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Unit 8

Mathematical Relationships

Lesson 1:

Moles and Molar Mass

Objective

Determine the number of atoms in a

molecule

Calculate molar mass

Wednesday, March 11

• LT: Moles

• List ways that we group items

– Example: a dozen cookies = 12 cookies

Review

• Subscripts: Number of atoms in a formula

• Coefficients: Total number of molecules or

compounds

Ex: 3Ca3(PO4)2

Ca = 9 P = 6 O = 24

Examples: How many atoms

are in each substance?

• NH4NO3

• Al2(SO4)3

• 3Al2(SO4)3

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First Something Familiar

What do the following items have in common?

The Mole

1 dozen =

1 gross =

1 score =

1 mole =

12

144

20

6.02 x 1023

There are exactly 12 grams of carbon-12 in one mole of carbon-12.

• A mole is a number—it is a constant—a mole will always

equal 6.02 x 1023

• It relates the mass of a single atom in amu to the mass in

grams (It is the same number of particle as there are in

exactly 12 grams of carbon-12.)

1 mol = 6.02 x 1023 particles (atoms, molecules, things)

1 mol = gram formula mass

Mole

Molar Mass(aka Formula Mass or Molecular Mass)

• Mass of the formula expressed in grams

• Equal to 1 mole

• Units (g/mol)*** Elements molar mass are reported on the periodic table

(remember avg. atomic mass)

Calculating Molar Mass

1. Count the atoms in the compound

2. Look up the mass of each element on the

periodic table

3. Multiply mass by the number of atoms of each

element

4. Add up the total mass

* Always add g/mol unit

* Round to 2 decimal places

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Molar Mass Example: Elements

1. What it the molar mass of iron? 55.85 g/mol

2. What is the molar mass of copper?

Molar Mass Examples: Compounds

1. What is the molar mass of water?H2O = 2(1.01) + 16.0 = 18.01 g/mol

2. What is the molar mass of calcium

chloride?

Lesson 2:

Mole Conversions

Objective

Calculate moles given the number of

grams

Calculate grams given the number of

moles

Moles/Gram Relationship

• Molar Mass (g/mol)

• Equations

Calculations with Moles:Converting moles to grams

How many grams of lithium are in 3.50 moles of lithium?

3.50 mol Li= g Li

1 mol Li

6.94 g Li

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Calculations with Moles:Converting grams to moles

How many moles of lithium are in 18.2 grams of lithium?

18.2 g Li= mol Li

6.94 g Li

1 mol Li

Practice

• Pages 5-6

• Add Vocabulary

Objective

Complete 1 step mole conversions using

g, L, or particles.

Mole/Particle Relationship

• Avogadro's number

Calculations with Moles:Using Avogadro’s Number

How many atoms of lithium are in 3.50 moles of lithium?

3.50 mol Li= atoms Li

1 mol Li

6.022 x 1023 atoms Li2.11 x 1024

Mole/Liter Relationship

• At STP (Standard Temperature and Pressure), 1 mol of 6.02 x 1023

representative particles of any gas occupies a volume of 22.4 L

• Equations

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Calculations with Moles:Converting Liters to Moles

How many moles of Chlorine gas are in 33.6L Cl2?

33.6 L Cl2=

22.4 L Cl2

1 mol Cl21.50 mol Cl2

Calculations with Moles:Converting Moles to Liters

How many L of water are in 2.4 mol of H2O?

2.4 mol H2O=

22.4 L H2O

1 mol H2O54 L H2O

Practice

• Turn in Chalk lab

• Pages 7-8

• Add vocabulary

• Homework due tomorrow

• Quiz Friday

Lesson 3:

Percent Composition and Empirical Formulas

Objective

Determine the empirical formula from

molecular formula

Calculate the molecular formula from the

empirical formula

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Molecular to Empirical Formula

• The empirical formula of compound shows the

smallest whole-number ratio of the atoms in the

compound. (Cannot be reduced further.)

Determining Empirical Formula

• Divide subscripts by the greatest common

factor

• Example: molecular formula = C4H10

Divide by 2 (greatest common factor)

C2H5

Examples

Molecular Empirical

P4O10 P2O5

C10H22

C6H18O3

C5H12O

N2O4

Molecular Formula

• “Actual Formula” – the actual number of

atoms in a compound

– Whole # multiple of empirical

– If the empirical formula is CH4 a molecular

formula could be CH4, C2H8, C3H12, etc.

Calculating Molecular Formula

from Empirical Formula1. Calculate Molar mass (gram formula

mass) of the Empirical Formula

2. Divide molar mass given for molecular

formula by the empirical formula mass.

3. Multiply all of the subscripts in the

empirical formula by the number

(multiple) you calculated in step 2.

Example

1.The empirical formula for ethylene is CH2. Find

the molecular formula if the molecular mass is 28.1

g/mol.

empirical mass CH2 =

(1 C X 12.011 g/mol) + (2 H X 1.008 g/mol) = 14.03g/mol

28.1 g/mol

14.03 g/mol

(CH2) x 2 ⇒ C2H4

= 2.00

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Example

2. What is the molecular formula of a compound

that has an empirical formula of NO2 and

molecular mass of 92.0 g?

