Page 50 - Theory and Problems of BEGINNING CHEMISTRY

CHAP. 3] ATOMS AND ATOMIC MASSES 39

The Law of Conservation of Mass states that mass is neither created nor destroyed in a chemical reaction or
physical change.
The Law of Definite Proportions states that every chemical compound is made up of elements in a definite ratio
by mass.
The Law of Multiple Proportions states that when two or more different compounds are formed from the same
elements, the ratio of masses of each element in the compounds for a given mass of any other element is a small
whole number.

EXAMPLE 3.1. Calculate the mass of sodium chloride formed by the complete reaction of 10.0 g of sodium with 15.4 g
of chlorine. What law allows this calculation?

Ans. The Law of Conservation of Mass:
10.0g + 15.4g = 25.4 g total

EXAMPLE 3.2. Calculate the mass of oxygen that will combine with 2.00 g of magnesium if 0.660 g of oxygen reacts
with 1.00 g of magnesium. What law allows this calculation?
Ans. The Law of Definite Proportions states that twice as much oxygen will react with twice as much magnesium to yield
the same ratio of masses:
2.00 g magnesium

0.660 g oxygen = 1.32 g oxygen
1.00 g magnesium
EXAMPLE 3.3. Show that the following data illustrate the Law of Multiple Proportions:

Element 1 Element 1

Compound 1 1.00 g 1.33 g
Compound 2 1.00 g 2.66 g

Ans. For a fixed mass of element 1 in the two compounds (1.00 g), the ratio of masses of the other element is a small
integral ratio: (2.66 g)/(1.33 g) = 2.00.

Dalton argued that these laws are entirely reasonable if the elements are composed of atoms. For example,
the reason that mass is neither gained nor lost in a chemical reaction is that the atoms in the reaction merely
change partners with one another; they do not appear or disappear. The definite proportions of compounds stem
from the fact that the compounds comprise a definite ratio of atoms (postulate 3), each with a definite mass
(postulate 2). The law of multiple proportions is due to the fact that different numbers of atoms of one element
can react with a given number of atoms of a second element (postulate 4), and since atoms must combine in
whole-number ratios, the ratio of masses must also be in whole numbers.

3.3. ATOMIC MASSES
Once Dalton’s hypotheses had been proposed, the next logical step was to determine the relative masses of
the atoms of the elements. Since there was no way at that time to determine the mass of an individual atom, the
relative masses were the best information available. That is, one could tell that an atom of one element had a
mass twice as great as an atom of a different element (or 15/4 times as much, or 17.3 times as much, etc.). How
could even these relative masses be determined? They could be determined by taking equal (large) numbers of
atoms of two elements and by determining the ratio of masses of these collections of atoms.
For example, a large number of sodium atoms have a total mass of 23.0 g, and an equal number of chlorine
atoms have a total mass of 35.5 g. Since the number of atoms of each kind is equal, the ratio of masses of one
sodium atom to one chlorine atom is 23.0 to 35.5. How can one be sure that there are equal numbers of sodium
and chlorine atoms? One ensures equal numbers by using a compound of sodium and chlorine in which there
are equal numbers of atoms of the two elements (i.e., sodium chloride, common table salt).