Chemical Formulas and the Mole

Introduction• 84 potatoes• 63 carrots• 15 onions• 3 heads of garlic• 27 turnips• 42 pieces of celery• 9 cans of green beans• 6 cans of tomato puree• 6 cans of diced peppers• 9 cans of corn• 6 cans of lima beans• Serves 81

• If only 1 head of garlic is available, how many of each ingredient will be needed to adjust the recipe in order to make the stew correctly and how many people will it feed?

• If you wanted to feed 324 people, how much of each ingredient would you need?

How are formulas represented?

• Calculate the % composition of the formula you were given.

• % composition comes from experimental analysis and provides information about the make up of the compound.

• Compare your calculations with the students around you having a different colored card.

• What did you find regarding your % compositions? • Although the formulas are different, are there any

similarities among your formulas that could account for the similarities of your calculations?

Empirical Formulas• The molecular formula of a compound gives the actual number of

atoms of each element making up a compound.• (The molecular formula is the formula that is written on your card)• The empirical formula of a compound is the formula with the

smallest whole number ratio of the elements making up the compound.

• What is the empirical formula for the compound written on your card?

• The empirical formula may or may not be the same as the actual molecular formula.

• If the two formulas are different, the molecular formula will always be a simple multiple of the empirical formula.

Practice Problems

• Write the empirical formula for each of the following molecular formulas.

1.C6H12O6

2.H2O2

3.C4H10

4.H2O5.N2O4

6.C3H6O2

Determining Empirical Formulas

• If % composition can be determined from the formula, then the formula can be determined from the % composition of the compound.

Rules for determining Empirical Formulas

1. Assume a 100 g sample, so % becomes “g”.2. Convert grams to moles by dividing by the

atomic mass of each element.3. Divide each result (mole) by the smallest

result present (mole ratio).4. Look for whole number ratios.5. The whole number ratios become the

subscripts for the formula.

Rhyme for Remembering Rules

“Percent to massMass to moleDivide by smallMultiply 'til whole“

• A Simple Rhyme for a Simple Formulaby Joel S. ThompsonJournal of Chemical EducationVol. 65, No. 8; August 1988, p. 704

Sample Problems

• Determine the empirical formula for a compound that is 27.3% carbon and 72.7% oxygen.

• Determine the empirical formula for a compound that is 56.6% K, 8.7% C, and

34.7% O. • Determine the empirical formula for a

compound that is 69.9% Fe and 30.1% O.

Multiples for use when ratio is not initially a whole number

Decimal Multiplier

0.5 X 2

0.30-.35 X 3

0.63 - .67 X 3

0.22-0.25 X 4

0.72-0.75 X 4

Molecular Formulas

• Molecular formulas are multiples of empirical formulas.

Compound Empirical Formula

Molar Mass Molecular Formula

Formaldehyde CH2O 30 CH2O

Acetic acid CH2O 60 C2H4O2

Glucose CH2O 180 C6H12O6

Sample Problems

• The empirical formula for a compound containing phosphorus and oxygen was found to be P2O5. Experiments show that the molar mass of the compound is 284 g/mol. What is the molecular formula and name of the compound?

• Determine the molecular formula of a compound having an empirical formula of CH and a molar mass of 78.11 g/mol.

Putting it All Together

• A compound with a molar mass of 92 g/mol contains 0.608 g of nitrogen and 1.388 g of oxygen. What is the empirical and molecular formula of the compound?

• A compound with a molar mass of 86 g/mol contains 83.62% C and 16.38% H. What is the molecular formula of the compound?

Hydrates• Hydrates are solid ionic compounds in which

water molecules are trapped.• Some products, such as electronic equipment,

are boxed with small packets labeled dessicant. These packets control moisture by absorbing water. Some contain ionic compounds called hydrates.

• Each hydrate has a specific number of water molecules bound to its atoms.

Example

• An opal is hydrated silicon dioxide (SiO2) The presence of water and various mineral impurities

» accounts for the variety of» colors.

Naming Hydrates• In the formula for a hydrate, the number of water molecules associated

with each formula unit of the compound is written following a dot.• For example: Na2CO3 10 H∙ 2O

• This compound is called sodium carbonate decahydrate.• The prefix deca- means ten and the root word hydrate refers to water. • When naming hydrates use the same prefixes for the water as used

with covalent molecules.• A decahydrate has ten water molecules associated with each formula

unit of compound. • The number of water molecules associated with hydrates varies widely.

Examples of Hydrates

The hydrate CoCl2 ∙ 6 H2OAnhydrous (without water) CoCl2

Hydrating CuSO4 Anhydrous CuSO4Hydrated CuSO4 ∙ 5H2O

Calculating the Formula Mass of Hydrates

Na2CO3 10 H∙ 2O

Na: 2 x 23 = 46C: 1 x 12 = 12O: 3 x 16 = 48H2O: 10 x 18 = 180 (H: 20 x 1 = 20; O: 10 x 16 = 160; 20 + 160 = 180)

Total = 286 g/mol**Reminder-the “dot” in the formula means to add

the mass of the water (not multiply as in math)

Practice Problem

Calculate the formula mass of the following:1. CuSO4 5 H∙ 2O

Answer : 249.5 g/mol2.BaCl2 2 H∙ 2O

Answer : 244 g/mol

Determining the Formula of Hydrates from Experimental Data

• The composition of a hydrate is determined to contain 48.8% MgSO4 and 51.2% H2O.

• What is the formula of the hydrate?48.8/120 (mass of MgSO4) = 0.407 moles MgSO4

51.2/18 (mass of H2O) = 2.84 moles H2O

0.407/0.407 = 12.84/0.407 = 7Formula is MgSO4 7 H∙ 2O

Let’s Try Another

• A 1.628 g sample of a sample of a hydrate of magnesium iodide (MgI2) heated until its mass is reduced to 1.072 g and all water has been removed. What is the formula of the hydrate?

Answer: 1.072/278=0.00386 moles MgI2

1.628-1.072 = 0.556 g water/18 = 0.0309 moles H2O

0.00386/0.00386 = 10.0309/0.00386 = 8Formula: MgI2 8 H∙ 2O