Page 288 - 9780077418427.pdf

/Users/user-f465/Desktop
tiL12214_ch10_251-274.indd Page 265 9/3/10 6:11 PM user-f465
tiL12214_ch10_251-274.indd Page 265 9/3/10 6:11 PM user-f465 /Users/user-f465/Desktop

the ratio of coefficients in a balanced equation means a ratio of atomic mass. So the mass of a mole of C-12 atoms is
any number of molecules, from 2 of H 2 and 1 of O 2 , 20 of H 2 12.00 g, or
and 10 of O 2 , 2,000 of H 2, and 1,000 of O 2 , or however many are mass of one atom × one mole = mass of a mole of C-12

23

found in 2 L of H 2 and 1 L of O 2 .
(6.02 × 10 ) =
(12.00 u) 12.00 g

The masses of all the other isotopes are based on a comparison
to the C-12 atom. Thus, a He-4 atom has one-third the mass of
EXAMPLE 10.9
a C-12 atom. An atom of Mg-24 is twice as massive as a C-12
Propane is a hydrocarbon with the formula C 3 H 8 that is used as a bot- atom. Thus
tled gas. (a) How many liters of oxygen are needed to burn 1 L of pro-
pane gas? (b) How many liters of carbon dioxide are produced by the 1 Atom × 1 Mole = Mass of Mole
reaction? Assume all volumes to be measured at the same temperature C-12: 12.00 u × 6.02 × 10 = 12.00 g
23
and pressure. 23
He-4: 4.00 u × 6.02 × 10 = 4.00 g
23
Mg-24: 24.00 u × 6.02 × 10 = 24.00 g
SOLUTION
Therefore, the mass of a mole of any element is numerically
The balanced equation is
equal to its atomic mass. Samples of elements with masses that
are the same numerically as their atomic masses are 1 mole
C 3 H 8 ( g) + 5 O 2 ( g) → 3 CO 2 ( g) + 4 H 2 O( g)
The coefficients tell you the relative number of molecules involved measures, and each will contain the same number of atoms
in the reaction, that 1 molecule of propane reacts with 5 molecules of (Figure 10.16).
oxygen to produce 3 molecules of carbon dioxide and 4 molecules of This reasoning can be used to generalize about for mula
water. Since equal volumes of gases at the same temperature and pres- weights, molecular weights, and atomic weights since they are
sure contain equal numbers of molecules, the coefficients also tell you all based on atomic mass units relative to C-12. The gram-
the relative volumes of gases. Thus, 1 L of propane (a) requires 5 L of atomic weight is the mass in grams of 1 mole of an element
oxygen and (b) yields 3 L of carbon dioxide (and 4 L of water vapor) that is numerically equal to its atomic weight. The atomic
when reacted completely.
weight of carbon is 12.01 u; the gram-atomic weight of car-
bon is 12.01 g. The atomic weight of magnesium is 24.3 u; the
gram-atomic weight of magnesium is 24.3 g. Any gram-atomic
weight contains Avogadro’s number of atoms. Therefore, the
UNITS OF MEASUREMENT USED gram-atomic weights of the elements all contain the same
number of atoms.
WITH EQUATIONS
Similarly, the gram-formula weight of a compound is
The coefficients in a balanced equation represent a ratio of any the mass in grams of 1 mole of the compound that is nu-
number of molecules involved in a chemical reaction. The equa- merically equal to its formula weight. The gram-molecular
tion has meaning about the atomic weights and formula weights weight is the gram-formula weight of a molecular com-
of reactants and products. The counting of numbers and the use pound. Note that 1 mole of Ne atoms (6.02 × 10 neon
23
of atomic weights are brought together in a very important mea- atoms) has a gram-atomic weight of 20.2 g, but 1 mole of
surement unit called a mole (from the Latin meaning “a mass”). O 2 molecules (6.02 × 10 oxygen molecules) has a gram-
23
Here are the important ideas in the mole concept: molecular weight of 32.0 g. Stated the other way around,
1. Recall that the atomic weights of elements are average 32.0 g of O 2 and 20.2 g of Ne both contain Avogadro’s number
relative masses of the isotopes of an element. Th e weights of particles.
are based on a comparison to carbon-12, with an assigned
mass of exactly 12.00 (see chapter 8).
2. Th e number of C-12 atoms in exactly 12.00 g of C-12 has EXAMPLE 10.10
23
been measured experimentally to be 6.02 × 10 . Th is
(a) A 100 percent silver chain has a mass of 107.9 g. How many silver
number is called Avogadro’s number, named aft er the
atoms are in the chain? (b) What is the mass of 1 mole of sodium chlo-
scientist who reasoned that equal volumes of gases contain
ride, NaCl?
equal numbers of molecules.
3. An amount of a substance that contains Avogadro’s
number of atoms, ions, molecules, or any other chemical SOLUTION

unit is defined as a mole of the substance. Thus, a mole The mole concept and Avogadro’s number provide a relationship be-
23
is 6.02 × 10 atoms, ions, etc., just as a dozen is 12 eggs, tween numbers and masses. (a) The atomic weight of silver is 107.9 u,

apples, etc. The mole is the chemist’s measure of atoms, so the gram-atomic weight of silver is 107.9 g. A gram-atomic weight
+ 23
molecules, or other chemical units. A mole of Na ions is is 1 mole of an element, so the silver chain contains 6.02 × 10
+
23
6.02 × 10 Na ions. silver atoms. (b) The formula weight of NaCl is 58.5 u, so the gram-

4. A mole of C-12 atoms is defined as having a mass of formula weight is 58.5 g. One mole of NaCl has a mass of 58.5 g.
exactly 12.00 g, a mass that is numerically equal to its
10-15 CHAPTER 10 Chemical Reactions 265