3.3 Moles, 3.4 Molar Mass, and 3.5 Percent Composition

3.3 Moles, 3.4 Molar Mass, and 3.5 Percent Composition

Collection Terms A collection term states a specific number of items. 1 dozen donuts = 12 donuts 1 ream of paper = 500 sheets 1 case = 24 cans Copyright 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings Copyright Houghton Mifflin Company. All rights reserved. 3 2

A Mole of Atoms A mole is a collection that contains the same number of particles as there are pure 12- carbon atoms in 12.0 g of carbon. 6.022 x 10 23 atoms of an element (Avogadro s number). 1 mole element Number of Atoms 1 mole C = 6.022 x 10 23 C atoms 1 mole Na = 6.022 x 10 23 Na atoms 1 mole Au = 6.022 x 10 23 Au atoms Copyright Houghton Mifflin Company. All rights reserved. 3 3

A Mole of a Compound A mole of a covalent compound has Avogadro s number of molecules. 1 mole CO 2 = 6.022 x 10 23 CO 2 molecules 1 mole H 2 O = 6.022 x 10 23 H 2 O molecules of an ionic compound contains Avogadro s number of formula units. 1 mole NaCl = 6.022 x 10 23 NaCl formula units 1 mole K 2 SO 4 = 6.022 x 10 23 K 2 SO 4 formula units Copyright Houghton Mifflin Company. All rights reserved. 3 4

Samples of One Mole Quantities 1 mole C = 6.02 x 10 23 C atoms 1 mole Al = 6.02 x 10 23 Al atoms 1 mole S = 6.02 x 10 23 S atoms 1 mole H 2 O = 6.02 x 10 23 H 2 O molecules 1 mole CCl 4 = 6.02 x 10 23 CCl 4 molecules Copyright Houghton Mifflin Company. All rights reserved. 3 5

Avogadro s Number Avogadro s number 6.022 x 10 23 can be written as an equality and two conversion factors. Equality: 1 mole = 6.022 x 10 23 particles Conversion Factors: 6.022 x 10 23 particles and 1 mole 1 mole 6.022 x 10 23 particles Copyright Houghton Mifflin Company. All rights reserved. 3 6

Using Avogadro s Number Avogadro s number is used to convert moles of a substance to particles. How many Cu atoms are in 0.50 mole Cu? 0.50 mole Cu x 6.022 x 10 23 Cu atoms 1 mole Cu = 3.0 x 10 23 Cu atoms Copyright 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings Copyright Houghton Mifflin Company. All rights reserved. 3 7

Using Avogadro s Number Avogadro s number is used to convert particles of a substance to moles. How many moles of CO 2 are in 2.50 x 10 24 molecules CO 2? 2.50 x 10 24 molecules CO 2 x 1 mole CO 2 6.02 x 10 23 molecules CO 2 = 4.15 mole CO 2 Copyright Houghton Mifflin Company. All rights reserved. 3 8

Learning Check 1. The number of atoms in 2.0 mole Al is A. 2.0 Al atoms. B. 3.0 x 10 23 Al atoms. C. 1.2 x 10 24 Al atoms. 2. The number of moles of S in 1.8 x 10 24 atoms S is A. 1.0 mole S atoms. B. 3.0 mole S atoms. C. 1.1 x 10 48 mole S atoms. Copyright Houghton Mifflin Company. All rights reserved. 3 9

Solution A. The number of atoms in 2.0 mole Al is 2.0 mole Al x 6.02x10 23 Al atoms = 1.2 x 10 24 Al atoms 1 mole Al Avogadro s Number B. The number of moles of S in 1.8 x 10 24 atoms S is 1.8 x 10 24 atoms S x 1 mole S 6.02 x 10 23 S atoms Avogadro s Number = 3.0 moles of S atoms Copyright Houghton Mifflin Company. All rights reserved. 3 10

Subscripts and Moles The subscripts in a formula show the relationship of atoms in the formula. the moles of each element in 1 mole of compound. Glucose C 6 H 12 O 6 In 1 molecule: 6 atoms C 12 atoms H 6 atoms O In 1 mole: 6 mole C 12 mole H 6 mole O Copyright Houghton Mifflin Company. All rights reserved. 3 11

Subscripts State Atoms and Moles 9 mole C 8 mole H 4 mole O Copyright Houghton Mifflin Company. All rights reserved. 3 12

Factors from Subscripts The subscripts are used to write conversion factors for moles of each element in 1 mole compound. For aspirin C 9 H 8 O 4, the following factors can be written: 9 mole C 8 mole H 4 mole O 1 mole C9H8O4 1 mole C9H8O4 1 mole C9H8O4 and 1 mole C9H8O4 1 mole C9H8O4 1 mole C9H8O4 9 mole C 8 mole H 4 mole O Copyright Houghton Mifflin Company. All rights reserved. 3 13

