The Mole

Chapter 11 – Chemistry L1LSM High School

Section 11.1: Measuring MatterObjectives:

Describe how a mole is used in chemistry Relate a mole to common counting units Covert moles to number of representative particles and number of

representative particles to moles.

How do Chemists measure how much of a substance?

Chemists can measure mass or volume or they can count pieces.

Chemists can measure mass in grams.

Chemists can measure volume in liters.

Chemists can count pieces in MOLESMOLES.

No, not that kind of mole!!!

What are MOLES?

Moles are defined as the number of carbon atoms in exactly 12 grams of the carbon-12 isotope.

1 mole of _____ = 6.02 x 1023 particles Mole: unit = “mol” Avogadro’s number

dozen, baker’s dozen, pi

A Little History

Amedeo Avogadro was born in 1776 in Turin, Italy.

He went on to study molecular theory and helped other scientists distinguish between atoms and molecules.

Because of his accomplishments in this field, the variable that tells the number of molecules in one mole was named after him

What are Representative Particles?

These particles are the smallest pieces of a substance.

• The types of representative particles that chemists generally work with are:• atoms – the smallest particle of an element

• ions – atoms with positive or negative charges

• molecules – two or more covalently bonded atoms

• formula units – the simplest ratio of ions that make up an ionic compound

Converting Moles to Particles

and Particles to MolesUsing Avogadro’s Number as a Conversion Factor:

Practice Problem 1

How many atoms are in 2.50 mol of zinc? K: UK:

Answer: 1.51 x 1024 atoms Zn

Practice Problem 2

How many molecules of CO2 are there in 4.56 moles of CO2 ?

K: UK:

Answer: 2.75 x 1024 molecules of CO2 How many atoms is this?

Practice Problem 3

How many moles of water is 5.87 x 1022 molecules of water?

K: UK:

ANSWER: 0.0975 moles of water

Practice Problem 4

Given 3.25 mol AgNO3, determine the number of formula units.

K: UK:

ANSWER: 1.96 x 1024 formula units AgNO3

Section 11.2:Mass and the Mole

Objectives:

•Relate the mass of an atom to the mass of a mole of atoms.

•Calculate the number of moles in a given mass of an element, and the mass of a given number of moles of an element.

•Calculate the number of moles of an element when given the number of atoms of an element.

•Calculate the number of atoms of an element when given the number of moles of the element.

Let’s Look at the Periodic Table!

Atomic Numbers - always increase across a row. The atomic number is the number of protons in an atom of that

element. This number identifies it as an atom of a particular element.

Atomic Mass - usually increase across a row Why do they have decimal values?

The atomic mass (sometimes called average atomic mass) is the weighted average of the masses of all the naturally occurring isotopes of that element.

A relative scale: Uses isotope carbon-12 as the standard Each atom of carbon-12 has a mass of exactly 12 amu (atomic

mass units) Ex: One atom of hydrogen-1 has a mass of 1 amu, meaning 1 atom

of hydrogen-1 is one-twelfth the mass of one atom of carbon-12

The mass in grams of one mole of ANY pure substance is its molar mass. Same value as atomic mass - has units of g/mol Occasionally referred to as:

Gram atomic mass (gam) – for atoms Gram molecular mass (gmm) – for molecules Gram formula mass (gfm) – for formula units (ionic compounds)

12.01 grams of carbon has the same number of particles as 1.01 grams of hydrogen and 55.85 grams of iron. The molar mass is found in the periodic table!

Avogadro’s number tells us the number of particles.

Using Molar Mass as a Conversion Factor:

# of grams or 1mol 1 mol # of grams

Practice Problems:

1. What is the mass, in grams, of 2.34 moles of carbon?

K: UK:

28.1 g carbon

2. How many moles of magnesium are in 4.61g of Mg?

K: UK:

0.190 mol Mg

Section 11.3: Moles of Compounds

Objectives:

• Recognize the mole relationships shown by a chemical formula.

• Calculate the molar mass of a compound.• Calculate the number of moles of a compound

from a given mass of the compound, and the mass of a compound from a given number of moles of the compound.

• Determine the number of atoms or ions in a mass of a compound.

Enough about atoms:What about compounds?

The chemical formula for a compound tells us the types of elements and the number of each element contained in one unit of the compound.

