1. Chapter 6
Chemical Quantities

2. Homework Recommended Required “Questions” 1-15 (odd)
“Problem” (odd)
“Cumulative Problems” (odd)
“Highlight Problems” 125, 127

3. Counting Particles By Weighing
If a person requests 500 quarter inch hexagonal nuts for purchase
How would you count 500 hex nuts?
You could count the hex nuts individually
Or, count the number of hex nuts by weight
First, find the average weight by weighing out 10 hex nuts and obtaining the total weight (10 hex nuts weigh 105 g)
Average
Weight

4. Counting Particles By Weighing
What size (wt.) will contain 500 hex nuts?
Calculate what weight will contain 500 hex nuts
So, weigh out 5.25 kg of the hex nuts

5. Counting Atoms by the Gram
Many chemical calculations require counting atoms and molecules
There are two common methods for specifying the quantity of material in a sample of a substance: in terms of mass and in terms of amount
It is difficult to do chemical calculations in terms of atoms or formula units
Since atoms are so small, extremely large numbers are needed in calculations
Need to use a special counting unit just as used for other items
A ream of paper
One dozen donuts
A pair of shoes
Because it requires working with large numbers. See Stoker page 281

6. Counting Atoms by the Gram
It is more convenient to use a special counting unit for such large quantities of particles
Mole: A unit that contains х 1023 objects
It is used due to the extremely small size of atoms, molecules, and ions
6.022x1023 particles in 1 mole
Called Avogadro’s Number
Periodic Table
The average atomic mass in amu (one atom)
The weight of 1 mole of the element in grams
Avogadro’s number provides the connecting relationship between molar masses and atomic masses
Chemist use a special counting units
Objects can be anything
“Objects” can be anything
Particles in the sense of atoms and molecules

7. Converting Between Moles and Number of Atoms
Avogadro’s number relates the number of particles present to moles present
Use when solving chemical calculations involving atoms, molecules, or ions present in a given amount of a substance.
Avogadro’s
Number
10 moles
2 moles
1 mole
1.204 × 1024
6.022 × 1024
6.022 × 1023
Moles of
substance
Number of Atoms
(Particles)

8. Converting Between Moles and Number of Molecules
How many molecules of bromine are present in mole of bromine gas?
Avogadro’s number
Given: mol Br2
Find: molecules of Br2
Equality:
Conversion factors:
Solution:

9. Converting Between Grams and Moles of an Element: The Atomic Mass Unit
Atoms are too small to conveniently count individually
The usual standards of mass (g or lbs.) are not convenient for use with atoms
To avoid such small numbers scientists use a mass value for atoms relative to a standard instead of an actual mass value
The standard is the atomic mass unit (amu) with all masses measured relative to carbon-12
The mass of this isotope is set at amu
The mass of one atom of uranium-238 = 3.95 × g

10. Converting Between Grams and Moles of an Element: The Atomic Mass Unit
One amu is defined as the mass of one-twelfth the mass of a carbon-12 atom (nearly equal to one proton)
The masses of all other atoms are determined relative to carbon-12
The masses of these particles in amu brings the mass of the proton and neutron close to 1.
The atomic mass unit brings the mass of the proton and neutron numerically close to 1.

11. Converting Between Grams and Moles of an Element: The Atomic Mass Unit
Atomic masses are determined on a relative scale
The standard scale references the carbon-12 isotope = amu
All other atomic masses are determined relative to carbon-12

12. Converting Between Grams and Moles of an Element: The Atomic Mass Unit
Atoms of the same element do not necessarily have exactly the same mass
Each element exists as a mixture of isotopes so use an average mass
To calculate the average mass of a sample of atoms
Use a “weighted average” for the atomic mass
Number on the bottom of each square in the periodic table is the average weight of the element (in amu)
All masses of other atoms are measured relative to carbon-12

13. Converting Between Grams and Moles of an Element: The Atomic Mass Unit
Using Atomic Mass to Count Atoms
Calculating the number of atoms in a specific mass
If you have a sample of an element, can calculate the number of atoms in that sample
From the atomic mass per one atom a conversion factor can be made
For example: One nitrogen atom has an atomic mass of amu

14. Calculating Atomic Mass in amu (Sample Calculation)
Calculate the mass (in amu) of 1.0 х 104 carbon atoms
1) Given:
2) Plan: Convert from atoms to amu
Find: total mass of C atoms (amu)
3) CF
4) Set Up Problem

15. Converting Between Grams and Moles of an Element
The molar mass of an element (monatomic) is the mass of one mole of atoms of the element
The molar mass of one mole of carbon-12 atoms g
The molar mass (in grams) of any element has the same numerical value as the atomic mass (in amu) of the same element
This mass contains х 1023 particles of that element
Use the periodic table to obtain the molar mass of any element
It was determined experimentally that Avogadro’s number of atoms gives the same numerical value between amu and mol
This is connection between the microscopic and macroscopic values

