chemical formulas could be
  established with a consistent scheme that used
  Avogadros hypothesis but avoided any extra
  assumptions about molecular formulas.
• Many gaseous elements (hydrogen, oxygen,
  nitrogen, fluorine, chlorine, etc.) did indeed
  consist of diatomic molecules under ordinary
  conditions.

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Stoichiometry

• The study of mass relationships in chemical
  compounds and chemical reactions.
• The mass balance makes possible the elucidation
  of stoichiometry.

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The Atomic Theory Explains Stoichiometry
According to the atomic theory, the mass of one
molecule of a compound, mcpd, is related to the
number and masses of its constituent atoms as
follows
It is assumed that one molecule of the compound
is comprised of N types of atoms, identified by
the subscript i. The number of atoms of type i
in the molecule is given the symbol niatom and
the mass of each type of atom is given the symbol
miatom. According to the fifth statement of the
atomic theory, the niatoms are integers. Note
also that the above equation is equivalent to a
statement of the conservation of mass.
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The Catch
The masses of individual atoms and the molecules
formed from them are vanishingly small, on the
order of 10-23 - 10-21 grams. The laboratory
balance can measure masses only as small as
milligrams. This forces the chemist to work with
gram amounts of compounds. How can such
measurements relate to and be used to confirm the
atomic theory?
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The Solution
According to atomic theory, the mass of a sample
of a compound, mcpdsam is simply the mass of one
molecule of the compound, mcpd, multiplied by
the number of molecules in the sample, ncpdsam
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In Context
F ma
Newton
E mc2
Einstein
Dalton
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Working in Mass Per Cent Eliminates the Need to
Know ncpdsam
The percent by mass of the ith atom in a compound
is given by the ratio
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The Law of Multiple Proportions

• When two elements form a series of compounds, the
  masses of one element that combine with a fixed
  mass of the other element are in the ratio of
  small integers to each other.
• Now we can make a table of calculations using the
  symbolic notation developed above.

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How Dalton Predicts the Law of Multiple
Proportions
These are ratios of integers.
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Problem 4-3 Multiple Proportions
A chemist obtains the following composition data
for four compounds of nitrogen and oxygen.
Compound a contains 63.65 nitrogen and 36.35
oxygen. Compound b contains 46.68 nitrogen and
53.32 oxygen. Compound c contains 30.45
nitrogen and 69.55 oxygen. Compound d contains
25.94 nitrogen and 74.06 oxygen. (1)
calculate the mass of oxygen per gram of nitrogen
in each compound. (2) Calculate the ratio of
ratios using the smallist ratio. How do the
ratio of ratios support Daltons atomic theory?
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Multiple Proportions Problem
Cmp (symbolic rep) Ratio of Ratios (from Dalton) Amt N, g Amt O, g mO/mN Ratio of Ratios (from masses)
N2O (NiOn) 63.65 36.35
NO (NjOo) 46.68 53.32
NO2 (NkOp) 30.45 69.55
N2O5 (NlOq) 25.94 74.06
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Caution! There are limitations to the information
in Daltons interpretation of the multiple
proportions table.

• You can use Daltons equation to go from known
  composition to predicted ratios.
• But you cannot go from the experimental ratios to
  prediction of molecular composition (inverse
  direction).
• Examination of the multiple proportions table
  shows that for N (Ngt1) compounds, it provides N-1
  equations in 2N unknowns. For a table of two
  compounds there is one equation in four unknowns.
  For three compounds there are two equations in
  six unknowns, etc.

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Answers to Problems in Lecture 4

1. 388 g Ca
2. 2/1
3. 1245