Learning Check A. How many mole O are in 0.150 mole aspirin C 9 H 8 O 4? B. How many O atoms are in 0.150 mole aspirin C 9 H 8 O 4? Copyright Houghton Mifflin Company. All rights reserved. 3 14

Solution A. How many mole O are in 0.150 mole aspirin C 9 H 8 O 4? 0.150 mole C 9 H 8 O 4 x 4 mole O = 0.600 mole O 1 mole C 9 H 8 O 4 subscript factor B. How many O atoms are in 0.150 mole aspirin C 9 H 8 O 4? 0.150 mole C 9 H 8 O 4 x 4 mole O x 6.02 x 10 23 O atoms 1 mole C 9 H 8 O 4 1 mole O subscript Avogadro s factor Number = 3.61 x 10 23 O atoms Copyright Houghton Mifflin Company. All rights reserved. 3 15

Molar Mass The molar mass is the mass of one mole of an element or compound. is the atomic mass expressed in grams. Copyright 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings Copyright Houghton Mifflin Company. All rights reserved. 3 16

Molar Mass from Periodic Table Molar mass is the atomic mass expressed in grams. 1 mole Ag 1 mole C 1 mole S = 107.9 g = 12.01 g = 32.07 g Copyright Houghton Mifflin Company. All rights reserved. 3 17

Molar Mass of a Compound The molar mass of a compound is the sum of the molar masses of the elements in the formula. Example: Calculate the molar mass of CaCl 2 to the tenths decimal place. Element Number Atomic Mass Total Mass of Moles Ca 1 40.1 g/mole 40.1 g Cl 2 35.5 g/mole 71.0 g CaCl 2 111.1 g Copyright Houghton Mifflin Company. All rights reserved. 3 18

Some One-mole Quantities One-Mole Quantities 32.1 g 55.9 g 58.5 g 294.2 g 342.2 g Copyright Houghton Mifflin Company. All rights reserved. 3 20

Learning Check What is the molar mass of each of the following? A. K 2 O B. Al(OH) 3 Copyright Houghton Mifflin Company. All rights reserved. 3 21

Solution A. K 2 O 94.2 g/mole 2 mole K (39.1 g/mole) + 1 mole O (16.0 g/mole) 78.2 g + 16.0 g = 94.2 g B. Al(OH) 3 78.0 g/mole 1 mole Al (27.0 g/mole) + 3 mol O (16.0 g/mole) + 3 mol H (1.01 g/mole) 27.0 g + 48.0 g + 3.03 g = 78.0 g Copyright Houghton Mifflin Company. All rights reserved. 3 22

Learning Check Prozac, C 17 H 18 F 3 NO, is an antidepressant that inhibits the uptake of serotonin by the brain. What is the molar mass of Prozac? 1) 40.1 g/mole 2) 262 g/mole 3) 309 g/mole Copyright Houghton Mifflin Company. All rights reserved. 3 23

Solution Prozac, C 17 H 18 F 3 NO, is an antidepressant that inhibits the uptake of serotonin by the brain. What is the molar mass of Prozac? 3) 309 g/mole 17 C (12.0) + 18 H (1.01) + 3 F (19.0) + 1 N (14.0) + 1 O (16.0) = 204 + 18.2 + 57.0 + 14.0 + 16.0 = 309 g/mole Copyright Houghton Mifflin Company. All rights reserved. 3 24

Molar Mass Factors Molar mass conversion factors are written from molar mass. relate grams and moles of an element or compound. Example: Write molar mass factors for methane, CH 4,used in gas stoves and gas heaters. Molar mass: 1 mol CH 4 = 16.0 g Conversion factors: 16.0 g CH 4 and 1 mole CH 4 1 mole CH 4 16.0 g CH 4 Copyright Houghton Mifflin Company. All rights reserved. 3 25

Learning Check Acetic acid C 2 H 4 O 2 gives the sour taste to vinegar. Write two molar mass conversion factors for acetic acid. Copyright Houghton Mifflin Company. All rights reserved. 3 26

Solution Acetic acid C 2 H 4 O 2 gives the sour taste to vinegar. Write two molar mass factors for acetic acid. Calculate molar mass: 24.0 + 4.04 + 32.0 = 60.0 g/mole 1 mole of acetic acid = 60.0 g acetic acid Molar mass factors 1 mole acetic acid and 60.0 g acetic acid 60.0 g acetic acid 1 mole acetic acid Copyright Houghton Mifflin Company. All rights reserved. 3 27

