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Chapter 7 Chemical Quantities The Mole Atomic Mass and Formula Mass Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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The Mole Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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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 © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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A mole (mol) is a collection that contains The same number of particles as there are carbon atoms in 12.01 g of carbon. 6.022 x 10 23 atoms of an element (Avogadro’s number). 1 mol C = 6.022 x 10 23 C atoms 1 mol Na = 6.022 x 10 23 Na atoms 1 mol Au = 6.022 x 10 23 Au atoms A Mole of Atoms
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A mole Of a covalent compound has Avogadro’s number of _________________. 1 mol CO 2 = 6.022 x 10 23 CO 2 molecules 1 mol H 2 O = 6.022 x 10 23 H 2 O molecules Of an ionic compound contains Avogadro’s number of ___________ units. 1 mol NaCl = 6.022 x 10 23 NaCl formula units 1 mol K 2 SO 4 = 6.022 x 10 23 K 2 SO 4 formula units A Mole of A Compound
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Samples of One Mole Quantities Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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Avogadro’s number 6.022 x 10 23 can be written as an equality and two conversion factors. As an equality: 1 mol particles = 6.022 x 10 23 particles As conversion Factors: 6.022 x 10 23 particles and 1 mol particles 1 mol particles 6.022 x 10 23 particles Avogadro’s Number
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Using Avogadro’s Number Avogadro’s number Converts moles of a substance to the number of particles. How many Cu atoms are in 0.50 mol Cu? 0.50 mol Cu x 6.022 x 10 23 Cu atoms 1 mol Cu = 3.0 x 10 23 Cu atoms Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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Using Avogadro’s Number Avogadro’s number Converts particles of a substance to moles. How many moles of CO 2 are 2.50 x 10 24 CO 2 molecules? 2.50 x 10 24 CO 2 x 1 mol CO 2 6.022 x 10 23 CO 2 = 4.15 mol CO 2
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The number of atoms in 2.0 mol Al is 2.0 mol Al x 6.022 x 10 23 Al atoms = 1 mol Al 1.2 x 10 24 Al atoms Learning Check
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The number of moles of S in 1.8 x 10 24 atoms S is 1.8 x 10 24 S atoms x 1 mol S = 6.022 x 10 23 S atoms 3.0 mol S atoms Learning Check
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Subscripts and Moles The subscripts in a formula state The relationship of atoms in the formula. The moles of each element in 1 mol of compound. Glucose C 6 H 12 O 6 In 1 molecule: 6 atoms C 12 atoms H6 atoms O In 1 mol: 6 mol C 12 mol H 6 mol O
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Subscripts State Atoms and Moles 1 mol C 9 H 8 O 4 = 9 mol C 8 mol H 4 mol O Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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Factors from Subscripts Subscripts used for conversion factors Relate moles of each element in 1 mol compound. For aspirin C 9 H 8 O 4 can be written as: 9 mol C 8 mol H 4 mol O 1 mol C 9 H 8 O 4 1 mol C 9 H 8 O 4 1 mol C 9 H 8 O 4 and 1 mol C 9 H 8 O 4 1 mol C 9 H 8 O 4 1 mol C 9 H 8 O 4 9 mol C 8 mol H 4 mol O
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Learning Check How many moles O are in 0.150 mol aspirin C 9 H 8 O 4 ? 0.150 mol C 9 H 8 O 4 x 4 mol O = 0.600 mol O 1 mol C 9 H 8 O 4 subscript factor
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Learning Check How many O atoms are in 0.150 mol aspirin C 9 H 8 O 4 ? 0.150 mol C 9 H 8 O 4 x 4 mol O x 6.022 x 10 23 O atoms 1 mol C 9 H 8 O 4 1 mol O subscript Avogadro’s factor number = 3.61 x 10 23 O atoms
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Atomic Mass Atomic mass is the Mass of a single atom in atomic mass units (amu). Mass of an atom compared to a 12 C atom. Number below the symbol of an element. (the average atomic mass)
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Periodic Table and Atomic Mass Ag has atomic mass = 107.9 amu C has atomic mass = 12.01 amu S has atomic mass = 32.07 amu
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Atomic Mass Factors The atomic mass Can be written as an equality. Example: 1 P atom = 30.97 amu Can be written as two ___________ ________. Example: 1 P atom and 30.97 amu 30.97 amu 1 P atom
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Uses of Atomic Mass Factors The atomic mass factors are used to convert A specific number of atoms to mass (amu). An amount in amu to ___________ of atoms.
