1. Mathematical Relationships with Chemical Formulas
The Mole I
Mathematical Relationships with Chemical Formulas

2. The Mole
mole (mol) - the amount of a substance that contains the same number of entities as there are atoms in exactly 12 g of carbon-12.
This amount is 6.022x The number is called Avogadro’s number and is abbreviated as N.
One mole (1 mol) contains 6.022x1023 entities (to four significant figures)

3. Oxygen
32.0 g
One mole of common substances.
Water
18.0 g
CaCO3
100.1 g
Copper
63.5 g

4. molar mass (MM) = mass of one mole of a substance
1 mol Ca = 40.1 g = 6.02 x 1023 Ca atoms
1 mol Cu = 63.5 g = 6.02 x 1023 Cu atoms
1 mol Hg = g = 6.02 x 1023 Hg atoms

6. Molar Mass 1 mol Cl2 = 71.0 g = 6.02 x 1023 Cl2 molecules
= 2(6.02 x 1023) Cl atoms
1 mol (NH4)2SO4
= 6.02 x 1023 units of (NH4)2SO4
= 15(6.02 x 1023) atoms
= [2(14.0g) + 8(1.0g) + 1(32.1g) (16.0g)] = g

7. Information Contained in the Chemical Formula of Glucose C6H12O6 ( M = 180.16 g/mol)
Carbon (C)
Hydrogen (H)
Oxygen (O)
Atoms/molecule
of compound
6 atoms
12 atoms
6 atoms
Moles of atoms/
mole of compound
6 moles of atoms
12 moles of atoms
6 moles of atoms
Atoms/mole of
compound
6(6.022 x 1023) atoms
12(6.022 x 1023) atoms
6(6.022 x 1023) atoms
Mass/molecule of compound
6(12.01 amu) =72.06 amu
12(1.008 amu) =12.10 amu
6(16.00 amu) =96.00 amu
Mass/mole of
compound
72.06 g
12.10 g
96.00 g

8. Calculating molesA from gramsA
How many moles of Ca are in 22 g of Ca?
1 mol Ca = 40.1 g so

9. Calculating gramsA from molesA
How many g of (NH4)2SO4 are in mol of (NH4)2SO4 ?
1 mol (NH4)2SO4 = g so

10. Mass percent from the chemical formula
Mass % of element X =
moles of X in formula x molar mass of X
molecular (or formula) mass of compound
x 100

11. Per mole glucose there are: 6 moles of C 12 moles H 6 moles O
Calculating the Mass Percents and Masses of Elements in a Sample of Compound
Glucose (C6H12O6) is the most important nutrient in the living cell for generating chemical potential energy. What is the mass percent of each element in glucose?
Per mole glucose there are:
6 moles of C moles H moles O

12. Calculating the Mass Percents and Masses of Elements in a Sample of Compound
1.008 g H
1 mol H
12.01 g C
1 mol C
12 mol H x
= g H
6 mol C x
= g C
16.00 g O
1 mol O
M = g/mol
6 mol O x
= g O
72.06 g C
g glucose
mass percent of C =
x 100 = mass %C
g H
g glucose
mass percent of H =
x 100 = mass %H
96.00 g
g glucose
mass percent of O =
x 100 = mass %O

13. Empirical and Molecular Formulas
Empirical Formula -
The simplest formula for a compound that agrees with the elemental analysis and gives rise to the smallest set of whole numbers of atoms.
C1H2O1
Molecular Formula -
The formula of the compound as it exists, it may be a multiple of the empirical formula.
C6H12O6

14. Determining the Empirical Formula from Masses of Elements
Elemental analysis of a sample of an ionic compound showed 2.82 g of Na, 4.35 g of Cl, and 7.83 g of O. What are the empirical formula and name of the compound?
1 mol Na
22.99 g Na
2.82 g Na
= mol Na
Divide each mole value by the
smallest value to get the whole number subscripts.
1 mol Cl
35.45 g Cl
4.35 g Cl
= mol Cl
1 mol O
16.00 g O
7.83 g O
= mol O
Na1 Cl1 O3.98
NaClO4
NaClO4 is sodium perchlorate.