Calculations Using Molar Mass Molar mass factors are used to convert between the grams of a substance and the number of moles. Grams Molar mass factor Moles Copyright Houghton Mifflin Company. All rights reserved. 3 28

Moles to Grams Aluminum is often used to build lightweight bicycle frames. How many grams of Al are in 3.00 mole Al? Molar mass equality: 1 mole Al = 27.0 g Al Setup with molar mass as a factor: 3.00 mole Al x 27.0 g Al = 81.0 g Al 1 mole Al molar mass factor for Al Copyright Houghton Mifflin Company. All rights reserved. 3 29

Learning Check Allyl sulfide C 6 H 10 S is a compound that has the odor of garlic. How many moles of C 6 H 10 S are in 225 g? Copyright Houghton Mifflin Company. All rights reserved. 3 30

Solution Calculate the molar mass of C 6 H 10 S. (6 x 12.0) + (10 x 1.01) + (1 x 32.1) = 114.2 g/mole Set up the calculation using a mole factor. 225 g C 6 H 10 S x 1 mole C 6 H 10 S 114.2 g C 6 H 10 S molar mass factor (inverted) = 1.97 mole C 6 H 10 S Copyright Houghton Mifflin Company. All rights reserved. 3 31

Grams, Moles, and Particles A molar mass factor and Avogadro s number convert grams to particles. molar mass Avogadro s number g mole particles particles to grams. Avogadro s molar mass number particles mole g Copyright Houghton Mifflin Company. All rights reserved. 3 32

Learning Check How many H 2 O molecules are in 24.0 g H 2 O? 1) 4.52 x 10 23 2) 1.44 x 10 25 3) 8.03 x 10 23 Copyright Houghton Mifflin Company. All rights reserved. 3 33

Solution How many H 2 O molecules are in 24.0 g H 2 O? 3) 8.02 x 10 23 24.0 g H 2 O x 1 mole H 2 O x 6.02 x 10 23 H 2 O molecules 18.0 g H 2 O 1 mole H 2 O = 8.03 x 10 23 H 2 O molecules Copyright Houghton Mifflin Company. All rights reserved. 3 34

Learning Check If the odor of C 6 H 10 S can be detected from 2 x 10-13 g in one liter of air, how many molecules of C 6 H 10 S are present? Copyright Houghton Mifflin Company. All rights reserved. 3 35

Solution If the odor of C 6 H 10 S can be detected from 2 x 10-13 g in one liter of air, how many molecules of C 6 H 10 S are present? 2 x 10-13 g x 1 mole x 6.02 x 10 23 molecules 114.2 g 1 mole = 1 x 10 9 molecules C 6 H 10 S Copyright Houghton Mifflin Company. All rights reserved. 3 36

Percent Composition of Compounds: What is the mass percentage of C in CO 2? The mass percentage is calculated using the following equation: If a sample consisting of 1 mole of CO 2 is used, the molebased relationships given earlier show that 1 mole CO 2 =44.01 g CO 2 (12.01 g C + 32.00 g O). Thus, the mass of C in a specific mass of CO 2 is known, and the problem is solved as follows: Copyright Houghton Mifflin Company. All rights reserved. 3 37

What is the mass percentage of oxygen in CO 2? The mass percentage is calculated using the following equation: Once again, a sample consisting of 1 mole of CO 2 is used to take advantage of the mole-based relationships given earlier where: 1 mole CO 2 = 44.01g CO 2 = 12.01 g C + 32.00g O Copyright Houghton Mifflin Company. All rights reserved. 3 38

Thus, the mass of O in a specific mass of CO 2 is known, and the problem is solved as follows: We see that the % C + % O = 100%, which should be the case because C and O are the only elements present in CO 2. Copyright Houghton Mifflin Company. All rights reserved. 3 39

QUESTION Morphine, derived from opium plants, has the potential for use and abuse. It s formula is C 17 H 19 NO 3. What percent, by mass, is the carbon in this compound? 1. 42.5% 2. 27.9% 3. 71.6% 4. This cannot be solved until the mass of the sample is given. Copyright Houghton Mifflin Company. All rights reserved. 3 40

ANSWER Choice 3 is correct. First determine the molar mass of the compound, then divide that into the total mass of carbon present, and finally, multiply that by 100. (17 12.01) / ((17 12.01) + (19 1.008) + (1 14.01) + 3 16.00)) = 0.716 0.716 100 = 71.6 % Section 3.5: Percent Composition of Compounds Copyright Houghton Mifflin Company. All rights reserved. 3 41