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### Chemical Quantities

### 10-2 Mass & the Mole 10-3 Moles of Compounds

Or How I Learned to Love the Mole

A mole?

Not the type of mole we are talking about

Vocabulary

- Mole
- Avogadro’s Number
- Representative Particle
- Molar Mass

How do you measure the amount of something?

- Look at the dozen things that you brought to class. Think about how you could measure the amount of matter in that stuff.
- Brain storm 3 ways and compare your ways to your neighbor.
- What ways did you come up with?

Count it!

- What are the advantages of this method?
- What if your stuff is differently sized?
- What if something is too small to count?

Weight it! (take the mass)

- Standardized method of measuring amount of matter!
- What if it is too small to weigh?
- Too big?

Size it! (take the volume)

- Volume is how much space it takes up.
- Advantages of this system?
- Disadvantages?

Counting Matter

What are some everyday ways we count matter?

1.

2.

3.

DOZEN = 12 things

1 GROSS = 144 things

What about molecules? Or atoms?

BUSHEL of corn = 21.772 kg

1 MOLE = ???

Problem!

- Atoms are too small to count
- Too small to put on a scale
- Too small to take a volume
- They vary in size
- Small variations in size add up to big differences!
- Can we figure out how many atoms are in some stuff?

Solution!

- Come up with a way to count atoms by taking the mass of the stuff!
- Let’s try it with your dozen items…

The Mole

- It represents a counted number of things.
- IN Chemistry the term MOLE represents the number of particles in a substance.

In Chemistry is NOT this furry little animal or the spot on your face…

Procedure

- Find the mass of your dozen items together
- Divide this total mass by 12 to find the average mass of one of these items.
- Weigh one of the items individually and compare this number to the number you got in step 2.
- Now estimate the mass of 8 of these items using the number from step 2.
- Weight 8 of your items. How close was this?
- Repeat this process with 5 items.
- Now estimate the mass of your stuff if you had 6.02x10^23 items. This is a mole!
- Let’s calculate the mass of a mole of pennies.

A mole of pennies is very large.

Just how many is a mole?

- One mole represents 6.02 x 1023 of things (units, molecules, compounds, formula units). This is called Avogadro’s number.
- One mole of most elements contains 6.02 x 1023atoms.
- 1 mole O2 = 6.02x1023molecules of O2
- 602 000 000 000 000 000 000 000

Just how big is a mole?

- Listen to The Mole Song!
- An Avogadro's number of standard soft drink cans would cover the surface of the earth to a depth of over 200 miles
- If you had Avogadro's number of un-popped 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.

Counting stuff…

- Count it! If it is something large like the number of beans in a bag, you just count them.
- If, however, it is something exceedingly small like an atom or ion, how do you count it?
- Counting individual particles is not possible, but you can “count” particles if you introduce a term that represents a specific number of particles.
- A “dozen” represents 12 of that item.
- and a mole represents 6.02 x 1023 representative particles of a substance.

Solving the Problems Samples Required: dimensional analysis/factor label

- How many molecules are in 3.00 moles of N2?
- How many moles of Na are in 1.10 x 1023 atoms?

Practice moles to particles

- Determine the number of atoms in 2.50 mol Zn.
- Given 3.25 mol AgNO3, determine the number of formula units.
- Calculate the number of molecules in 11.5 mol H2O.

Practice Particles to Moles

- How many moles contain each of the following?
- 5.75 x 1024 atoms Al
- 3.75 x 1024 molecules CO2
- 3.58 x 1023 formula units ZnCl2
- 2.50 x 1020 atoms Fe

Molar Mass

Defn: is the mass (think grams) of one mole of a substance

- Atomic masses (from periodic table) represent molar mass.
- Units g/mol
- 1 mole of Carbon has 6.02 x 1023 atoms of C and they have a mass of 12.01 grams.
- To calculate the molar mass of a compound, you add up the molar masses of all the elements in that compound

Molar Mass Practice

- What is the mass of 1.00 mole of Oxygen? Of Nitrogen?
- Find the molar mass for:
- SO3
- Na2SO4

1 mole O = 16.0 grams

1 mole N = 14.0 grams

SO3= 80 g/mole

1 Mole = 142.043g

Tutorial Site

Molar Mass Calculator for homework help

Molar Mass Practice

- When you see 1.00 mole = _?_ g, think “g means GO to the PERIODIC TABLE” to find the molar mass.

http://www.webelements.com/

Practice Problems

- Determine the molar mass of each of the following ionic compounds:
- NaOH
- CaCl2
- KC2H3O2
- HCN
- CCl4
- H2O

Grams-Mole Conversions

- How many moles are in 56.8 g of HCl?
- How many grams are in .05 moles Na2SO4?

