The Mole

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The Mole. 6.02 X 10 23. The Mole. A counting unit Similar to a dozen, except instead of 12, it’s 602 billion trillion 602,000,000,000,000,000,000,000 6.02 X 10 23 (in scientific notation)

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The Mole

6.02 X 1023

The Mole
• A counting unit
• Similar to a dozen, except instead of 12, it’s 602 billion trillion 602,000,000,000,000,000,000,000
• 6.02 X 1023 (in scientific notation)
• This number is named in honor of Amedeo Avogadro (1776 – 1856), who studied quantities of gases and discovered that no matter what the gas was, there were the same number of molecules present
Just How Big is a Mole?
• Enough soft drink cans to cover the surface of the earth to a depth of over 200 miles.
• If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles.
• If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole.
• It was NOT just picked! It was MEASURED.
• One of the better methods of measuring this number was the Millikan Oil Drop Experiment
• Since then we have found even better ways of measuring using x-ray technology
Learning Check

Suppose we invented a new collection unit called a rapp. One rapp contains 8 objects.

1. How many paper clips in 1 rapp?

a) 1 b) 4 c) 8

2. How many oranges in 2.0 rapp?

a) 4 b) 8 c) 16

3. How many rapps contain 40 gummy bears?

a) 5 b) 10 c) 20

Molar Mass
• The molar mass is the mass of one mole of a substance.
• These are listed on your Periodic chart.
• Examples;
• Na = 22.98977 g/mole
• H = 1.00794 g/mole
• O = 15.9994 g/mole
• U= 238.029 g/mole

usually we round to the tenths place

Molar Mass
• What is the molar mass of C?
• C = 12.011 g/mole
• What is the molar mass of H20?
• H = 2 x 1.00794 g/mole
• O = 15.9994 g/mole
• 18.0153 g/mole
Molar Mass
• What is the molar mass of calcium nitrate?
• Ca(NO3)2
• Ca = 40.078 g/mole
• N = 2 x 14.0067 g/mole
• O = 6 x 15.9994 g/mole
• 164.088 g/mole
Other Names Related to Molar Mass
• Molecular Mass/Molecular Weight: If you have a single molecule, mass is measured in amu’s instead of grams. But, the molecular mass/weight is the same numerical value as 1 mole of molecules. Only the units are different. (This is the beauty of Avogadro’s Number!)
• Formula Mass/Formula Weight: Same goes for compounds. But again, the numerical value is the same. Only the units are different.
• THE POINT: You may hear all of these termswhich mean the SAME NUMBER… just different units
Learning Check!
• Molar Mass of K2O = ? Grams/mole

B. MolarMass of antacid Al(OH)3 = ? Grams/mole

Learning Check

Prozac, C17H18F3NO, is a widely used antidepressant that inhibits the uptake of serotonin by the brain. Find its molar mass.

The Mole
• 1 dozen cars = 12 cars
• 1 mole of cars = 6.02 X 1023 cars
• 1 dozen Al atoms = 12 Al atoms
• 1 mole of Al atoms = 6.02 X 1023 atoms

Note that the NUMBER is always the same, but the MASS is very different!

Mole is abbreviated mol (gee, that’s a lot quicker to write, huh?)

A Mole of ParticlesContains 6.02 x 1023 particles

1 mole C

1 mole H2O

1 mole NaCl

= 6.02 x 1023 C atoms

= 6.02 x 1023H2O molecules

= 6.02 x 1023NaCl “molecules”

(technically, ionics are compounds not molecules so they are called formula units)

6.02 x 1023 Na+ ions and

6.02 x 1023Cl– ions

Ways to use the mole.
• We now have two mole relationships.
• 6.02X1023 = 1 mole
• The molar mass = 1 mole
• These are both unitary rates and can be expressed as fractions.
• Using water as an example;

Unitary rates can be inverted when needed

6.02 x 1023 particles

1 mole

or

1 mole

6.02 x 1023 particles

Note that a particle could be an atom OR a molecule!

Converting Moles and Grams

Aluminum is often used for the structure of light-weight bicycle frames. How many grams of Al are in 3.00 moles of Al?

