Chapter 10 Chemical Quantities 10.1 The Mole: A Measurement of Matter 10.2 Mole-Mass and Mole-Volume Relationships 10.3 Percent Composition and Chemical Formulas Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

What does the percent composition tell you? CHEMISTRY & YOU What does the percent composition tell you? A tag sewn into the seam of a shirt usually tells you what fibers were used to make the cloth and the percent of each. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Percent Composition of a Compound The relative amounts of each element in a compound is expressed as the percent composition or the percent by mass of each element in the compound. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Percent Composition of a Compound The percent composition of potassium chromate, K2CrO4, is: K = 40.3% Cr = 26.8% O = 32.9% Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Percent Composition of a Compound The percents must total 100%. K = 40.3% Cr = 26.8% + O = 32.9% 100% Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Percent Composition of a Compound The percent composition of any compound is always the same no matter how much you have of it. (ex: 100 grams or 0.5 grams) The percents must always total 100%. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Percent Composition of a Compound How do you calculate the percent composition of a compound? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Percent Composition of a Compound Percent Composition from Mass Data Percent composition of an element in a compound is the number of grams of the element divided by the mass in grams of the compound, multiplied by 100. % composition = mass of element mass of compound × 100 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Percent Composition of a Compound Percent Composition from Mass Data If you know the relative masses of each element in a compound, you can calculate the percent composition of the compound. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Calculating Percent Composition from Mass Data Sample Problem Calculating Percent Composition from Mass Data When a 7.58-g sample of a compound containing only aluminum and nitrogen is decomposed, 2.99 g of nitrogen is obtained. What is the percent composition of this compound? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Analyze List the knowns and the unknowns. Sample Problem Analyze List the knowns and the unknowns. 1 The percent by mass of an element in a compound is the mass of that element divided by the mass of the compound multiplied by 100. KNOWNS mass of compound = 7.58 g mass of nitrogen = 2.99 g N mass of aluminum = 7.58 g – 2.99 g N = 4.59 g Aℓ UNKNOWNS percent by mass of Aℓ = ?% Aℓ percent by mass of N = ?% N Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

= 60.6 % Aℓ Calculate Solve for the unknowns. Sample Problem Calculate Solve for the unknowns. 2 Determine the percent by mass of Aℓ in the compound. % Aℓ = mass of Aℓ mass of compound × 100 = 4.59 g 7.58 g = 60.6 % Aℓ Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

= 39.4 % N Calculate Solve for the unknowns. Sample Problem Calculate Solve for the unknowns. 2 Determine the percent by mass of N in the compound. % N = mass of N mass of compound × 100 2.99 g = 7.58 g = 39.4 % N Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Evaluate Does the result make sense? Sample Problem Evaluate Does the result make sense? 3 The percents of the elements add up to 100%. 60.6% + 39.4% = 100% Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Percent Composition of a Compound Percent Composition from the Chemical Formula You can also calculate the percent composition of a compound using its chemical formula. The subscripts are used to calculate the mass of each element in a mole of that compound. Using the individual masses of the elements and the molar mass, you can calculate the percent composition. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Percent Composition of a Compound Percent Composition from the Chemical Formula You can also calculate the percent composition of a compound using its chemical formula. % composition mass of element in 1 mol compound molar mass of compound × 100 = Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Calculating Percent Composition from a Formula Sample Problem Calculating Percent Composition from a Formula Glucose (C6H12O6), commonly referred to as sugar, is Coach McKnight’s favorite compound. Calculate the percent composition of glucose. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Analyze List the knowns and the unknowns. Sample Problem Analyze List the knowns and the unknowns. 1 Calculate the percent by mass of each element by dividing the mass of that element in one mole of the compound by the molar mass of the compound and multiplying by 100. KNOWNS mass of C in 1 mol C6H12O6 = 12 g/mol × 6 mol = 72.0 g mass of H in 1 mol C6H12O6 = 1 g/mol × 12 mol = 12.0 g mass of O in 1 mol C6H12O6 = 16 g/mol x 6 mol = 96.0 g molar mass of C6H12O6 = 72.0 + 12.0 + 96.0 = 180.0 g UNKNOWNS percent by mass of C = ?% C percent by mass of H = ?% H percent by mass of O = ?% O Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

= 40.0 % C Calculate Solve for the unknowns. Sample Problem Calculate Solve for the unknowns. 2 Determine the percent by mass of C in C6H12O6. % C = mass of C in 1 mol C6H12O6 molar mass of C6H12O6 × 100 = 72.0 g 180.0 g = 40.0 % C Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

= 6.70 % H Calculate Solve for the unknowns. Sample Problem Calculate Solve for the unknowns. 2 Determine the percent by mass of H in C3H12O6. % H = mass of H in 1 mol C6H12O6 molar mass of C6H12O6 × 100 = 12.0 g 180.0 g = 6.70 % H Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