Practice Mole to Grams

- Determine the mass in grams of each of the following.
- 3.57 mol Al
- 42.6 mol Si
- 3.45 mol Co
- 2.45 mol Zn

Practice Gram to Mole

- How many atoms are in each of the following samples?
- 55.2 g Li
- 0.230 g Pb
- 11.5 g Hg
- 45.6 g Si
- 0.120 kg Ti

Ex: Mass to Particle Conversion

- Gold is one of a group of metals called the coinage metals (copper, silver and gold). How many atoms of gold (Au) are in a pure gold nugget having a mass of 25.0 g?
Known:Unknown:

Mass = 25.0 g Au

Molar mass Au = 196.97 g/mol Au

25.0 g Au x 1 mole Au x 6.02 x 1023 atoms Au = 7.65 x 1022 atoms Au

196.97 g Au 1 mol Au

Number of atoms = ? Atoms Au

Practice Problems

- How many atoms are in each of the following samples?
- 55.2 g Li
- 0.230 g Pb
- 11.5 g Hg
- 45.6 g Si
- 0.120 kg Ti

Ex: Particle to Mass Conversion

- A party balloon contains 5.50 x 1022 atoms of helium (He) gas. What is the mass in grams of the helium?
Known:Unknown:

Number of atoms = 5.50 x 1022 atoms He

Molar mass He = 4.00 g/mol He

5.50 x 1022 atoms He x 1 mol He x 4.00 g He = 0.366 g He

6.02 x 1023 atoms He 1 mol He

Mass = ? G He

Practice Problems

- What is the mass in grams of each of the following?
- 6.02 x 1024 atoms Bi
- 1.00 x 1024 atoms Mn
- 3.40 x 1022 atoms He
- 1.50 x 1015 atoms N
- 1.50 x 1015 atoms U

Molar Volume

- The volume of a gas is usually measured at standard temperature and pressure (_STP_)
- Standard temp = ___0°_ C
- Standard pressure = ___1___ atmosphere (atm)
- 1 mole of any gas occupies __22.4__ L of space at STP

Molar Volume Practice

- How many moles would 45.0 L of He gas be?
- How many liters of O2 would 3.8 moles occupy?

Putting it all together

- 1.0 mole = _6.02 x 1023___atoms or molecules
- 1.0 mole = _?__ g(PT)
- 1.0 mole = _22.4 L (at STP)

Chemical Formulas and the Mole

- Chemical formula for a compound indicates the types of atoms and the number of each contained in one unit.
- Ex. CCl2F2 - Freon
- Ratio of carbon to chlorine to fluorine is 1:2:2
- Ratios can be written: or
- In one mole of freon you would have 1 mole of carbon, 2 moles of chlorine and 2 moles of fluorine.

- Ex. CCl2F2 - Freon

Ex: Mole Relationship from Chemical Formulas

- Determine the moles of aluminum ions (Al3+) in 1.25 moles of aluminum oxide.
1.25 molAl2O3 x 2 mol Al3+ ions = 2.50 mol Al3+ ions

1 mole Al2O3

Practice Problems

- Determine the number of moles of chloride ions in 2.53 mol ZnCl2.
- Calculate the number of moles of each element in 1.25 mol glucose (C6H12O6).
- Determine the number of moles of sulfate ions present in 3.00 mol iron (III) sulfate (Fe(SO4)3).
- How many moles of oxygen atoms are present in 5.00 mol diphosphoruspentoxide?
- Calculate the number of moles of hydrogen atoms in 11.5 mol water.

Practice Problems

- A sample of silver chromate has a mass of 25.8 g.
- How many Ag+ ions are present?
- How many CrO42- ions are present?
- What is the mass in grams of one unit of silver chromate?

- What mass of sodium chloride contains 4.59 x 1024 units?
- A sample of ethanol (C2H5OH) has a mass of 45.6 g.
- How many carbon atoms does the sample contain?
- How many hydrogen atoms are present?
- How many oxygen atoms are present?

Warm-up review

You have 10.0 grams of ordinary sugar on a scale. Sugar is sucrose and has a formula of C12H22O11.