16. Converting Between Grams and Moles of an Element
When the number of grams (weighed out) of a substance equals the formula mass of that substance, Avogadro’s number of atoms or molecules of that substance are present
Molar mass
of water
= g
Formula mass
of water molecule
= amu
Formula mass of
I2 molecule
= amu
Molar mass of
I2 = g

17. Converting Between Grams and Moles of an Element
The three quantities most often calculated in chemical problems
Number of particles
Number of moles
Number of grams
Using molar mass as a conversion factor is one of the most useful in chemistry
Can be used for gram to mole and mole to gram conversions
Three most commonly calculated quantities for chemical problems
Molar mass can be used to calculate concentrations of solution, to calculate yields of products formed in reactions based on the limiting reagent

18. Converting Between Grams and Moles of an Element
The molar mass provides a relationship between the number of grams of an element and the number of moles of the same element
The molar mass becomes part of the conversion factor used to convert from grams to moles or moles to grams
Solution map
Molar Mass
Grams of
Element
Moles of
Element

19. Converting Between Grams of an Element and Number of Particles
The grams, moles, and number of particles of a substance are interrelated through the conversion factors of molar mass and Avogadro’s number
These two relationships can be combined into a single diagram which is useful to convert grams of a substance to the number of particles (atoms) of a substance
Molar Mass
Grams of
substance
Moles of
substance
Avogadro’s
Number
Moles of
substance
Particles of
substance

20. How many lead atoms are there in a lead weight with a mass of 1.2 g?
Converting Between Grams of an Element and Number of Atoms (Sample Calculation)
How many lead atoms are there in a lead weight with a mass of 1.2 g?
Given: 1.2 g Pb
Find: Pb atoms
Conversion Factors
1 mol Pb= g
1 mol Pb= × 1023 Pb atoms
Solution Map
Molar mass
Avog. Number
1.2 g Pb
mol Pb
number of Pb atoms
Solution
3.5 × 1021 Pb atoms

21. Converting Between Grams and Moles of a Compound
The molar mass provides a relationship between the number of grams of a substance and the number of moles of the same substance
The molar mass of any substance is always numerically equal to its formula mass in amu
Solution map
Molar Mass
Grams of
substance
Moles of
substance

22. Converting Between Grams and Moles of a Compound
Calculate the mass (in grams) of mol of Al2O3
Given: mol Al2O3
Find: g Al2O3
Conversion Factors
1 mol Al2O3 = g
Solution Map
Molar mass
mol Al2O3
g Al2O3
Solution
56.6 g Al2O3

23. Converting Between Grams of an Compound and Number of Molecules
The molar mass provides a relationship between the number of grams of a substance and the number of moles of the same substance
Avogadro’s number provides a relationship between the number of particles of a substance and the number of moles of the same substance
These two relationships can be combined into a single diagram which is useful to convert grams of a substance to the number of particles (molecules) of a substance
Molar Mass
Grams of
substance
Moles of
substance
Avogadro’s
Number
Moles of
substance
Particles of
substance

24. How many molecules of CO2 are in a 5.61 g sample of CO2?
Converting Between Grams of an Element and Number of Molecules (Sample Calculation)
How many molecules of CO2 are in a 5.61 g sample of CO2?
Given: 5.61 g CO2
Find: CO2 molecules
Conversion Factors
1 mol CO2= g
1 mol CO2 = × 1023 CO2 molec
Solution Map
Molar mass
Avog’s No.
5.61 g CO2
mol CO2
number of CO2 molecules
Solution
7.68 × 1022 CO2 molecules

25. Converting Between Grams of an Element and Number of Molecules (Sample Calculation)
Ethylene glycol has the chemical formula: C2H6O2. Find the mass of 1.24 × 1024 molecules of ethylene glycol (antifreeze)
Given: 1.24 × molecules C2H6O2
Find: g of C2H6O2
Conversion Factors
1 mol C2H6O2= g
1 mol C2H6O2= × 1023 C2H6O2 molec
Solution Map
Avog No.
molar mass
molecules C2H6O2
mol C2H6O2
g of C2H6O2
Solution
128 g C2H6O2

26. Chemical Formulas as Conversion Factors
The subscripts in a chemical formula indicate the number of atoms of each element present in a single molecule or formula unit of a compound
The subscripts in a chemical formula can also indicate the number of moles of atoms of each element present in one mole of a compound
e.g. In one molecule of glucose (C6H12O6) there are 6 atoms of carbon, 12 atoms of hydrogen, and 6 atoms of oxygen
e.g. In one mole of glucose (C6H12O6) there are 6 moles of carbon, 12 moles of hydrogen, and 6 moles of oxygen
First case is the microscopic level per molecule
Second case is the macroscopic level per mole