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Using Atomic Mass Factors 1. What is the mass in amu of 75 P atoms? 75 P atoms x 30.97 amu = 2323 amu (2.323 x10 3 amu) 1 P atom 2. How many Cu atoms have a mass of 4.500 x 10 5 amu? 4.500 x 10 5 amu x 1 Cu atom = 7081 Cu atoms 63.55 amu
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Learning Check What is the mass in amu of 75 silver atoms? 75 Ag atoms x 107.9 amu = 8093 amu 1 Ag atom
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Learning Check How many gold atoms have a mass of 1.85 x 10 5 amu? 1.85 x 10 5 amu x 1 Au atom = 939 Au atoms 197.0 amu
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Formula Mass The formula mass is The mass in amu of a compound. The _____ of the atomic masses of the elements in a formula. Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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Calculating Formula Mass To calculate the formula mass of Na 2 SO 4 Multiply the atomic mass of each element by its subscript, then total the masses of the atoms. 2 Na x 22.99 amu = 45.98 amu 1 Na 1 S x 32.07 amu = 32.07 amu 142.05 amu 1 S 4 O x 16.00 amu = 64.00 amu 1 O
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Learning Check Using the periodic table, calculate the formula mass of aluminum sulfide Al 2 S 3. 2 Al x 26.98 amu = 53.96 amu 1 Al 3 S x 32.07 amu = 96.21 amu 1 S 150.17 amu
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Molar Mass Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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Molar Mass The molar mass Is the mass of one mol of an element or compound. Is the atomic mass expressed in grams. Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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Molar Mass from the Periodic Table Molar mass Is the atomic mass expressed in grams. Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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Give the molar mass for: A. 1 mol K atoms = B.1 mol Sn atoms = Learning Check
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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. ElementNumber of Moles Atomic MassTotal Mass Ca140.08 g/mol 40.08 g Cl235.45 g/mol 70.90 g CaCl 2 110.98 g
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Molar Mass of K 3 PO 4 Calculate the molar mass of K 3 PO 4. ElementNumber of Moles Atomic MassTotal Mass in K 3 PO 4 K339.10 g/mol 117.3 g P130.97 g/mol 30.97 g O416.00 g/mol 64.00 g K 3 PO 4 212.3 g
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Some One-Mol Quantities 32.07 g 55.85 g 58.44 g 294.20 g 342.30 g Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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A. K 2 O 94.20 g/mol 2 mol K (39.10 g/mol) + 1 mol O (16.00 g/mol) 78.20 g + 16.00 g = 94.20 g B. Al(OH) 3 78.00 g/mol 1 mol Al (26.98 g/mol) + 3 mol O (16.00 g/mol) + 3 mol H (1.008 g/mol) 26.98 g + 48.00 g + 3.024 g = 78.00 g Learning Check
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Calculations Using Molar Mass Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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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 cook tops and gas heaters. Molar mass: 1 mol CH 4 = 16.04 g Conversion factors: 16.04 g CH 4 and 1 mol CH 4 1 mol CH 4 16.04 g CH 4 Molar Mass Factors
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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: 24.02 + 4.032 + 32.00 = 60.05 g/mol 1 mol of acetic acid = 60.05 g acetic acid Molar mass factors 1 mol acetic acid and 60.05 g acetic acid 60.05 g acetic acid 1 mol acetic acid Learning Check
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Molar mass factors are used to convert between the grams of a substance and the number of moles. Calculations Using Molar Mass Grams Molar mass factor Moles
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Aluminum is used to build lightweight bicycle frames. How many grams of Al are 3.00 mol Al? Molar mass equality: 1 mol Al = 26.98 g Al Setup with molar mass as a factor: 3.00 mol Al x 26.98 g Al = 80.9 g Al 1 mol Al molar mass factor for Al Moles to Grams
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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 C 6 H 10 S? Action Plan: Calculate the molar mass, and convert 225 g to moles. Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Grams Molar mass factor Moles
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Calculate the molar mass of C 6 H 10 S. 6 C (6 x 12.01) + 10 H (10 x 1.008) + 1 S (1 x 32.07) = 114.21 g/mol Set up the calculation using a mole factor. 225 g C 6 H 10 S x 1 mol C 6 H 10 S 114.21 g C 6 H 10 S molar mass factor(inverted) = 1.97 mol C 6 H 10 S Solution
