1. Chapter 10: The Mole

2. 10.1 Measuring Matter

3. Counting Particles
Chemists need a convenient method for accurately counting the number of atoms, molecules, or formula units in a sample of a substance.
Chemists created a counting unit called the mole.

4. The mole
The mole (mol) is the SI base unit used to measure the amount of a substance
A mole is defined as the number of carbon atoms in exactly 12 g of pure carbon-12
A mole of anything contains x 1023 representative particles
A representative particle is any particle, such as an atom, molecule, formula unit, electron, or ion
This number is called Avogadro’s number
Round to 6.02 x 1023

5. Converting Between Moles and Particles
The relationship between moles and representative particles is given by Avogadro’s number.
1 mol of representative particles = x 1023 representative particles
Conversion factors:
6.02 x 1023 representative particles ← Avogadro’s # conversion mol
1 mol ← inverse Avogadro’s # conversion
6.02 x 1023 representative particles

6. By using the correct conversion factor, you can find the number of representative particles in a given number of moles.
Number of moles x x 1023 representative particles = particles
1 mole
You can find how many moles are represented by a certain number of representative particles by using the inverse of Avogadro’s number as a conversion.
Number of particles x 1 mole = # moles
6.02 x 1023 representative particles
You can convert between moles and number of representative particles by multiplying the known quantity by the proper conversion factor.

7. 10.2 Mass and the Mole

8. The Mass of a Mole
One-mole quantities of two different substances have different masses
The atomic masses of all elements are established relative to carbon-12.
Atomic masses on the periodic table are weighted averages of the masses of all the naturally occurring isotopes of each element

9. The mass in grams of one mole of any pure substance is called its molar mass
Numerically equal to an element’s atomic mass
Units = g/mol
Ex: manganese
atomic mass = amu
molar mass = g/mol

10. Using Molar Mass The molar mass can be used as a conversion factor
Molar mass conversion factor: (atomic mass) grams
1 mol
Inverse molar mass conversion factor: 1 mol (atomic mass) grams

11. The number of moles can be converted to an equivalent mass using the molar mass conversion factor
number of moles x mass in grams = mass in grams
1 mol
The mass of a substance can be converted to the number of moles using the inverse molar mass conversion factor
mass x mol = number of moles
mass in grams

12. Converting between mass and atoms
You cannot make a direct conversion from the mass of a substance to the number of representative particles of that substance
First convert the mass to moles using the inverse molar mass conversion
Then convert the number of moles to number of representative particles using Avogadro’s number conversion factor.
Mass must always be converted to moles before being converted to atoms
Atoms must be converted to moles before calculating their mass

13. 10.3 Moles of Compounds

14. Chemical Formulas and the Mole
The chemical formula for a compound indicates the numbers and types of atoms contained in one unit of the compound
The ratio of elements within a compound does not change depending on the amount, is the same when there is a mole of that compound.
Ex: CO2
1 molecule of CO2 has a C-O ratio of 1:2
1 carbon atom
2 oxygen atoms
1 mole of CO2 has a C-O ratio of 1:2
1 mole of carbon atoms
2 moles of oxygen atoms

15. Conversion factors can be written for any element in a compound
In some chemical calculations, you might need to convert from moles of a compound to moles of individual atoms in the compound
Conversion factors can be written for any element in a compound
The number of moles of the element that goes in the numerator of the conversion factor is the subscript for that element in the chemical formula
Ex: 2 mol F/ 1 mol CCl2F2

16. The Molar Mass of Compounds
The mass of a mole of a compound equals the sum of the masses of all the particles that make up the compound

17. To determine the molar mass of potassium chromate (K2CrO4):
Calculate the mass of each of the parts using the subscripts and molar masses
2 mol K x (39.1g K/ 1 mol K) = 78.2 g K
1 mol Cr x (52.0g Cr/ 1 mol Cr) = 52.0 g Cr
4 mol O x (16.0 g O/ 1 mol O) = 64.0 g O
Add the masses together
78.2 g K + 52.o g CR g O = g K2CrO4

18. Converting Moles of a Compound to Mass
In order to convert moles of a compound to mass of the compound first you must calculate the molar mass of the compound
The molar mass of the compound can then be used as a conversion factor to determine the mass present in a given number of moles of a compound