27. Converting Between Moles of a Compound and Moles of a Constituent Element
Some problems require a calculation of the moles of a particular element in a chemical formula of the compound
The subscript of the particular element in the compound becomes part of the conversion factor used to convert moles of compound to moles of element within the compound
To quantify a particular element, the subscript becomes part of the conversion factor.
Solution map
Formula
subscript
Moles of
compound
Moles of
Element
(within compound)

28. How many moles of carbon atoms are present in 1.85 moles of glucose?
Converting Between Moles of a Compound and Moles of a Constituent Element (Sample Calculation)
How many moles of carbon atoms are present in 1.85 moles of glucose?
Given: 1.85 mol C6H12O6
Find: mol C
Conversion Factors
1 mol C6H12O6= 6 mol C
Solution Map
Formula
Subscript
mol C6H12O6
mol C
Solution
11.1 mol C

29. Converting Between Grams of a Compound and Moles of a Constituent Element (Sample Calculation)
International Foods Coffee contains 3.0 mg of sodium chloride per cup of coffee. How many moles of sodium are in each cup of coffee?
Given: 3.0 mg NaCl
Find: mol Na
Conversion Factors
1 mg NaCl = 10-3 g NaCl
1 mol NaCl= g NaCl
1 mol Na =1 mol NaCl
Solution Map
mg NaCl
g NaCl
mol NaCl
mol Na
Solution
5.13 × 10-5 mol Na

30. Converting Between Grams of a Compound and Grams of a Constituent Element
In chemical problems, the three quantities most often calculated for a substance are number of particles (atoms, molecules, or formula units), number of moles, number of grams
All of these quantities are interrelated and the conversion factors which deal with these relationships are Avogadro’s number, molar mass, and chemical formula subscripts
The three concepts can be combined into a single diagram that is useful for problem solving
mol NaCl
1 mol Na =
1 mol NaCl
mol Na
1 mol = g NaCl
0.003 g NaCl

31. Converting Between Grams of a Compound and Grams of a Constituent Element
Throughout Chapter 6, there are calculations for which the initial information is given: moles, grams, or particles.
Additional information is then requested concerning a component of that same substance (find): moles, grams, or particles
Now, use concepts illustrated in previous problems to solve problems in which a given mass of a sample substance is given and we need to calculate the mass of a constituent element
Molar
mass
Formula
subscript
Molar
Mass
Grams of
compound
Moles of
compound
Moles of
element
Grams of
element

32. Converting Between Grams of a Compound and Grams of a Constituent Element
Caffeine is the stimulant found in coffee and tea. It has the chemical formula C8H10N4O2. How many grams of carbon are present in a 50.0 g sample?
Given: 50.0 g C8H10N4O2
Find: g of C
Conversion Factors
1 mol C8H10N4O2= 194 g C8H10N4O2
1 mol C= g C
8 mol C= 1 mol C8H10N4O2
Solution Map
Mol-mol
ratio
Molar
Mass
Molar
Mass
50.0 g C8H10N4O2
mol C8H10N4O2
mol of C
g of C
Solution
24.8 g C

33. Mass Percent Composition of Compounds
The mass percent of an element may be obtained by:
Decomposition of a sample of a known mass
Then, the masses of the constituent elements present in each sample are then obtained
Each element’s mass, and the original sample mass, is used to calculate the percent composition
Mass data obtained from the combination of elements which combine to form a compound
Each element’s mass, and the product’s mass, is used to calculate the percent composition
Stoker page 280

34. Mass Percent Composition of Compounds
The composition of compounds is determined by their formulas (e.g. the formula of carbon dioxide tells us it’s composed of carbon and oxygen (2 oxygen atoms and 1 carbon atom)
Another way to describe the composition of compounds is in terms of the mass percent of each element in the compound
The mass percent composition is the percent by mass of each element in a compound

35. Mass Percent Composition from a Chemical Formula
The mass percent composition is the percent by mass of each element in a compound
To determine a compound’s mass percent composition:
its chemical formula is needed
the molar mass of each element that composes the compound
the subscript numbers in the formula are equal to the number of moles of each element in one mole of the compound (its molar mass)
“In one mole” of a compound is a key fact that allows the calculation of percent composition from chemical formulas. The formula of carbon dioxide indicates it is composed of one atom of carbon and two atoms of oxygen. Now we will express it in terms of mass percent

36. Mass Percent Composition of Compounds
Percent numbers are always in terms of parts per hundred
For example, the percent composition of water is 88.81% oxygen and 11.19% hydrogen
The percent composition for each element is determined by dividing the mass contributed by each element, by the molar mass and multiplied by 100
The sum of the percents of all of the elements in a compound equals 100%
If the mass percent of a particular element in a compound is known, you can calculate the amount of the element present in any sample size of that compound
The number of items of a specified type in a group of 100 items

