Although mass is conserved, most chemical and
physical properties are not conserved during a reaction. Volume is
one of those properties which is not conserved, particularly when
the reaction involves gases as reactants or products. For example,
hydrogen and oxygen react explosively to form water vapor. If we
take 1 liter of oxygen gas and 2 liters of hydrogen gas, by careful
analysis we could find that the reaction of these two volumes is
complete, with no left over hydrogen and oxygen, and that 2 liters
of water vapor are formed. Note that the total volume is not
conserved: 3 liters of oxygen and hydrogen become 2 liters of water
vapor. (All of the volumes are measured at the same temperature and
pressure.)

More notable is the fact that the ratios of
the volumes involved are simple whole number ratios: 1 liter of
oxygen : 2 liters of hydrogen : 2 liters of water. This result
proves to be general for reactions involving gases. For example, 1
liter of nitrogen gas reacts with 3 liters of hydrogen gas to form
2 liters of ammonia gas. 1 liter of hydrogen gas combines with 1
liter of chlorine gas to form 2 liters of hydrogen chloride gas.
These observations can be generalized into the
Law of Combining Volumes.

When gases combine during a
chemical reaction at a fixed pressure and temperature, the ratios
of their volumes are simple whole number
ratios.

These simple integer ratios are striking,
particularly when viewed in the light of our conclusions from the
Law of Multiple Proportions. Atoms combine in simple
whole number ratios, and evidently, volumes of gases also combine
in simple whole number ratios. Why would this be? One simple
explanation of this similarity would be that the volume ratio and
the ratio of atoms and molecules in the reaction are the same. In
the case of the hydrogen and oxygen, this would say that the ratio
of volumes (1 liter of oxygen : 2 liters of hydrogen : 2 liters of
water) is the same as the ratio of atoms and molecules (1 atom of
oxygen: 2 atoms of hydrogen: 2 molecules of water). For this to be
true, equal volumes of gas would have to contain equal numbers of
gas particles (atoms or molecules), independent of the type of gas.
If true, this means that the volume of a gas must be a direct
measure of the number of particles (atoms or molecules) in the gas.
This would allow us to "count" the number of gas
particles and determine molecular formulae.

There seem to be big problems with this
conclusion, however. Look back at the data for forming hydrogen
chloride: 1 liter of hydrogen plus 1 liter of chlorine yields 2
liters of hydrogen chloride. If our thinking is true, then this is
equivalent to saying that 1 hydrogen atom plus 1 chlorine atom
makes 2 hydrogen chloride molecules. But how could that be
possible? How could we make 2 identical molecules from a single
chlorine atom and a single hydrogen atom? This would require us to
divide each hydrogen and chlorine atom, violating the postulates of
the atomic-molecular theory.

Another problem appears when we weigh the
gases: 1 liter of oxygen gas weighs more than 1 liter of water
vapor. If we assume that these volumes contain equal numbers of
particles, then we must conclude that 1 oxygen particle weighs more
than 1 water particle. But how could that be possible? It would
seem that a water molecule, which contains at least one oxygen
atom, should weigh more than a single oxygen particle.

These are serious objections to the idea that
equal volumes of gas contain equal numbers of particles. Our
postulate appears to have contradicted common sense and
experimental observation. However, the simple ratios of the
Law of Combining Volumes are also equally compelling.
Why should volumes react in simple whole number ratios if they do
not represent equal numbers of particles? Consider the opposite
viewpoint: if equal volumes of gas do not contain equal numbers of
particles, then equal numbers of particles must be contained in
unequal volumes not related by integers. Now when we combine
particles in simple whole number ratios to form molecules, the
volumes of gases required would produce decidedly non-whole number
ratios. The
Law of Combining Volumes should not be contradicted
lightly.

There is only one logical way out. We will
accept our deduction from the
Law of Combining Volumes that *equal
volumes
of gas
contain equal numbers of particles*, a conclusion known as
Avogadro's Hypothesis. How do we account for the
fact that 1 liter of hydrogen plus 1 liter of chlorine yields 2
liters of hydrogen chloride? There is only one way for a single
hydrogen particle to produce 2 identical hydrogen chloride
molecules: each hydrogen particle must contain more than one atom.
In fact, each hydrogen particle (or molecule) must contain an even
number of hydrogen atoms. Similarly, a chlorine molecule must
contain an even number of chlorine atoms.

More explicitly, we observe that

1 liter of hydrogen
+
1 liter of chlorine
→
2 liters of hydrogen chloride
1 liter of hydrogen
+
1 liter of chlorine
→
2 liters of hydrogen chloride

(1)Assuming that each liter volume contains an
equal number of particles, then we can interpret this observation
as

1
H
2
molecule
+
1
Cl
2
molecule
→
2
H
Cl
molecules
1
H
2
molecule
+
1
Cl
2
molecule
→
2
H
Cl
molecules

(2)(Alternatively, there could be any fixed even
number of atoms in each hydrogen molecule and in each chlorine
molecule. We will assume the simplest possibility and see if that
produces any contradictions.)

This is a wonderful result, for it correctly
accounts for the
Law of Combining Volumes and eliminates our concerns
about creating new atoms. Most importantly, we now know the
molecular formula of hydrogen chloride. We have, in effect, found a
way of "counting" the atoms in the reaction by
measuring the volume of gases which react.

This method works to tell us the molecular
formula of many compounds. For example,

2 liters of hydrogen
+
1 liter of oxygen
→
2 liters of water
2 liters of hydrogen
+
1 liter of oxygen
→
2 liters of water

(3)This requires that oxygen particles contain an
even number of oxygen atoms. Now we can interpret this equation as
saying that

2
H
2
molecules
+
1
O
2
molecule
→
2
H
2
O
molecules
2
H
2
molecules
+
1
O
2
molecule
→
2
H
2
O
molecules

(4)Now that we know the molecular formula of
water, we can draw a definite conclusion about the relative masses
of the hydrogen and oxygen atoms. Recall from the
Table
that the mass ratio in
water is 8:1 oxygen to hydrogen. Since there are two
hydrogen atoms for every oxygen atom in water, then the mass ratio
requires that a single oxygen atom weigh 16 times the mass of a
hydrogen atom.

To determine a mass scale for atoms, we simply
need to choose a standard. For example, for our purposes here, we
will say that a hydrogen atom has a mass of 1 on the atomic mass
scale. Then an oxygen atom has a mass of 16 on this scale.

Our conclusions account for the apparent
problems with the masses of reacting gases, specifically, that
oxygen gas weighs more than water vapor. This seemed to be
nonsensical: given that water contains oxygen, it would seem that
water should weigh more than oxygen. However, this is now simply
understood: a water molecule, containing only a single oxygen atom,
has a mass of 18, whereas an oxygen molecule, containing two oxygen
atoms, has a mass of 32.

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