Unit 8Chemical Quantities

Chemistry IMr. Patel

SWHS

Topic Outline• MUST have a scientific calculator (not graphing)!!!• Review of Factor-label Method• The Mole: Particle to Mole Conversion (10.1)• Molar Mass: Gram to Mole Conversion (10.2)• Molar Volume: Volume to Mole Conversion (10.2)• Chemical Formula as a Conversion Factor (N/A)• Percent Composition (10.3)• Empirical and Molecular Formulas (10.3)• Solution Concentration (16.2)

PART I:CHEMICAL

CONVERSIONS

Conversion Factors

• Conversion factor – allows us to convert from one unit to another unit– Example: 1m = 1000mm, 1 dozen = 12 items

• We use the factor label method to convert

Old Unit

New UnitGiven

= Desired

Quantity

Remember:Multiply the topDivide the bottom

Measuring by Count

• A count refers to a grouping or a word representing a number– Pair (2), Dozen (12), Ream (500)

• A count is a conversion factor – can convert between a count unit and the number of items– Ex: 1 dozen egg is the same as 12 actual eggs

Ex: Convert 3 dozen apples to number of apples. Use the factor-label method.

1 dozen apples

12 apples3 dozen apples= 36 apples

Representative Particle

• Representative Particle – species present in a substance– Atoms (elements; ex: Fe atom)– Molecules (covalent compounds; ex: diatomics)– Ions (species with a charge; ex: Na1+)– Formula Units (ionic compounds; ex: NaCl)

The Mole

• The fundamental count in chemistry is the mole – SI unit for amount– Very similar to a dozen; represents a number– Abbreviation: mol– Contains an Avogadro’s Number of items– Avogadro’s Number = 6.02 x 1023 (memorize this!)

Conversion Factor 1: 1 mole = 6.02 x 1023 items

The Mole

• It is not appropriate to consider only one atom of an element or one formula unit of a compound– It is easier to group atoms using a large number– NOTE: 1 mole contains the same number of item…

but does not necessarily have the same mass!!!

The Mole

• Just like a dozen, the mole is a conversion factor!

• We can convert between the unit (mole) and the number of items

• Remember:– 1 mole X = 6.02 x 1023 X– You can substitute any item for the X

MOLES

PARTICLES(atoms, molecules,ions, formula units)

6.02x10231 mole

Ex: Convert 1 mole of Fe to number of Fe atoms. Use the factor-label method.

mol Fe

atoms Fe1 mol Fe = 6.02 x 1023 atoms Fe

Math: (1) x (6.02 x 1023) / (1) = 6.02 x 1023

6.02 x 1023

1

MOLES

PARTICLES(atoms, molecules, ions, formula units )

6.02x10231 mole

Ex: Convert 7.8 mol of clipped fingernails to number of clipped fingernails (CF).

Use the factor-label method.

mol CF

CF7.8 mol CF = 4.7 x 1024 CF

Math: (7.8) x (6.02 x 1023) / (1) = 4.7 x 1024

6.02 x 1023

1

MOLES

PARTICLES(atoms, molecules, ions, formula units )

6.02x10231 mole

Ex: Convert 2.1 x 109 atoms of Li to moles of Li. Use the factor-label method.

atoms Li

mol Li2.1 x 109 atom Li = 3.49 x 10-15 mol Li

Math: (2.1 x 109) x (1) / (6.02 x 1023) = 3.49 x 10-15

1

6.02 x 1023

MOLES

PARTICLES(atoms, molecules, ions, formula units )

6.02x10231 mole

Try the following conversions.

1) 1.75 molecules CHCl3 to mol CHCl3

2) 1.7 x 1015 mol of H+ to ions H+

3) 2.80 x 1024 atoms Si to mol Si

1) 2.91 x 10-24 mol CHCl3

2) 1.0 x 1039 ions H+

3) 4.65 mol Si

Mass of an Element

• On the periodic table, the mass of an element is given in units of atomic mass unit– 1/12 the mass of a carbon-12 atom

• In the laboratory, we do not use amu. We measure chemicals in grams.