Ammonia (NH3) 1 molecule contains:

1 atom of nitrogen and 3 atoms of hydrogen

Baking soda (sodium hydrogen carbonate, NaHCO3) 1 formula unit contains:

1 atom of sodium, 1 atom of hydrogen, 1 atom of carbon, and 3 atoms of oxygen

Example Problems:

1. Calculate the number of moles of hydrogen found in 3.50 moles of NH3.

K: UK:

10.5 mol Hydrogen

2. Calculate the number of moles of carbon found in 9.85 moles of C6H12O6 (sugar).

K: UK:

59.1 mol carbon

The Molar Mass of Compounds

Summary of Getting the Molar Mass of Compounds:

The mass of a mole of a compound equals the sum of the masses of every particle that makes up the compound.

Use the formula to tell you how many of each element that is in the compound

Use the periodic table to get the masses of each element Add them all up and you get the molar mass of the

compound in units of g/mol (NH4)2SO4

Example Problems of Molar Masses:

1) What is the molar mass of NH3?

17.04 g/mol 2) What is the molar mass of Sr(NO3)2?

211.64 g/mol

Example Problems of Mole-Mass Conversions:

1) How many moles is 4.56 g of CO2 ?

K: UK:

0.104 moles CO2

2) How many moles is 46.8 g of CH4?

K: UK:

2.92 mol CH4

3) How many grams is 9.87 moles of H2O?

K: UK:

178g H2O

4) How many grams is 0.157 mol Fe2O3?

K: UK:

25.0 g Fe2O3

Using Molar Volume as a Conversion Factor:

Molar Volume: for any gas at STP, 1 mol = 22.4 L Standard Temperature and Pressure is 0°C or 273 K and 101.3 kPa or 1 atm

22.4 L or 1mol 1 mol 22.4 L

Practice Problem:

What is the volume of 1.5 moles of nitrogen gas?

K: UK:

34 L N2 (17 2-Liter bottles!)

REVIEW:

What types of particles are contained in covalent compounds?

What types of particles are contained in ionic compounds?

Multi-step Conversions

You must first convert to moles and then convert to the desired unit either using molar mass or Avogadro’s number or molar volume.

Example Problems:

1. What is the volume of 45.6 g of water vapor?

K: UK:

? L H2O(g)

2. How many atoms are in 0.120 kg Ti?

K: UK:

1.51 x 1024 atoms Ti

4. What is the mass, in grams, of 1.50 x 1015 atoms uranium?

K: UK:

5.93 x 10-7 g U

3. What is the mass, in grams, of 1.50 x 1015 formula units of NaCl?

K: UK:

? g NaCl

More Example Problems…

1) How many molecules in 6.8 g of CH4?

2a) How many formula units are there in 4.9 g of NaNO3?

2b) How many ions if the compound is made of Na+ and NO3

- ions?

11.4 – Empirical and Molecular Formulas

Percent Composition

Every chemical compound has a definite composition. What law is this referring to?

The composition of a compound is usually stated as the percent by mass of each element in the compound.

The type of chemist whose job it is to identify the elements & their percent by mass in a compound is an analytical chemist.

The equation used to determine the percent composition of an element in a compound is:

total mass of element in compound% by mass of an element = *100

molar mass of compound

Percent Composition Example Problems:

1) Determine the percent by mass of each element in calcium chloride (CaCl2).

K: UK:

36.11% Ca and 63.89% Cl

2) What is the percent of oxygen in H3PO4?

K: UK:

65.31% oxygen

3) Calculate the percent composition of a compound that is 29.0 g of Ag with 4.30 g of S.

K: UK:

87.1% Ag and 12.9% S

4) Which has the larger percent by mass of sulfur, H2SO3 or H2S2O8?

K: UK:

H2SO3 39.06% S

Empirical Formula

The information from the percent composition can be used to determine the formula for a compound.

The empirical formula is the simplest whole-number ratio of atoms of elements in the compound. In many cases, the empirical formula is the actual formula for the compound.

EX: H2O or H2SO4

Molecular Formula

For many compounds, the empirical formula is not the true formula. Examples: CH2 (empirical formula) vs. C2H4 (molecular

formula) The molecular formula identifies the actual number

of elements in a molecule. Sometimes the empirical and molecular formulas are the

same. Ex: Water H2O To determine the molecular formula the molar

mass of the compound must be determined through experimentation and compared with the mass represented by the empirical formula.

Notice that the molecular formula for acetic acid (C2H4O2) has exactly twice as many atoms of each element as the empirical formula (CH2O).

The molecular formula for a compound is always a whole-number multiple of the empirical formula.

Calculating Empirical Formulas

If percent composition is given:1. Assume that the total mass of the compound is 100.00 g.