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Grams, Moles, and Particles A molar mass factor and Avogadro’s number convert Grams to particles molar mass Avogadro’s number (g mol particles) Particles to grams Avogadro’s molar mass number (particles mol g)
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Learning Check How many H 2 O molecules are in 24.0 g H 2 O? A) 4.52 x 10 23 B) 1.44 x 10 25 C) 8.02 x 10 23
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Learning Check How many H 2 O molecules are in 24.0 g H 2 O? 24.0 g H 2 O x 1 mol H 2 O x 6.022 x 10 23 H 2 O molecules 18.02 g H 2 O 1 mol H 2 O = 8.02 x 10 23 H 2 O molecules
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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? 2 x 10 -13 g x 1 mol x 6.022 x 10 23 molecules 114.21 g 1 mol = 1 x 10 9 molecules C 6 H 10 S Odor Threshhold – lower detectable limit
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Percent Composition and Empirical Formulas Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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Percent Composition Percent composition Is the percent by mass of each element in a formula. Example: Calculate the percent composition of CO 2. CO 2 = 1 C(12.01g) + 2 O(16.00 g) = 44.01 g/mol) 12.01 g C x 100 = 27.29 % C 44.01 g CO 2 32.00 g O x 100 = 72.71 % O 44.01 g CO 2
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What is the percent composition of lactic acid, C 3 H 6 O 3, a compound that appears in the blood after vigorous activity? → Learning Check
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STEP 1 3 C(12.01) + 6 H(1.008) + 3 O(16.00) = 90.08 g/mol 36.03 g C + 6.048 g H + 48.00 g O = 90.08 g/mol STEP 2 %C = 36.03 g C x 100= 40.00% C 90.08 g cpd %H = 6.048 g H x 100 = 6.714% H 90.08 g cpd %O = 48.00 g O x 100 = 53.29% O 90.08 g cpd Solution C3H6O3C3H6O3
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Learning Check The chemical isoamyl acetate C 7 H 14 O 2 contributes to the odor of pears. What is the percent carbon in isoamyl acetate? Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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Molar mass C 7 H 14 O 2 = 7 C(12.01) + 14 H(1.008) + 2 O(16.00) = 130.18 g/mol Total C = 7 C(12.01) = g % C = total g C x 100 total g cpd % C= 84.07 g C x 100 = 64.58 % C 130.18 g cpd Solution C 7 H 14 O 2
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The empirical formula Is the simplest whole number ratio of the atoms. Is calculated by dividing the subscripts in the actual (molecular) formula by a whole number to give the lowest ratio. C 5 H 10 O 5 5 = C 1 H 2 O 1 = CH 2 O actual (molecular) empirical formula formula Empirical Formulas
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Some Molecular and Empirical Formulas The molecular formula is the same or a multiple of the empirical. Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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1. What is the empirical formula for _________? A) C 2 H 4 B) CH 2 C) CH 2. What is the empirical formula for _________? A) C 4 H 7 B) C 6 H 12 C) C 8 H 14 3. Which is a possible molecular formula for ______? A) C 4 H 4 O 4 B) C 2 H 4 O 4 C) C 3 H 6 O 3 Learning Check
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A compound contains 7.31 g Ni and 20.0 g Br. Calculate its empirical (simplest) formula. Lets ask, what does the empirical formula tell us? The ratio of atoms of each element, ratio of moles of each element. Action Plan: Convert mass (g) to moles. Learning Check
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Convert 7.31 g Ni and 20.0 g Br to moles. 7.31 g Ni x 1 mol Ni = 0.125 mol Ni 58.69 g Ni 20.0 g Br x 1 mol Br = 0.250 mol Br 79.90 g Br Divide by smallest: 0.125 mol Ni = 1 Ni0.250 mol Br = 2 Br 0.125 0.125 Write ratio as subscripts: NiBr 2 Solution
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Converting Decimals to Whole Numbers When the number of moles for an element is a decimal, all the moles are multiplied by a small integer to obtain whole number. Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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Aspirin is 60.0% C, 4.5 % H and 35.5 % O. Calculate its empirical (simplest) formula. We have percentages, not grams. However, the percentages are really an expression of grams of an element in 100. (exact) grams of compound. Learning Check
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STEP 1. Calculate the moles of each element in 100. g of the compound. 100. g aspirin contains 60.0% C or 60.0 g C, 4.5% H or 4.5 g H, and 35.5% O or 35.5 g O. 60.0 g C x 1 mol C = 5.00 mol C 12.01 g C 4.5 g H x 1 mol H = 4.5 mol H 1.008 g H 35.5 g O x 1mol O = 2.22 mol O 16.00 g O Solution