- How many moles of sugar are on your scale?
- How many molecules of sucrose are on your scale?
- How many moles of carbon atoms are on your scale?
- How many atoms of hydrogen are on your scale?
- How many atoms of oxygen are on your scale?
- What is the ratio of oxygen atoms to hydrogen atoms?
- What is the ratio of carbon atoms to sugar molecules?

Warm-up Review #2

- You have 30.0 g of barium hydroxide on a scale.
- What is the chemical formula of this substance?
- What is the molar mass?
- How many moles do you have of the compound?
- How many moles do you have of barium?
- How many moles do you have of oxygen?
- How many moles of (OH)- ions do you have?
- How many ions of (OH)- do you have?
- What is the ratio of (OH)- ions to Ba2+ ions?

Percent Composition

- the percentage by massof each element in a compound
- The percent comp. is found by using the following formula:

Percent Composition Example

Ex. Compound XY is 55g element X and 45g element Y

55 g of element Xx 100 = 55 % element X

100 g of compound

45 g of element Y x 100 = 45 % element Y

100 g of compound

Percent Composition from Chemical Formula

- First find the molar mass of each element and the molar mass of the compound
- Ex: what is the % composition of H in 1 mole of H2O?
- Multiply the molar mass of the element by its subscript in the formula.
- 1.01 g/mol H x 2 mol = 2.02 g H
% by mass H = 2.02 g x 100 = 11.2% H

18.02 g H2O

Percent Composition from Chemical Formula

Example continued –

- Molar mass of O for each mole of H2O?
- 16.00 g/mol O x 1mol O = 16.00 g O
16.00 g x 100 = 88.8 % O

18.02 g

% Composition Practice

- What is the percent of C & H in C2H6? Hint… assume 1 mole!
- What is the percent of each element in Na2SO3?

Empirical Formulas

- This is the LOWEST whole number ratio of the elements in a compound. For example, the empirical formula for
- Molecular Formula C6H6
- Empirical Formula CH

- What is the empirical formula for each?
- C2H6
- C6H12O6

10-3: Calculating Empirical Formula

- Steps for calculating Empirical Formula give mass or percent composition:
- If given a percent sign (%), remove the sign & change to GRAMS.
- You are assuming you have 100 g of the compound.
- Convert grams ---> moles.
1. Select lowest number of moles

2. Divide each number of moles by this number.

3. If the number divides out evenly, these are the subscripts of the elements in the compound.

4. If any of the numbers have a .5, MULTIPLY them ALL by TWO & then place these numbers as the subscripts.

- If given a percent sign (%), remove the sign & change to GRAMS.

Example Using Percent Composition

- The percent composition of an oxide of sulfur is 40.05% S and 59.95% O. Assuming you have a 100g sample, it contains 40.05g S and 59.95g O.
- Convert to moles using molar mass:
40.05 g S x 1 mol = 1.249 mol S

32.07g

59.95 g O x 1 mol = 3.747 mol O

16.00g

Example Using Percent Composition

The mole ratio of S atoms to O atoms in the oxide is 1.249 : 3.747.

Recognize that S has the smallest possible number of moles at ~1. Make the mole value of S equal to 1 by dividing both mole values by 1.249.

1.249 mol S = 1 mol S

1.249

3.747 mol O = 3 mol O

1.249

The simplest whole number mole ratio of S atoms to O atoms is 1 : 3. The empirical formula for the oxide of sulfur is SO3.

Sample Problems

- What is the empirical formula for a compound which is 75 % C and 25 % H?
- What is the empirical formula for a compound which has
- 48.64 % C,
- 8.16 % H
- 43.20 % O

Sample Problems #2

- What is the empirical formula of
- 40.68 % C
- 5.08 % H
- 54.24 % O

Practice Problems

- A blue solid is found to contain 36.894% N and 63.16% O. What is the empirical formula for this solid?
- Determine the empirical formula for a compound that contains 35.98% Al and 64.02% S.
- Propane is a hydrocarbon, a compound composed only of carbon and hydrogen. It is 81.82% C and 18.18% H. What is the empirical formula?
- The chemical analysis of aspirin indicates that the molecule is 60.00% C, 4.44% H and 35.56% O. Determine the empirical formula.
- What is the empirical formula for a compound that contains 10.89% Mg, 31.77% Cl, and 57.34% O?