19. Converting the Mass of a Compound to Moles
First calculate the molar mass of the compound
Use the inverse of the molar mass as the conversion factor to solve for moles

20. Converting the Mass of a Compound to Number of Particles
No direct conversion is possible between mass and number of particles in a compound
First convert the given mass to moles by multiplying by the inverse of the molar mass
Then convert moles to the number of representative particles by multiplying by Avogadro’s number
To determine the numbers of atoms or ions in a compound, use the conversion factors that are ratios of the number of atoms or ions in the compound to one mole of compound
Based on the chemical formula

21. 10.4 Empirical and Molecular Formulas

22. Percent Composition
The percent by mass of any element in a compound can be found by dividing the mass of the element by the mass of the compound and multiplying by 100.
Percent by mass (element) = mass of element/ mass of compound x 100
The percents by mass of all the elements of a compound must always add up to 100
The percent by mass of each element in a compound is called the percent composition of a compound

23. Percent composition from the chemical formula
To find the percent composition of a compound from its chemical formula, assume you have exactly 1 mol of the compound and use the chemical formula to calculate the compound’s molar mass. Then, determine the mass of each element in a mole of the compound by multiplying the element’s molar mass by its subscript in the chemical formula.
To find the percent by mass of an element, divide the element’s mass by the molar mass of the compound and multiply by 100.
Percent by mass = Mass of element in 1 mol of compound x 100
Molar mass of compound

24. Empirical Formula
When a compound’s percent composition is known, its formula can be calculated by determining the smallest whole-number ratio of the moles of the elements in the compound.
The empirical formula for a compound is the formula with the smallest whole number mole ratio of the elements
Might or might not be the same as the actual molecular formula
If different, the molecular formula will always be a simple multiple of the empirical formula
Ex: hydrogen peroxide
Empirical formula = HO
Molecular formula = H2O2

25. If percent composition is given, you can assume that the total mass of the compound is g and that the percent by mass of each element is equal to the mass of that element in grams.
The mass of each element can be converted to a number of moles by multiplying by the inverse of the molar mass
If the resulting values for moles are not whole numbers then
Recognize that the element with the smaller number of moles might have the smallest subscript possible = 1
Divide all mole values by the smallest number of moles
Not changing the ratio
If all values are still not whole numbers then multiply all the mole values by the smallest factor that will make them whole numbers

26. Molecular Formula
The simplest ratio does not always indicate the actual ratio in the compound
The molecular formula specifies the actual number of atoms of each element in one molecule or formula unit of the substance.
To determine the molecular formula for a compound, the molar mass of the compound must be determined through experimentation and compared with the mass represented by the empirical formula

27. Dividing the actual molar mass by the mass of the empirical formula indicates the integer n.
The integer is the factor by which the subscripts in the empirical formula must be multiplied to obtain the molecular formula.
Molecular formula = (empirical formula)n

28. 10.5 The Formula for a Hydrate

29. Naming Hydrates
Solid ionic compounds in which water molecules are trapped are called hydrates
A hydrate is a compound that has a specific number of water molecules bound to its atoms.
In the formula for a hydrate, the number of water molecules associated with each formula unit of the compound is written following a dot
Ex: Na2CO3  10H2O
Sodium carbonate decahydrate
The prefix attached to the root word hydrate refers to the number of water molecules

30. Analyzing a Hydrate
When a hydrate is heated, water molecules (water of hydration) are driven off leaving an anhydrous compound, or one “without water.”
In order to determine the formula of a hydrate you must find the number of moles of water associated with 1 mol of the hydrate

31. To find the coefficient of the water molecules you would compare the masses before and after heating the sample
The mass of the water of hydration is the difference between the mass of the hydrate and the mass of the anhydrous compound
You can convert the masses of the anhydrous sample and the water of hydration to moles using their molar masses
Once the moles have been determined you can calculate the ratio of moles of water to the anhydrous hydrate
# mol water = ratio = coefficient of water
# mol anhydrous hydrate

32. Uses of hydrates
Anhydrous calcium chloride is used to remove moisture from the air, creating a dry atmosphere, and calcium sulfate is often added to solvents to keep them free of water.
Desiccants, drying agents
Electronic and optical equipment that are transported overseas by ship are packaged with packets of desiccants that absorb water from the air and prevent moisture from interfering with sensitive electronic circuitry.
Some hydrates are used to store solar energy