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### Empirical Formula

### Molecular Formula

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.

Everybody Has Avogadro’s Number!But Where Did it Come From?

- 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

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

The Mole

- 1 dozen cookies = 12 cookies
- 1 mole of cookies = 6.02 X 1023 cookies
- 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

Avogadro’s Number as Conversion Factor

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

Answer = 81.0 g Al

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

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!

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

Ex. 1 What is the percent composition of the elements in H2O?

- 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

Step 2 Use molar mass to find percent of each element

- % 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

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

What is the formula of a compound with 11.1 % Hydrogen and 88.9 % Oxygen?H

= 11.0125602714 moles H

O

= 5.5564836719 mole O

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.

Standard Molar Volume

Definition of mole

Mole Ratio

How many atoms of hydrogen are in 138.56 L of CH4 (methane) at STP?Standard Molar Volume

Molar Mass

Mole Ratio

How many grams of nitrogen are in 24.3 L of ammonia , NH3, at STP?STOICHIOMETRY

- the study of the quantitative aspects of chemical reactions.

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