Molecular Formula

- Specifies the actual number of atoms of each element in one molecule or formula unit of the substance
- n= ratio between experimentally determined mass of compound and the molar mass of the empirical formula.

Calculating Molecular Formula

- Molar mass of acetylene – 26.04 g/mol
Mass of empirical formula (CH) – 13.02 g/mol

- n – Obtained by dividing the molar mass by the mass of the empirical formula indicates that the molar mass of acetylene is two times the mass of the empirical formula.
Experimentally determined molar mass of acetylene = 26.04 g/mol = 2.000

mass of empirical formula CH 13.02 g/mol

- Molecular Formula = (CH)2
- Acetylene = C2H2

Determining a Molecular Formula

- Succinic acid is a substance produced by lichens. Chemical analysis indicates it is composed of 40.68% C, 5.08% H, and 54.24% O and has a molar mass of 118.1 g/mol. Determine the empirical and molecular formulas for succinic acid.
Known: Unknown:

Percent by mass = 40.68% C empirical formula = ?

Percent by mass = 5.08% H molecular formula = ?

Percent by mass = 54.24% O

Practice Problems

- Analysis of a chemical used in photographic developing fluid indicates a chemical composition of 65.45% C, 5.45% H, and 29.09% O. The molar mass is found to be 110.0 g/mol. Determine the molecular formula.
- A compound was found to contain 49.98 g C, and 10.47 g H. The molar mass of the compound is 58.12 g/mol. Determine the molecular formula.
- A colorless liquid composed of 46.68% N and 53.32% O has a molar mass of 60.01 g/mol. What is the molecular formula?

Naming Hydrates

Hydrate: a compound that has a specific number of water molecules bound to its atoms.

In the formula for a hydrate, the number of water molecules associated with each formula unit of the compound is written following a dot.

ex. Na2CO3·10H2O

called sodium carbonate decahydrate

deca- means 10 and hydrate means water

Therefore there are 10 water molecules are associated with one formula unit of the compound.

Analyzing a Hydrate

- Must drive off the water by heating the compound
- Substance remaining after heating is anhydrous (without water)
- Example: hydrated cobalt(II) chloride is a pink solid that turns a deep blue when the water of hydration is driven off and anhydrous cobalt(II) chloride is produced

Formula for a Hydrate

- To determine the formula for a hydrate, you must determine the number of moles of water associated with one mole of the hydrate.

Example Problem – Determining the Formula for a Hydrate

- A mass of 2.5 g of blue, hydrated copper sulfate (CuSO4·xH2O) is placed in a crucible and heated. After heating, 1.59 g white anhydrous copper sulfate (CuSO4) remains. What is the formula for the hydrate? Name the hydrate.

Example Problem – (cont.)

Known:

Mass of hydrated compound = 2.50 g CuSO4·xH2O

Mass of anhydrous compound = 1.59 g CuSO4

Molar mass = 18.02 g/mol H2O

Molar mass = 159.6 g/mol CuSO4

Unknown:

Formula for hydrate = ?

Name of hydrate = ?

Example Problem – (cont.)

Subtract the mass of the anhydrous copper sulfate from the mass of the hydrated copper sulfate to determine the mass of water lost:

mass of hydrates copper sulfate 2.50 g

mass of anhydrous copper sulfate - 1.59 g

mass of water lost 0.91 g

Calculate the number of moles of H2O and anhydrous CuSO4

1.59 g CuSO4 x 1 mol CuSO4 = 0.00996 mol CuSO4

159.6 g CuSO4

0.91 g H2O x 1 mol H2O = 0.050 mol H2O

18.02 g H2O

Example Problem – (cont.)

Determine the value of x.

x = moles H2O = 0.050 mol H2O = 5.0 mol H2O = 5

moles CuSO4 0.00996 mol CuSO4 1.0 mol CuSO4 1

The ratio of H2O to CuSO4 is 5 : 1, so the formula for the hydrate is CuSO4·5H2O, copper(II) sulfate pentahydrate.

Practice Problems

- A hydrate is found to have the following percent composition: 48.18% MgSO4 and 51.2% H2O. What is the formula and name for this hydrate?
- If 11.75 g of the common hydrate cobalt(II) chloride is heated, 9.25 g of anhydrous cobalt chloride remains. What is the formula and name for this hydrate?

Uses of Hydrates

- Drying agents: CaCl2, CaSO4
- Storage of solar energy: Na2SO4·10H2O

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