• We can treat the amu as “grams per mole”.– Carbon: 12 amu 12 grams in 1 mole

Mole-Atom-Mass Relationship

Element Moles # of Atoms Mass Molar Mass

Al 1 mol 6.02 x 1023 26.98g 26.98 g/mol

N 1 mol 6.02 x 1023 14.01g 14.01 g/mol

Pb 1 mol 6.02 x 1023 207.2g 207.2 g/mol

S 1 mol 6.02 x 1023 32.07g 32.07 g/mol

Molar Mass (MM)

• The mass of one mole of an element of compound– Units: grams/mole (g/mol) – Can be called Molecular Weight (MW)– For element, MM comes directly from mass on PT– For compound, add the mass of each atom• CO2 = Add (mass of C) and 2 x (mass of O)

Conversion Factor 2: 1 mole = Mass in Grams (from PT)

Ex: What is the molar mass of iron?

55.85 g/mol Fe (from Periodic Table)

Ex: What is the molar mass of boron? 10.81 g/mol B (from Periodic Table)

Ex: What is the molar mass of H2O?

H: 2 x 1.01g = 2.02g O: 1 x 16.00g = 16.00g 18.02 g/mol H2O

Ex: What is the molar mass of C6H12O6?

C: 6 x 12.01g = 72.06g H: 12 x 1.01g = 12.12g O: 6 x 16.00g = 96.00g 180.18 g/mol C6H12O6

Molar Mass Conversions

• The molar mass is a conversion between the mole and grams.– Moles are used in theory– Grams are used in lab/practice

• Molar Mass allows: mole grams

• Using 2 conversion factors: particle grams– We must go through the mole!!!

GRAMS

MOLES

PARTICLES(atoms, molecules,ions, formula units )

MM=P.T.

6.02x10231 mole

1 mole

Ex: Convert 2.00 mol Carbon to grams C. Use the factor-label method.

mol C

12.012.0 mol C = 24.02 g C

Math: (2.0) x (12.01) / (1) = 24.02

This is Molar Massfrom periodic table1 mol C = 12.01 g C

g C

1

GRAMS

MOLES

PARTICLES(atoms, molecules, ions, formula units )

MM=P.T.

6.02x10231 mole

1 mole

Ex: Convert 9.73 mol Fe to grams Fe. Use the factor-label method.

mol Fe

55.859.73 mol Fe = 543 g Fe

Math: (9.73) x (55.85) / (1) = 543

This is Molar Massfrom periodic table

1 mol Fe = 55.85 g Fe

g Fe

1

GRAMS

MOLES

PARTICLES(atoms, molecules, ions, formula units )

MM=P.T.

6.02x10231 mole

1 mole

Ex: Convert 122 g Al to moles Al. Use the factor-label method.

g Al

1122 g Al = 4.52 mol Al

Math: (122) x (1) / (26.98) = 4.52

This is Molar Massfrom periodic table

1 mol Al = 26.98 g Al

mol Al

26.98

GRAMS

MOLES

PARTICLES(atoms, molecules, ions, formula units )

MM=P.T.

6.02x10231 mole

1 mole

Ex: Convert 413 g C6H12O6 to moles C6H12O6.

Use the factor-label method.

g C6H12O6

1413 g C6H12O6= 2.29 mol C6H12O6

Math: (413) x (1) / (180.18) = 2.29

This is Molar Massfrom periodic table

1 mol C6H12O6 = 180.18 g C6H12O6

mol C6H12O6

180.18

GRAMS

MOLES

PARTICLES(atoms, molecules, ions, formula units )

MM=P.T.

6.02x10231 mole

1 mole

Ex: Convert 26 g He to atoms He. Use the factor-label method.

g He

126 g He = 3.9 x 1024 atom He

Math: (26) x (1) / (4.00) x (6.02 x 1023) / (1) = 3.9 x 1024

This is Molar Massfrom periodic table

1 mol He = 4.00 g He

mol He

4.00

GRAMS

MOLES

PARTICLES(atoms, molecules, ions, formula units )

MM=P.T.