(Percentages of each element equals the mass in grams.)2. Convert grams to moles (using the molar mass of each

element). 3. Find the mole ratio by dividing everything by the smallest # of

moles.4. If those numbers are whole numbers you have just found the

subscripts for the formula.

If actual masses are given you can skip to step 3.

Example Problem:

What is the empirical formula for a compound that contains 10.89% magnesium, 31.77% chlorine and the rest is oxygen?K: UK:

MgCl2O8

Determine the empirical formula of a compound containing 2.644g of gold and 0.476g of chlorine.K: UK:

AuCl

BUT…often in determining empirical formulas, the calculated mole ratios are still not whole numbers. In such cases all the mole ratio values must be multiplied by the smallest factor that will make them whole numbers.

More Examples:

1. A blue solid is found to contain 36.84% nitrogen and 63.16% oxygen. What is the empirical formula for the solid?K: UK:

N2O3

2. Propane is a hydrocarbon. It is composed of 81.82% carbon and 18.18% hydrogen. What is the empirical formula?K: UK:

C3H8

In order to determine the molecular formula for an unknown compound, you must know the molar mass of the compound in addition to its empirical formula.

Then you can compare the molar mass of the compound with the molar mass represented by the empirical formula.

Calculating Molecular Formulas

This is done using the following equation:

You get a number to multiply the subscripts of the empirical formula by to get the molecular formula.

Let’s do some practice problems.

given molar mass of compound

mass of empirical formula

Practice Problems:

1) Maleic acid is a compound that is used in the plastics and textiles industries. The composition of maleic acid is 41.39% carbon, 3.47% hydrogen, and 55.14% oxygen. Its molar mass is 116.10 g/mol. Calculate the molecular formula for maleic acid.

K: UK:

Start by determining the empirical formula:

What is the mole ratio of the elements? 1C:1H:1O

So the empirical formula is: CHO

Next, calculate the molar mass represented by the empirical formula. 29.02 g/mol

As stated in the problem, the molar mass of maleic acid is known to be 116.10 g/mol.

To determine the molecular formula for maleic acid, calculate the whole number multiple to apply to its empirical formula.

This calculation shows that the molar mass of maleic acid is four times the molar mass of its empirical formula CHO.

Therefore, the molecular formula must have four times as many atoms of each element as the empirical formula.

Thus, the molecular formula is C4H4O4

116.10 /4.001

29.02 /

g mol

g mol

To Review:

= n

More Practice Problems:

2) Caffeine is 49.48% C, 5.15% H, 28.87% N and 16.49% O. It has a molar mass of 194 g/mol. What is its molecular formula?K: UK:

3) A compound was found to contain 49.98 g carbon and 10.47 g hydrogen. The molar mass of the compound is 58.12 g/mol. Determine the molecular formula.

K: UK:

C4H10

11.5 – The Formula for a Hydrate

What is a hydrate?

A hydrate is a compound that has a specific number of water molecules that are “trapped” inside its crystal structure.

Common ones are opal and cobalt chloride.

Images from wikipedia

What’s in a name?

To show the number of water molecules in a formula unit of a hydrate chemists write the formula with a dot and the number of water molecules in it.

Example: CaCl2 . 2H2O

The name is calcium chloride dihydrate This means that for every one formula unit of

calcium chloride there are 2 water molecules associated with it.

Counting the Water Molecules

Chemists use prefixes to count how many water molecules are associated with a hydrated compound.

Each prefix means a certain number.

The root word hydrate means water

Prefix Molecules of H2O

mono- 1

di- 2

tri- 3

tetra- 4

penta- 5

hexa- 6

hepta- 7

octa- 8

nona- 9

deca- 10

Analyzing a Hydrate

To analyze a hydrate you must remove the water of hydration.

Usually this is done by heating it so that the remaining substance has no water. It is then called an anhydrous substance.

You must find the number of moles of water associated with one mole of the hydrate.

Hydrated cobalt chloride anhydrous cobalt chloride

Example:

Suppose you have a sample of a hydrate of copper(II) sulfate.

The formula is CuSO4 . xH2O. You must

determine “x”. The “x” is the number of moles of water associated with one mole of CuSO4.

We are going to heat a sample and figure it out together.

What data should be collected?

What calculations should be done?

Let’s name the compound

Uses of hydrates

They can absorb water into their structure so they are used as drying agents in the lab or in stores.

Examples: Calcium sulfate in the lab and the silica packets that sometimes come in shoe boxes or purses