= 53.3 % O Calculate Solve for the unknowns. Sample Problem Calculate Solve for the unknowns. 2 Determine the percent by mass of O in C3H12O6. % O = mass of H in 1 mol C6H12O6 molar mass of C6H12O6 × 100 = 96.0 g 180.0 g = 53.3 % O Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Evaluate Does the result make sense? Sample Problem Evaluate Does the result make sense? 3 The percents of the elements add up to 100% when the answers are expressed to two significant figures (40% + 6.7% + 53.3% = 100%). Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Percent Composition of a Compound Percent Composition as a Conversion Factor You can use percent composition to calculate the number of grams of any element in a specific mass of a compound. To do this, multiply the mass of the compound by a conversion factor based on the percent composition of the element in the compound. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Percent Composition of a Compound Percent Composition as a Conversion Factor Propane is 81.8% carbon and 18.2% hydrogen. If you have 100 grams of propane; then 81.8 grams will be carbon and 18.2 grams will be hydrogen. 81.8 g C 100 g propane and 18.2 g H Conversion factors Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Sample Problem Calculating the Mass of an Element in a Compound Using Percent Composition Calculate the mass of carbon and the mass of hydrogen in 149.6 g of propane based on the known percent composition. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Analyze List the known and the unknowns. Sample Problem Analyze List the known and the unknowns. 1 Use the conversion factors based on the percent composition of propane to make the following conversions: grams propane → grams C and grams propane → grams H. KNOWN mass of propane = 149.6 g percent C = 81.8% percent H = 18.2% UNKNOWNS mass of carbon = ? g C mass of hydrogen = ? g H Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

= 122.4 g C Calculate Solve for the unknowns. 2 Sample Problem Calculate Solve for the unknowns. 2 To calculate the mass of C, first write the conversion factor to convert from mass of propane to mass of C. 81.8 g C 100 g propane Multiply the mass of propane by the conversion factor. 81.8 g C 100 g propane 149.6 g propane × = 122.4 g C 1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

= 27.20 g H Calculate Solve for the unknowns. 2 Sample Problem Calculate Solve for the unknowns. 2 To calculate the mass of H, first write the conversion factor to convert from mass of propane to mass of H. 18.2 g H 100 g propane Multiply the mass of propane by the conversion factor. 18.2 g H 100 g propane 149.6 g propane × = 27.20 g H 1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Evaluate Does the result make sense? Sample Problem Evaluate Does the result make sense? 3 The sum of the two masses should equal the mass of the sample size. (122 g C + 27 g H = 149 g propane). Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

What data can you use to calculate percent composition? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

What data can you use to calculate percent composition? You can calculate percent composition if you know the mass of a compound and the masses of the elements contained in the compound, or if you know the chemical formula, the molar mass of the compound, and the molar mass of the elements contained in the compound. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Empirical Formulas The empirical formula of a compound gives the lowest whole-number ratio of the atoms or moles of the elements in a compound. An empirical formula may or may not be the same as a molecular formula. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Empirical Formulas The empirical formula of a compound gives the lowest whole-number ratio of the atoms or moles of the elements in a compound. An empirical formula may or may not be the same as a molecular formula. The molecular formula for hydrogen peroxide is, H2O2. The lowest ratio of hydrogen to oxygen in hydrogen peroxide is 1:1. Thus, the empirical formula of hydrogen peroxide is HO. Notice that the ratio of hydrogen to oxygen is still the same, 1:1. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

How can you calculate the empirical formula of a compound? Empirical Formulas Empirical Formulas How can you calculate the empirical formula of a compound? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Empirical Formulas The percent composition of a compound can be used to calculate the empirical formula of that compound. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Empirical Formulas The percent composition of a compound can be used to calculate the empirical formula of that compound. The percent composition tells the ratio of masses of the elements in a compound. The ratio of masses can be changed to ratio of moles by using conversion factors based on the molar mass of each element. The mole ratio is then reduced to the lowest whole-number ratio to obtain the empirical formula of the compound. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Determining the Empirical Formula of a Compound Sample Problem Determining the Empirical Formula of a Compound A compound is analyzed and found to contain 18.3% nitrogen and 81.7% oxygen. What is the empirical formula of the compound? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Analyze List the knowns and the unknown. Sample Problem Analyze List the knowns and the unknown. 1 The percent composition gives the ratio of the mass of nitrogen atoms to the mass of oxygen atoms in the compound. Change the ratio of masses to a ratio of moles and reduce this ratio to the lowest whole-number ratio. KNOWNS percent by mass of N = 18.3% N percent by mass of O = 81.7% O UNKNOWN empirical formula = N?O? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Calculate Solve for the unknown. Sample Problem Calculate Solve for the unknown. 2 Convert the percent by mass of each element to moles. Percent means “parts per 100,” so 100.0 g of the compound contains 18.3 g N and 81.7 g O. 18.3 g N × 1 mol N 14.0 g N = 1.31 mol N 1 81.7 g O × 1 mol O 16.0 g O = 5.11 mol O 1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