6.02x10231 mole

1 mole

mol He

6.02 x 1023 atom He

1

This is Avogadro’s Number 1 mol = 6.02 x 1023 atoms

Ex: Convert 345 g CO2 to molecule CO2.

Use the factor-label method.

g CO2

1345 g CO2 = 4.72 x 1024

molecules CO2

Math: (345) x (1) / (44.01) x (6.02 x 1023) / (1) = 4.72 x 1024

This is Molar Massfrom periodic table

1 mol CO2 = 44.01 g CO2

mol CO2

44.01

GRAMS

MOLES

PARTICLES(atoms, molecules, ions, formula units )

MM=P.T.

6.02x10231 mole

1 mole

mol CO2

6.02 x 1023molec CO2

1

This is Avogadro’s Number 1 mol = 6.02 x 1023 atoms

Try the following.

1) What is the Molar Mass of Platinum (Pt)?

2) Convert: 652.7 g H2O to molecules H2O

1) 195 g/mol

2) 2.18 x 1025 molec. H2O

GRAMS

MOLES

PARTICLES(atoms, molecules, ions, formula units )

MM=P.T.

6.02x10231 mole

1 mole

Mole to Volume Conversion

• Gases are often measured in volume rather than grams

• A conversion is available between mole and volume only at specific conditions– Only for gases (ideal) – Standard Temperature and Pressure (STP)– 0oC and 1 atm

Conversion Factor 5: 1 mole = 22.4 L

LITERS

GRAMS

MOLES PARTICLESAvogadro Number

1 mole

1 mole Molar Mass

1 moleMolar

Volume (atoms, molecules, ions, formula units)

Ex: Convert 5 mol N2 to liters of N2.

Use the factor-label method.

mol N2

L N25 mol N2 = 112 L N2

Math: (5) x (22.4) / (1) = 122

22.4

1

Ex: Convert 12.5 mol Ar to liters of Ar. Use the factor-label method.

mol Ar

L Ar12.5 mol Ar = 280 L Ar

Math: (12.5) x (22.4) / (1) = 280

22.4

1

Ex: Convert 69.8 L Ne to mol of Ne. Use the factor-label method.

L Ne

mol Ne69.8 L Ne= 3.17 mol Ne

Math: (69.8) x (1) / (22.4) = 3.17

1

22.4

Ex: Convert 49.87 g NH3 to liters NH3 at STP.

Use the factor-label method.

g NH3

149.87 g NH3 = 65.56 L NH3

Math: (49.87) x (1) / (17.04) x (22.4) / (1) = 65.56

This is Molar Massfrom periodic table

1 mol NH3 = 17.04 g NH3

mol NH3

17.04 mol NH3

22.4 L NH3

1

This is Molar Volume at STP1 mol = 22.4 L

Try the following.

1) What is the volume (L) of 589 g N2O?

2) Convert: 3.01 x 1023 molecules of SO2 to liters.

1) 300. L

2) 11.2 L H2O

Chemical Formula

• The chemical formula can act as a conversion• Example: Fe2O3

– The subscripts tell us the number of atoms– 2 atoms of Fe and 3 atoms of O in one formula

unit of Fe2O3

– Assume we have 6.02 x 1023 formula units then…– Fe: 2 x (6.02 x 1023 atom Fe) = 2 mole Fe– O: 3 x (6.02 x 1023 atom O) = 3 mole O

in 1 mol Fe2O3

Chemical Formula

• The chemical formula is a mole ratio!!!• If we have 1 mole C6H12O6 then…

1 mol C6H12O6 : 6 mol C : 12 mol H : 6 mol OColon (:) means chemically equivalent

Conversion Factor 3: Chemical Formula (mole to mole)

Chemical Formula

• NOTE!!! When you are changing from one chemical to another, you must do this through the mole stage! – Mole X Mole Y

• This is strictly a mole to mole conversion.– NOT GRAMS!!!