3.00 moles Al ? g Al

1. Molar mass of Al 1 mole Al = 27.0 g Al

2. Conversion factors for Al

27.0g Al or 1 mol Al

1 mol Al 27.0 g Al

3. Setup3.00 moles Al x 27.0 g Al

1 mole Al

Given over one

Molar Mass

How many moles are in 20.00 grams of H2O ?

To find the molar mass of water 2 H = 2 x 1.00794 g/mole+1 O = 1 x 15.9994 g/mol 18.01528 g/mol H2O

Given over one

Definition of Mole

How many molecules of water would this be?

Why are there four sig figs?

Learning Check

1. Number of atoms in 0.500 mole of Al

a) 500 Al atoms

b) 6.02 x 1023 Al atoms

c) 3.01 x 1023 Alatoms

2.Number of moles of S in 1.8 x 1024 S atoms

a) 1.0 mole S atoms

b) 3.0 mole S atoms

c) 1.1 x 1048 mole S atoms

Learning Check!

The artificial sweetener aspartame (Nutra-Sweet) formula C14H18N2O5 is used to sweeten diet foods, coffee and soft drinks. How many moles of aspartame are present in 225 g of aspartame?

Atoms/Molecules and Grams
• Since 6.02 X 1023 particles = 1 mole AND1 mole = molar mass (grams)
• You can convert atoms/molecules to moles and then moles to grams! (Two step process)
• You can’t go directly from atoms to grams!!!! You MUST go thru MOLES.
• That’s like asking 2 dozen cookies weigh how many ounces if 1 cookie weighs 4 oz? You have to convert to dozen first!
Calculations with Molar Mass

molar mass

Grams Moles

Calculations

molar mass Avogadro’s numberGrams Moles particles

Everything must go through Moles!!!

atoms

ions

molecules

Grams

moles

23

Molar mass

6.02x10

Convert 150.35 grams of C2H5OH to Molecules

Find molar mass of C2H5OH

2 Carbon 2 x 12.011 g/mol = 24.022 g

6 Hydrogen 6 x 1.00795 g/mol = 6.0477 g

1 Oxygen 1 x 15.9994 g/mol = 15.9994 g

Molar mass = 46.0691 g/mol

3.0 moles of CO2 to grams
• First find molar mass of CO2

1 carbon = 1 x 12.011 g/mol = 12.011 g

2 oxygen =2 x 15.9994 g/mol = 31.9988 g

44.0098 g/mol

• 3.0 moles CO2 x 44.0098 g = 130g CO2 1 1 mole
Atoms/Molecules and Grams

How many atoms of Cu are present in 35.4 g of Cu?

35.4 g Cu 1 mol Cu 6.02 X 1023 atoms Cu 63.5 g Cu 1 mol Cu

= 3.4 X 1023 atoms Cu

Learning Check!

How many atoms of K are present in 78.4 g of K?

Learning Check!

What is the mass (in grams) of 1.20 X 1024 molecules of glucose (C6H12O6)?

Learning Check!

How many atoms of O are present in 78.1 g of oxygen?

78.1 g O2 1 mol O2 6.02 X 1023molecules O2 2 atoms O 32.0 g O2 1 mol O2 1 molecule O2

Percent composition from mass
• Add total mass of all elements given
• Divide mass of element by total X 100
• Repeat for all elements
• Total percents to check for 100% total
Percent composition from formula
• Find atomic mass of each element
• Find molar mass by multiplying subscripts times atomic mass and totaling
• To find percent composition of each element, multiply subscript times atomic mass and divide by molar mass. Part X 100 = % Whole
• Hydrogen has an atomic mass of 1.00794 g/mole
• Oxygen has an atomic mass of 15.9994 g/mole
• molar mass= 2 x 1.00794g/mole = 2.01588grams + 1 x 15.9994g/mole = 15.9994grams 18.0153g/mole
• % Hydrogen = 2mole x 1.00794 g= 11.1 % 18.0153 g/mole
• % Oxygen = 1mole x 15.9994 g = 88.8 % 18.0153 g/mole

Total 11.1 + 88.8  100 %

Na 22.98977 g/mol

Cl 35.4527 g/mol

NaCl 58.4425 g/mol

% of Na

22.98977 g/mol x 100 = 39.3 % 58.4425 g/mol

% of Cl

35.4527 g/mol x 100 = 60.7 % 58.4425 g/mol

39.3% + 60.7% = 100 %

What is the percent composition of NaCl?
Percent Composition

What is the percent carbon in C5H8NO4 (the glutamic acid used to make MSG monosodium glutamate), a compound used to flavor foods and tenderize meats?

a) 8.22 %C

b) 24.3 %C

c) 41.1 %C

### Empirical Formula

The empirical formula of a compound is the smallest whole number ratio of the number of atoms of each element in the substance.