37. Mass Percent Composition from a Chemical Formula
Calculate the mass percent composition of each element in NH4OH?
Determine the mass of 1 mol of compound
Molar mass
14.01 g N
5.040 g H
16.00 g O
On a per mol basis
Determine the contribution of each element

38. Calculating Empirical Formulas for Compounds
Chemical formulas are determined by calculation using experimentally obtained information
Depending on the amount of experimental data available, two types of formulas can be obtained
Empirical formulas (simplest formula)
Molecular formulas (true formula)

39. Calculating Empirical Formulas for Compounds
The empirical formula gives the simplest ratio of elements in a compound
It uses the smallest possible whole number ratio of atoms present in a formula unit of a compound
The subscripts in the formula cannot be reduced any further to a simpler ratio by division with a small integer
If the percent composition of a compound is known, an empirical formula can be calculated
Formulas are determined by calculation of data experimentally obtained
Smallest possible set of subscript numbers
The subscript numbers in formulas can be read in terms of the number of moles of each element

40. Calculating an Empirical Formula from Experimental Data
To Determine the empirical formula:
Write down or calculate the given number of grams of each element present in a sample of the compound
Convert the mass of each element to moles of element using the appropriate molar mass
Using the calculated moles of each of the elements:
Write down a pseudoformula using the moles of each element as a subscript
Find the lowest whole number mole ratio
Divide all the subscripts in the formula by the smallest subscript

41. Arithmetic may need to be applied to convert decimals to whole numbers
Obtaining an Empirical Formula from Experimental Data Converting Decimal Numbers to Whole Numbers
The subscripts in a “true” formula are expressed as whole numbers, not as decimals
The resulting decimal numbers from a calculation represent each element’s subscript
Arithmetic may need to be applied to convert decimals to whole numbers
If the number(s) are NOT whole numbers, multiply each number by the same small integer (2, 3, 4, 5, or 6) until a whole number is obtained for each subscript number
Cannot have 1.5 atoms in a formula

42. Obtaining an Empirical Formula from Experimental Data
Lactic acid has a molar mass of g and has this percent composition:
40.0% C, 6.71% H, 53.3% O
What is the empirical and molecular formula of lactic acid?
Assume a g sample size
Convert percent numbers to grams
Lactic acid builds up in muscles after aerobic exercise
Since percent represents parts of one element per 100 parts of the total compound

43. Obtaining an Empirical Formula from Experimental Data
Step 1: Mass of each element
in a 100 g
sample of the compound
40.0 g C
6.71 g H
53.3 g O
Step 2: Convert mass to moles
Step 3: Pseudoformula
C3.33H6.66 O3.33
Step 4: Divide by smallest subscript
Empirical
formula is
CH2O

44. Calculating Molecular Formulas for Compounds
Molecular formulas are the formulas of molecules
They illustrate all of the atoms of each element in the molecule
It does not necessarily have the smallest set of subscript numbers: It can be the same as or a whole number multiplier of its empirical formula
To determine a molecular formula, the compound’s molecular mass is needed

45. Relating Empirical and Molecular Formulas
Empirical Formula
Smallest possible set of subscript numbers
Smallest whole number ratio
All ionic compounds are given as empirical formulas
Molecular Formulas
The actual formulas of molecules
When an empirical formula is known, the molar mass is needed to determine if the empirical formula and the molecular formula are the same
It shows all of the atoms present in a molecule
It may be the same as the EF or a whole-number multiple of its EF
Ionic compounds do not exist as molecules
Molecular formulas account for every atom in the structure
Molecular formula = n х Empirical formula

46. Calculating Molecular Formulas for Compounds
n represents a whole number multiplier from 1 to as large as necessary
Calculate the empirical formula and the mass of the empirical formula
Divide the given molecular mass by the calculated empirical formula molar mass
Answer is a whole number multiplier

47. Relating Empirical and Molecular Formulas
Multiply each subscript in the empirical formula by the whole number multiplier to get the molecular formula
For molecular compounds, the two types of formulas may or may not be the same

48. Relating Empirical and Molecular Formulas
For ionic compounds
The empirical and molecular formula are the same
For molecular compounds
The two types of formulas may be the same but not necessarily

49. Calculating Molecular Formulas for Compounds
What is the molecular formula of lactic acid?
Obtain the value of n (whole number multiplier)
Multiply the empirical formula by the multiplier
Empirical
formula is
CH2O
Empirical formula molar mass = g + 2 (1.008 g) g = g/mol
The small interger is the name of the small number multiplier
Molecular formula = n х empirical formula
C3H6O3
Molecular formula = 3 (CH2O)

50. end Ionic compounds do not exist as molecules
Molecular formulas account for every atom in the structure