Micro World atoms & molecules
Macro World grams
By definition:
1 atom 12 C “ weighs ” 12 amu
On this scale
1 H = 1.008 amu
16 O = 16.00 amu
3

The average atomic mass is the weighted average of all of the naturally occurring isotopes of the element .
4

Example: 3.1
Copper, a metal known since ancient times, is used in electrical cables and pennies, among other things.
The atomic masses of its two stable isotopes,
(69.09 percent) and (30.91 percent), are
62.93 amu and 64.9278 amu, respectively.
Calculate the average atomic mass of copper.
The relative abundances are given in parentheses.

Avogadro’s number: 6.022x10
23
(atoms, molecules, particles)
For any element atomic mass (amu) = molar mass (grams)

Example: 3.2
Helium (He) is a valuable gas used in industry, low-temperature research, deep-sea diving tanks, and balloons.
How many moles of He atoms are in
6.46 g of He?
A scientific research helium balloon.

1S 32.07 amu
2O + 2 x 16.00 amu
SO
2
64.07 amu
SO
2
For any molecule molecular mass (amu) = molar mass (grams)
1 molecule SO
2
1 mole SO
2
= 64.07 amu
= 64.07 g SO
2

Example: 3.5
Calculate the molecular masses (in amu) of the following compound:
(a) caffeine (C
8
H
10
N
4
O
2
), a stimulant present in tea, coffee, and cola beverages

Example: 3.6
Methane (CH
4
) is the principal component of natural gas.
How many moles of CH
4 present in 6.07 g of CH
4
?
are

Example: 3.7
How many hydrogen atoms are present in 25.6 g of urea
[(NH
2
)
2
CO], which is used as a fertilizer, in animal feed, and in the manufacture of polymers?
The molar mass of urea is
60.06 g.
urea

Na Cl
1Na 22.99 amu
1Cl + 35.45 amu
NaCl 58.44 amu
For any ionic compound formula mass (amu) = molar mass (grams)
1 formula unit NaCl = 58.44 amu
1 mole NaCl = 58.44 g NaCl

Mass Spectrum of Ne

Mass
Spectrum of Ne

n x molar mass of element molar mass of compound x 100% n is the number of moles of the element in 1 mole of the compound
C
2
H
6
O
%C =
2 x (12.01 g)
46.07 g
%H =
6 x (1.008 g)
46.07 g
%O =
1 x (16.00 g)
46.07 g x 100% = 52.14% x 100% = 13.13% x 100% = 34.73%
52.14% + 13.13% + 34.73% = 100.0%

Example: 3.8
Phosphoric acid (H
3
PO
4
) is a colorless, syrupy liquid used in detergents, fertilizers, toothpastes, and in carbonated beverages for a “ tangy ” flavor.
Calculate the percent composition by mass of H, P, and O in this compound.

Example: 3.10
Chalcopyrite (CuFeS
2
) is a principal mineral of copper.
Calculate the number of kilograms of Cu in
3.71 × 10 3 kg of chalcopyrite.
Chalcopyrite.

Steps:
1. Find the mass of water or mass of anhydrate
2. Turn mass of water and mass of anhydrate into moles
(individually)
3. Find the mole ratio; mole of anhydrate mole of water mole of anhydrate mole of anhydrate
4. Write the formula of the hydrate

A calcium chloride hydrate has a mass of 4.72 g. After heating for several minutes the mass of the anhydrate is found to be 3.56 g.
Use this information to determine the formula for the hydrate.

Steps:
1. Percent to mass
2. Mass to moles
3. Divide by small
4. Multiply ‘til whole

Example: 3.9
Ascorbic acid (vitamin C) cures scurvy.
It is composed of 40.92 percent carbon (C), 4.58 percent hydrogen
(H), and 54.50 percent oxygen (O) by mass.
Determine its empirical formula.

Combust 11.5 g ethanol
Collect 22.0 g CO
2 and 13.5 g H
2
O g CO
2 mol CO
2 mol C g C 6.0 g C = 0.5 mol C g H
2
O mol H
2
O mol H g H 1.5 g H = 1.5 mol H g of O = g of sample – (g of C + g of H) 4.0 g O = 0.25 mol O
Divide by smallest (0.25)
Empirical formula C
2
H
6
O
23

When ethanol is burned, carbon dioxide and water are given off.
Suppose that in one experiment the combustion of 11.5 g of ethanol produced 22.0 g of CO
2 and 13.5 g of H
2
O. Determine the empirical formula for ethanol.

Steps:
1. Find empirical formula
2. Determine the molar mass of the empirical formula
3. Find multiplier (molar mass given/empirical molar mass)
4. Multiply empirical formula subscripts by the multiplier

Example: 3.11
A sample of a compound contains 30.46 percent nitrogen and
69.54 percent oxygen by mass, as determined by a mass spectrometer.
In a separate experiment, the molar mass of the compound is found to be between 90 g and 95 g.
Determine the molecular formula and the accurate molar mass of the compound.

“Reactants with”
“to produce” or “yield”
2
2
(g)
+
2
(g)
Reactants
2
2
( l
)
Product(s)

Steps:
1. List elements present on each side
2. Add coefficients to balance (“met a non hairy oxen”)
3
2

Example: 3.12
When aluminum metal is exposed to air, a protective layer of aluminum oxide
(Al
2
O
3
) forms on its surface. This layer prevents further reaction between aluminum and oxygen, and it is the reason that aluminum beverage cans do not corrode. [In the case of iron, the rust, or iron(III) oxide, that forms is too porous to protect the iron metal underneath, so rusting continues.]
An atomic scale image of aluminum oxide.
Write a balanced equation for the formation of Al
2
O
3
.

• Mole method: coefficient in a reaction can be interpreted as the number of moles
• Allows us to write conversion factors from a chemical equation

Example: 3.13
The food we eat is degraded, or broken down, in our bodies to provide energy for growth and function. A general overall equation for this very complex process represents the degradation of glucose (C
6
H
12
O
6
) to carbon dioxide (CO
2
) and water
(H
2
O):
If 856 g of C
6
H
12
O
6 is consumed by a person over a certain period, what is the mass of CO
2 produced?

Example: 3.14
All alkali metals react with water to produce hydrogen gas and the corresponding alkali metal hydroxide.
A typical reaction is that between lithium and water:
How many grams of Li are needed to produce 9.89 g of H
2
?
Lithium reacting with water to produce hydrogen gas.

CO(g) + 2 H
2
(g) CH
3
OH(g)
2NO + O
2
2NO
2

Example: 3.15
Urea [(NH
2
)
2
CO] is prepared by reacting ammonia with carbon dioxide:
In one process, 637.2 g of NH
3 are treated with 1142 g of CO
2
.
(a) Which of the two reactants is the limiting reagent?
(b) Calculate the mass of (NH
2
)
2
CO formed.
(c) How much excess reagent (in grams) is left at the end of the reaction?

% Yield =
Actual Yield
Theoretical Yield x 100%

Example: 3.17
Titanium is a strong, lightweight, corrosion-resistant metal that is used in rockets, aircraft, jet engines, and bicycle frames. It is prepared by the reaction of titanium(IV) chloride with molten magnesium between 950 °C and 1150°C:
In a certain industrial operation 3.54 × 10 7 g of TiCl
4 with 1.13 × 10 7 g of Mg. are reacted
(a)Calculate the theoretical yield of Ti in grams.
(b)Calculate the percent yield if 7.91 × 10 6 g of Ti are actually obtained.