Empirical Formula
• The empirical formula can be found experimentally.
• The actual formula can be determined after the empirical formula is discovered
• Examples
• Dinitrogen tetrahydride
• N2H4
• Has an empirical formula of NH2
• Examples
• Hydrogen peroxide
• H2O2
• Has an empirical formula of HO
Steps for finding empirical formula
• Turn all given quantities into moles.
• Divide the larger number of moles by the smallest number of moles.
• Round to the tenths decimal place.
• Multiply by whole numbers to remove decimal values. {If whole numbers are not obtained (in step 3), multiply through by the smallest number that will give all whole numbers}
• Express the ratio as a chemical formula.
A sample of a brown gas, a major air pollutant, is found to contain 2.34 g N and 5.34g O. Determine a formula for this substance.

require mole ratios so convert grams to moles

moles of N = 2.34g of N = 0.167 moles of N

14.01 g/mole

moles of O = 5.34 g = 0.334 moles of O

16.00 g/mole

Formula:

1.4429614 mole S= 1.5 S 0.9621273 mole Fe Fe

FeS1.5x 2 = Fe2S3

What is the empirical formula of a compound which contains 53.73g of Fe and 46.27g of S?

Fe

=0.9621273 mole Fe

S

=1.4429614 mole S

1.587662 mole Na= 2.0 Na 0.7921162 mole S S

2.381339 mole O= 3.0 O 0.7921162 mole S S

Na2SO3

What is the empirical formula for sodium sulfite if it contains 36.5g sodium, 25.4 g sulfur and 38.1 g oxygen?

Na

=1.587662 mole Na

S

=0.7921162 mole S

O

=2.381339 mole O

11.01256027 mole H = 2 H 5.5564836719 mole O O

H2O

H

= 11.0125602714 moles H

O

= 5.5564836719 mole O

### Molecular Formula

The molecular formula is the actual ratio of atoms in a compound.

Steps for finding molecular formula
• Turn all given quantities into moles.
• Divide the larger number of mole by the smallest number of moles.
• Round to the tenth decimal place.
• Multiply by whole numbers to remove decimal values.
• Express the ratio as a chemical formula.
• Divide the actual molar mass by the empirical formula molar mass. (round to whole number)
• Multiply the empirical formula by this quotient.
HC

The molar mass of “HC” is 13.01894 g

A compound contains 92.25% carbon and 7.75% hydrogen. The molecular mass is 78 g. What is the molecular formula?

7.68895 moles H= 1.0 H

7.680459 moles C C

C

= 7.680459 moles C

H

=7.68895 moles H

6 x CH =C6H6

The molecular mass of an oxide of nitrogen is 216 g. The compound contains 4.02 g of nitrogen and 11.48 g of oxygen. What is the molecular formula?

0.7175269 mole O= 2.5 O

0.2870055 mole N N

N

NO2.5X 2 = N2O5

N2O5= 108.0 g

=0.2870055 mole N

O

2 X N2O5 = N4O10

=0.7175269 mole O

STP Standard Conditions
• STP stands for standard temperature and pressure. This is referred to as standard conditions.
• Standard conditions are a way to compare data from different places under different conditions.
• Standard temperature is 0.0oC.
• “C” stands for Celsius
• Standard Pressure is 101.325 kPa.
• “kPa” stands for kilopascals, which is a pressure unit.
Standard Molar Volume
• At STP, the volume of one mole of any gas is 22.4 L.
• This can be expressed as a unitary rate.

atoms

ions

molecules

Grams

moles

23

Molar mass

6.02x10

22.4 L

Liters of gas at STP

Given over one

Standard Molar Volume

Definition of mole

Mole Ratio

Given over one

Standard Molar Volume

Molar Mass

Mole Ratio

STOICHIOMETRY

- the study of the quantitative aspects of chemical reactions.