15. Determining a Molecular Formula from Elemental Analysis and Molar Mass
During physical activity, lactic acid (MM=90.08 g/mol) forms in muscle tissue and is responsible for muscle soreness. Elemental analysis shows that this compound contains 40.0 mass% C, 6.71 mass% H, and 53.3 mass% O.
(a) Determine the empirical formula of lactic acid.
(b) Determine the molecular formula.

16. Determining a Molecular Formula from Elemental Analysis and Molar Mass
Assuming there are 100. g of lactic acid, the constituents are:
40.0 g C
1 mol C
12.01g C
6.71 g H
1 mol H
1.008 g H
53.3 g O
1 mol O
16.00 g O
3.33 mol C
6.66 mol H
3.33 mol O
Divide each mole amount by the smallest value…
C 3.33
H6.66
O3.33
CH2O
empirical formula
3.33
3.33
3.33
Divide the molar mass by the mass of the empirical formula
mass of CH2O
molar mass of lactic acid
90.08 g
30.03 g 3
C3H6O3 is the molecular formula

17. Calculating moleB <-> moleA
How many moles of hydrogen are contained in 2.8 mol of (NH4)2SO4?
1 mol (NH4)2SO4 = 2 mol N, 8 mol H, 1 mol S, 4 mol O

18. Calculating particles from moles
Particles can be molecules, formula units (ionic compounds), atoms or ions.
1 mol particles = 6.02 x 1023 units
Ne atom
NH3 molecule
NaCl formula unit
O2 molecule

19. Calculating particles <-> moles
How many atoms of oxygen are in mol of iron (II) nitrate?
How many moles of sulfur trioxide can be made from 4.0 x 1023 oxygen atoms?

20. Calculating particles <-> g
How many atoms of potassium are in 23.4 g of potassium carbonate?
How many g of sulfur hexachloride can be made from 3.33 x 1024 chlorine atoms?

21. GramA <-> GramB with Formulas
How many g of oxygen are contained in 458 g of C12H22O11?

22. Summary of the mass-mole-number relationships in a chemical formula.
MASS(g)
of substance A
MASS(g)
of substance B
MM (g/mol) of compound A
MM (g/mol) of compound B
AMOUNT(mol)
of substance A
molar ratio from
formula subscripts
AMOUNT(mol)
of substance B
Avogadro’s number
(particles/mol)
Avogadro’s number
(particles/mol)
MOLECULES or ATOMS
(or formula units)
of substance A
MOLECULES or ATOMS
(or formula units)
of substance B
Modified from Silberberg, Principles of Chemistry

23. Questions to Ask When Solving a Problem
Are grams mentioned?
If yes you will need to use a molar mass conversion.
Are you comparing two different substances?
If yes you will need a conversion using the subscripts in a formula.
Are particles (atoms or molecules) involved?
If yes you will need a conversion with Avogadro’s number.
You may need any number of these conversions depending on the problem.

24. How many atoms of oxygen are required to form 6
How many atoms of oxygen are required to form 6.8 grams of aluminum nitrate?
Grams? Yes, need molar mass
Two substances? Yes, need subscripts
Particles? Yes, need Avogadro’s #
So at least 3 conversions are needed…

25. How many moles of nitrogen are contained in 45
How many moles of nitrogen are contained in grams of aluminum nitrate?
Grams? Yes, need molar mass
Two substances? Yes, need subscripts
Particles? No
So, at least 2 conversions are needed…

26. Molarity
Because many reactions happen between substances in solution it is helpful to have a concentration based on moles.

27. Calculating the Molarity of a Solution
Glycine (H2NCH2COOH) is the simplest amino acid. What is the molarity of an aqueous solution that contains mol of glycine in 495 mL?
Molarity is the number of moles of solute per liter of solution.
0.715 mol glycine
495 mL soln
1000mL
1 L
= 1.44 M glycine

28. mass-mole-number-volume relationships in solution.
MASS (g)
of compound
in solution
Summary of
mass-mole-number-volume relationships in solution.
MM (g/mol)
AMOUNT (mol)
of compound
in solution
Avogadro’s number
(molecules/mol)
M (mol/L)
MOLECULES
(or formula units)
of compound
in solution
VOLUME (L)
of solution