Conversion Factor 3: Chemical Formula (mole to mole)

LITERS

GRAMS

MOLES PARTICLES6.02x1023

1 mole

1 mole Molar MassPeriodic Table

1 mole

22.4 L

ChemicalFormula

Ex: How many mol of N are in 1.00 mol NO3?

Use the factor-label method.

mol NO3

11.00 mol NO3= 1.00 mol N

Math: (1.00) x (1) / (1) = 2.00

This is Mole ratiofrom chemical formula

1 mol NO3 = 1 mol N

mol N

1

Ex: How many mol of P are in 1.00 mol P2O5?

Use the factor-label method.

mol P2O5

21.00 mol P2O5= 2.00 mol P

Math: (1.00) x (2) / (1) = 2.00

This is Mole Ratiofrom chemical formula

1 mol P2O5 = 2 mol P

mol P

1

Ex: How many mol of S are in 6.80 mol Pb2S3?

Use the factor-label method.

mol Pb2S3

36.80 mol Pb2S3= 20.4 mol S

Math: (1.00) x (2) / (1) = 2.00

This is Mole Ratiofrom chemical formula1 mol Pb2S3 = 3 mol S

mol S

1

Ex: How many grams of Cl are in 8.00 mol CHCl3?

Use the factor-label method.

mol CHCl3

38.00 mol CHCl3 = 851 g Cl

Math: (8.00) x (3) / (1) x (35.45) / (1) = 851

This is Mole Ratiofrom chemical formula1 mol CHCl3 = 3 mol Cl

mol Cl

1 mol Cl

35.45 g Cl

1

This is Molar Massfrom periodic table1 mol Cl = 35.45 g Cl

Ex: How many grams of O are in 15 mol NO2?

Use the factor-label method.

mol NO2

215 mol NO2 = 480 g O

Math: (15) x (2) / (1) x (16.00) / (1) = 480

This is Mole Ratiofrom chemical formula

1 mol NO2 = 2 mol O

mol O

1 mol O

16.00 g O

1

This is Molar Massfrom periodic table

1 mol O = 16.00 g CO2

Ex: How many grams of F are in 10.2 g XeF6?

Use the factor-label method.

g XeF6

110.2 g XeF6 = 4.74 g F

Math: (10.2) x (1) / (245.29) x (6) / (1) x (19.00) / (1) = 4.74

This is Mole Ratiofrom chemical formula

1 mol XeF6 = 6 mol F

mol XeF6

245.29 mol XeF6

6 mol F

1

This is Molar Massfrom periodic table1 mol F = 19.00 g F

g F19.00

1 mol F

This is Molar Massfrom periodic table

1 mol XeF6 = 245.29 g XeF6

Try the following.

1) How many moles of acetate are in 2.00 mol Cr(C2H3O2)3?

2) Convert: 121 g NaOH to grams H.

1) 6 mol C2H3O21-

2) 3.03 g H

PART II:PERCENT

COMPOSITION

Percent Composition

• Describes the relative amounts of each element in a compound

• The percent composition is always the same - no matter the quantity of the sample

• Also called “Percent by Mass”

% X = mass of Xmass of sample x 100%

(X represents some element found in the sample)

Ex: When 13.60 g sample of MgO decomposes, it produces 8.20 g Mg and 5.40 g O.

What is the % composition?

% Mg = mass of Mg

mass of MgOx 100% = 8.20 g Mg

13.60 g MgOx 100%

% Mg = 60.3% Mg

% O = mass of O

mass of MgOx 100% = 5.40 g O

13.60 g MgOx 100%

% O = 39.7% O

Note: All percents should add up to about 100%

Ex: When 89.1 g H2O decomposes, it produces 9.89 g H.What is the % composition?

% H = mass of H

mass of H2Ox 100% = 9.89 g H

89.1 g H2Ox 100%

% H = 11.1% H

% O = mass of O

mass of H2Ox 100% = (13.60 – 9.89) g O

13.60 g H2Ox 100%

% O = 88.9% O

Total mass must equal the sum of its parts: mass H2O = mass H + mass O

Ex: What is the % composition of C3H8?