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Solution (continued) STEP 2. Divide by the smallest number of mol. 5.00 mol C= 2.25 mol C (decimal) 2.22 4.5 mol H = 2.0 mol H 2.22 2.22 mol O = 1.00 mole O 2.22
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Solution (continued) 3. Use the lowest whole number ratio as subscripts When the moles are not whole numbers, multiply by a factor to give whole numbers, in this case x 4. C: 2.25 mol C x 4 = 9 mol C H: 2.0 mol Hx 4 = 8 mol H O: 1.00 mol O x 4 = 4 mol O Using these whole numbers as subscripts the simplest formula is C 9 H 8 O 4
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Molecular Formulas Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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A molecular formula Is a multiple (or equal) of its empirical formula. Has a molar mass that is the empirical formula mass multiplied by a whole number. molar mass = a whole number empirical mass Is obtained by multiplying the empirical formula by a whole number. Relating Molecular and Empirical Formulas
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Diagram of Molecular and Empirical Formulas A small integer links A molecular formula and its empirical formula. A molar mass and its empirical formula mass. Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
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Determine the molecular formula of compound that has a molar mass of 78.11 g and an empirical formula of CH. STEP 1. Empirical formula mass of CH = 13.02 g STEP 2. Divide the molar mass by the empirical mass. 78.11 g = 5.999 ~ 6 13.02 g STEP 3. Multiply each subscript in C 1 H 1 by 6. molecular formula = C 1x 6 H 1 x 6 = C 6 H 6 Finding the Molecular Formula
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Some Compounds with Empirical Formula CH 2 O Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings formaldehyde
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A compound has a molar mass of 176.1g and an empirical formula of C 3 H 4 O 3. What is the molecular formula? What do we need to do? From the empirical formula, determine the empirical mass. Then determine the whole number integer. Learning Check
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A compound has a formula mass of 176.1 and an empirical formula of C 3 H 4 O 3. What is the molecular formula? C 3 H 4 O 3 = 88.06 g/EF 176.1 g (molar mass) = 2.00 88.06 g (empirical mass) Molecular formula = 2 x empirical formula C 3 x 2 H 4 x 2 O 3 x 2 = C 6 H 8 O 6 Solution
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A compound contains C 24.27%, H 4.07%, and Cl 71.65%. The molar mass is about 99 g. What are the empirical and molecular formulas? STEP 1. Calculate the empirical formula. Write the mass percents as the grams in a 100.00-g sample of the compound. C 24.27 g H 4.07 g Cl 71.65 g Molecular Formula
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Finding the Molecular Formula ( Continued) Calculate the number of moles of each element. 24.27 g C x 1 mol C = 2.021 mol C 12.01 g C 4.07 g H x 1 mol H = 4.04 mol H 1.008 g H 71.65 g Cl x 1 mol Cl = 2.021 mol Cl 35.45 g Cl
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Finding the Molecular Formula ( Continued) Divide by the smallest number of moles: 2.021 mol C =1 mol C 2.021 4.04 mol H =2 mol H 2.021 2.02 mol Cl=1 mol Cl 2.021 Empirical formula = C 1 H 2 Cl 1 = CH 2 Cl Calculate empirical mass (EM) CH 2 Cl = 49.48 g
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Finding the Molecular Formula ( Continued) STEP 2. Divide molar mass by empirical mass. Molar mass = 99 g = 2 Empirical mass 49.48 g STEP 3. Multiply the empirical formula by the small integer to determine the molecular formula. 2 x (CH 2 Cl) C 1 x2 H 2 x 2 Cl 1x 2 = C 2 H 4 Cl 2
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A compound is 27.4% S, 12.0% N and 60.6 % Cl. If the compound has a molar mass of 351 g, what is the molecular formula? Learning Check
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In 100. g, there are 27.4 g S, 12.0 g N, and 60.6 g Cl. 27.4 g S x 1 mol S = 0.854 mol S 32.07 g S 12.0 g N x 1 mol N = 0.857 mol N 14.01 g N 60.6 g Cl x 1mol Cl = 1.71 mol Cl 35.45 g Cl Solution
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Divide by the smallest number of moles 0.854 mol S /0.854 = 1.00 mol S 0.857 mol N/0.854 = 1.00 mol N 1.71 mol Cl/0.854 = 2.00 mol Cl empirical formula = SNCl 2 = 116.98 g Molar Mass/ Empirical mass 351 g = 3 116.98 g molecular formula = (SNCl 2 ) 3 = S 3 N 3 Cl 6 Solution (continued)
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