N= 14.007 x 1 = 14.007g

O= 15.999 x 2 = 32.00g

+ = 46.01g/mol

92.0 g/mol

46.01 g/mol

(NO2) x 2 ⇒ N2O4

= 1.9995 = 2

Practice

• Page 9

• Add Vocabulary

Objective

Calculate the percent composition of a

substance

Determine the empirical formula from

percent composition

Percent Composition

• The percentage by mass of each element

in a compound

• Formula

Steps for Calculating Percent

Composition1. Find the molar mass of each element and

the compound.

2. Divide element x 100

compound

Examples

1. What is the percent composition of

CaCl2?

2. What is the percent by mass of nitrogen in

NH4NO3?

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Empirical Formula from %

Composition

1. Assume a 100g sample so that your % =

g

2. Convert each sample to moles

3. Divide all values by the smallest

4. These results are your subscripts of the

empirical formula

Example: Empirical Formula

from Percent Composition

• A compound is analyzed and found to

contain 25.9% nitrogen and 74.1%

oxygen. What is the empirical formula of

the compound?

Practice

• Page 10-12

• Add Vocabulary

• HW#3 Due Wednesday

• Quiz Wednesday

Practice

• Page 10-12

• Add Vocabulary

• Quiz!!!

Lesson 4:

Mole Ratio/Stoichiometry

Objective

Calculate mole ratios for chemical

reactions.

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Mole Ratio

• Mole ratio is the ratio between the

amounts in moles of any two compounds

involved in a chemical reaction. Mole

ratios are used as conversion factors

between products and reactants in many

chemistry problems.

• Simply put, the ratio of the coefficients in a

balanced chemical equation.

Mole Ratio Steps

1. Balance the Chemical Equation

2. Use the coefficients as ratios

Mole Ratios

__H2 + __O2 __H2O

1. What is the molar ratio between H2 and

O2?

2. What is the molar ratio between O2 and

H2O?

Example: Mole Ratios Conversions

__H2 + __O2 __H2O

3. How many moles of oxygen are consumed

when 0.6 moles of hydrogen burns to produce

water?

4. How many moles of water are produced when 5

moles of hydrogen gas are consumed?

Example: Mole Ratios

__N2 + __H2 __NH3

5. What is the molar ratio between H2 and N2?

6. What is the molar ratio between H2 and NH3?

Example: Mole Ratios

__N2 + __H2 __NH3

7. How many moles of nitrogen gas would be

needed to produce 10 moles of ammonia in the

above reaction?

8. How many moles of ammonia are produced

when 7.5 moles of hydrogen are consumed?

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Practice

• Page 13

• Add vocabulary

Stoichiometry

• The quantitative relationship between two

or more substances in a chemical

reaction.

Mass to Mass Stoichiometry Full Stoichiometry #1

__CH4 + __O2 __H2O + __CO2

• If 50. g of CH4 are combusted, how many

g of H2O will be produced?

Full Stoichiometry #2

• Write and balance the following equation:

Hydrochloric acid reacts with Magnesium metal

to produce hydrogen gas and magnesium

chloride.

• If 5.45 g of magnesium react, how many L of

hydrogen gas will you produce?

Practice• Pg 14-16

• Pg 15 exclude # 3 and 6

• Add vocabulary

• HW #4 Due Monday

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Combined Stoichimetry Practice

• Pages 16

• Add Vocabulary

• HW #4 Due Monday

• Quiz Monday Lesson 5:

Limiting Reactants and Percent Yield

Limiting Reactant

• A limiting reactant is the substance that is

completely consumed during a chemical

reaction.

Limiting Reactant Steps

1. Balance Equation

2. Convert both reactants into product

3. Reactant that produces the least is the

limiting reactant. The other is the excess.

Limiting Reactant Example

2 Al + 6 HBr → 2 AlBr3 + 3 H2

a. When 3.22 moles of Al reacts with 4.96 moles

of HBr, how many moles of H2 are formed?

b. What is the limiting reactant?

c. For the reactant in excess, how many moles are

left over at the end of the reaction?

Percent Yield

• Percent yield is the ratio of the actual yield

to the theoretical or expected yield.

• Theoretical yield: amount of product that

should be produced by a chemical

reaction according to stoichiometric

calculations.

• Actual yield: amount of product actually

obtained from a chemical reaction.

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Percent yield = Actual yield x 100

Theoretical yield

Examples

• What is the percent yield for the

decomposition of 24.8 g of calcium

carbonate if the reaction produces 13.1 g

of solid product?

• CaCO3 CaO + CO2

• What is the percent yield if 1.87 g

aluminum is reacted with an excess of

copper (II) sulfate and 3.74 g of solid metal

(Cu) is produced?

• Al + CuSO4 Cu + Al2(SO4)3

Practice

• Pages 17-18

• Add Vocabulary

• Quiz