% C = 36.03 g C

44.11 g C3H8

x 100% = 81.68% C

% H = 8.08 g H

44.11 g C3H8

x 100% = 18.32% H

If we assume 1.00 mol of sample, then we can use periodic table for the mass!!!

• Mass of C:

• Mass of H:

• Mass of C3H8:

3 mol 12.01 g/mol

8 mol

44.11 g/mol C3H8

1.01 g/molx

x = 36.03 g C

= 8.08 g H

Ex: What is the % composition of (NH4)2S?

% N = 28.02 g N

68.17 g (NH4)2S x 100% = 41.10% N

% H = 8.08 g H

68.17 g (NH4)2S x 100% = 11.85% H

If we assume 1.00 mol of sample, then we can use periodic table for the mass!!!

• Mass of N:

• Mass of H:

• Mass of S:

• Mass of (NH4)2S:

2 mol 14.01 g/mol

8 mol

68.17 g/mol (NH4)2S

1.01 g/molx

x = 28.02 g N

= 8.08 g H

% S = 32.07 g S

68.17 g (NH4)2S x 100% = 47.04% S

1 mol 32.07 g/molx = 32.07 g S

Try the following.

1) What is the percent composition of NaOH?

2) What is the percent composition of CH4?

1) 57.5% Na40.0% O2.5% H

2) 75.0% C25.0% H

PART III:EMPIRICAL & MOLECULAR

FORMULAS

Empirical and Molecular Formulas

• Each compound has a basic ratio of elements• C6H6 , C8H8 , C10H10 multiples of CH• Empirical Formula (EF)– Lowest whole number ratio of elements– Ex: CH, CH2O

• Molecular Formula (MF)– Actual ratio of elements in a compound– Can be the same or whole # multiple of empirical– Ex: C6H6, C6H12O6

Empirical and Molecular Formulas

• To determine the empirical, you need % comp– Assume 100g of compound to make math easier

• To determine the molecular, you need1. Molar Mass of Compound (Mass Spec)2. Calculate the Ratio of MF to EF

Ratio = Molecular Molar MassEmpirical Molar Mass

Molecular Molar Mass is given in the problem.

Step to Solve EF/MF Problems

1. Convert: percent grams2. Convert: grams mole3. Divide all by the smallest amount of moles– If needed, multiply to get all whole numbers– Use ratios to determine Empirical Formula

4. Calculate the Ratio– Multiply: Ratio x Empirical Formula (Subscripts)– This will give the Molecular Formula

Ex: A molecule was determined to be 30.4% N and 69.6% O with a molar mass of 92.02 g/mol.

Determine the empirical & molecular formulas.

g N

130.4 g N= 2.17 mol N

mol N

14.01

g O

169.6 g O= 4.31 mol O

mol O

16.00

2.17

2.17

=

1 mol N

= 2 mol O

EmpiricalNO2

Ratio =92.02 g/mol46.01 g/mol

2= 2 x NO2 Molecular

N2O4

Ex: 40.0% C, 6.67% H, 53.3% O; MM=90.00 g/mol. Determine the empirical & molecular formulas.

g C

140.0 g C= 3.33 mol C

mol C

12.01

g H

16.67 g H= 6.60 mol H

mol H

1.01

3.33

3.33

=

1 mol C

= 2 mol HEmpirical

CH2O

Ratio =90.00 g/mol30.03 g/mol

3= 3 x CH2O Molecular

C3H6O3

g O

153.3 g O= 3.33 mol O

mol O

16.003.33 = 1 mol O

Ex: A 150g sample consists of 74.25g C, 7.725g H, 43.35g N, and 24.75g O - molar mass of 195 g/mol. Determine the empirical and molecular formulas.

Answer:

Empirical: C4H5N2O

Molecular: C8H10N4O2

Try the following.

1) Find the EF & MF for:75.69 % C, 8.80% H, 15.51% O with MM = 206 g/mol

1) EF: C13H18O2

MF: C13H18O2

(Ibuprofen)