The empirical formula is NO4. Sample Problem Calculate Solve for the unknown. 2 Divide each molar quantity by the smaller number of moles to get 1 mol for that element. If the result is a decimal that is very close to a whole number round it. 1.31 mol N 1.31 = 1 mol N 5.11 mol O 1.31 = 3.9 mol O The empirical formula is NO4. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

1 mol of N × 2 = 2 mol N 3.5 mol of O × 2 = 7 mol O Sample Problem ** If the decimal was to end on a 5, you should then double all the answers. ** 1 mol of N × 2 = 2 mol N 3.5 mol of O × 2 = 7 mol O The empirical formula would then be N2O7 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Evaluate Does the result make sense? Sample Problem Evaluate Does the result make sense? 3 The subscripts are whole numbers, and the percent composition of this empirical formula equals the percents given in the original problem. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

You are doing an experiment to try to find the molecular formula of a compound. You discover the percent composition. Can you determine the molecular formula? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

You are doing an experiment to try to find the molecular formula of a compound. You discover the percent composition. Can you determine the molecular formula? You can determine the empirical formula. This might be the same as the molecular formula, or it might not. You would need more data to be sure of the molecular formula. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Molecular Formulas Molecular Formulas How does the molecular formula of a compound compare with the empirical formula? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Molecular Formulas The molecular formula of a compound is either the same as its experimentally determined empirical formula, or it is a simple whole-number multiple of its empirical formula. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Molecular Formulas The molecular formula of a compound is either the same as its experimentally determined empirical formula, or it is a simple whole-number multiple of its empirical formula. From the empirical formula, you can determine a compounds molecular formula, if you know the compound’s molar mass. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Comparison of Empirical and Molecular Formulas Interpret Data Notice that the molar masses of the compounds in these two groups are simple whole-number multiples of the molar masses of the empirical formulas, CH and CH2O. Comparison of Empirical and Molecular Formulas Formula (name) Classification of formula Molar mass (g/mol) CH Empirical 13 C2H2 (ethyne) Molecular 26 (2 × 13) C6H6 (benzene) 78 (6 × 13) CH2O (methanal) Empirical and molecular 30 C2H4O2 (ethanoic acid) 60 (2 × 30) C6H12O6 (glucose) 180 (6 × 30) Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Molecular Formulas You can calculate the empirical formula mass (efm) of a compound from its empirical formula. This is simply the molar mass of the empirical formula. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Molecular Formulas You can calculate the empirical formula mass (efm) of a compound from its empirical formula. This is simply the molar mass of the empirical formula. Then you can divide the experimentally determined molar mass by the empirical formula mass. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Molecular Formulas You can calculate the empirical formula mass (efm) of a compound from its empirical formula. This is simply the molar mass of the empirical formula. Then you can divide the experimentally determined molar mass by the empirical formula mass. This quotient gives the number of empirical formula units in a molecule of the compound and is the multiplier to convert the empirical formula to the molecular formula. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Finding the Molecular Formula of a Compound Sample Problem Finding the Molecular Formula of a Compound Calculate the molecular formula of a compound whose molar mass is 180.0 g/mol and empirical formula is CH4N. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Analyze List the knowns and the unknown. Sample Problem Analyze List the knowns and the unknown. 1 KNOWNS empirical formula = CH4N molar mass = 180.0 g/mol UNKNOWN molecular formula = C?H?N? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Calculate Solve for the unknown. Sample Problem Calculate Solve for the unknown. 2 First calculate the empirical formula mass. efm of CH4N = 12.0 g/mol + 4(1.0 g/mol) + 14.0 g/mol = 30.0 g/mol Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

= 6 = C6H24N6 (CH4N) × 6 Calculate Solve for the unknown. Sample Problem Calculate Solve for the unknown. 2 Divide the molar mass by the empirical formula mass. molar mass efm = 180.0 g/mol = 6 30.0 g/mol Multiply the formula subscripts by this value. (CH4N) × 6 = C6H24N6 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Evaluate Does the result make sense? Sample Problem Evaluate Does the result make sense? 3 The molecular formula (C6H24N6) has the molar mass of the compound from the problem. C = 12 x 6 = 72 H = 1 x 24 = 24 N = 14 x 6 = 84 + 180 g Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

What information, in addition to empirical formula, is necessary to determine the molecular formula of a compound? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

What information, in addition to empirical formula, is necessary to determine the molecular formula of a compound? Molecular formula can be determined if the empirical formula and the molar mass of a compound are known. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Key Concepts The percent by mass of an element in a compound is the number of grams of the element divided by the mass in grams of the compound, multiplied by 100%. The percent composition of a compound can be used to calculate the empirical formula of that compound. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

Key Concepts and Key Equations The molecular formula of a compound is either the same as its experimentally determined formula, or it is a simple whole-number multiple of its empirical formula. % by mass of element mass of element mass of compound = × 100 % by mass of element mass of element in 1 mol compound molar mass of compound × 100 = Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .

END OF 10.3 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. .