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1 Example Exercise 9.1 Atomic Mass and Avogadro s Number Refer to the atomic masses in the periodic table inside the front cover of this textbook. State the mass of Avogadro s number of atoms for each of the following elements: (a) Copper (c) sulfur (b) Mercury (d) helium The atomic mass of each element is listed below the symbol of the element in the periodic table: Cu = amu, Hg = amu, S = amu, and He = 4.00 amu. The mass of Avogadro s number of atoms is the atomic mass expressed in grams. Therefore, atoms of (a) Cu = g (c) S = g (b) Hg = g (d) He = 4.00 g Refer to the periodic table and state the mass for each of the following: (a) 1 atom of Au (b) atoms of Au Answers: (a) amu; (b) g What is the mass of an average platinum atom? What is the mass of Avogadro s number of Pt atoms?

2 Example Exercise 9.2 Mole Calculations I Calculate the number of sodium atoms in mol Na. Strategy Plan Step 1: What unit is asked for in the answer? Step 2: What given value is related to the answer? Step 3: What unit factor(s) should we apply? Since 1 mol Na = atoms Na, the two unit factors are 1 mol Na/ atoms Na, and its reciprocal atoms Na/1 mol Na. Unit Analysis Map

3 Example Exercise 9.2 Continued Mole Calculations I We apply the unit factor atoms Na/1 mol Na to cancel moles denominator., which appears in the The answer is rounded to three digits because the given value and unit factor each have three significant digits. Calculate the number of formula units in mol of sodium chloride, NaCl. Answers: formula units NaCl What is the number of molecules in 1.00 mol of any gas?

4 Example Exercise 9.3 Mole Calculations I Calculate the number of moles of potassium in atoms K. Strategy Plan Step 1: What unit is asked for in the answer? Step 2: What given value is related to the answer? Step 3: What unit factor(s) should we apply? Since mol K = atoms K, the two unit factors are 1 mol K/ atoms K, and its reciprocal atoms K/1 mol K. Unit Analysis Map

5 Example Exercise 9.3 Continued Mole Calculations I We apply the unit factor 1 mol K/ atoms K to cancel atoms denominator., which appears in the The answer is rounded to three digits because the given value and unit factor each have three significant digits. Calculate the number of moles of potassium iodide in formula units of KI. Answer: 88.7 mol KI What is the number of molecules in 1.00 mol of iodine crystals?

6 Example Exercise 9.4 Molar Mass Calculations Calculate the molar mass for each of the following substances: (a) silver metal, Ag (b) ammonia gas, NH 3 (c) magnesium nitrate, Mg(NO 3 ) 2 We begin by finding the atomic mass of each element in the periodic table. The molar mass equals the sum of the atomic masses expressed in g/mol. (a) The atomic mass of Ag is amu, and the molar mass of silver equals g/mol. (b) The sum of the atomic masses for NH 3 is amu + 3(1.01)amu = amu. The molar mass of ammonia equals g/mol. (c) The sum of the atomic masses for Mg(NO 3 ) 2 is amu + 2( )amu = amu. The molar mass of magnesium nitrate equals g/mol. Calculate the molar mass for each of the following substances: (a) manganese metal, Mn (b) sulfur hexafluoride, SF 6 (c) strontium acetate, Sr(C 2 H 3 O 2 ) 2 Answers: (a) g/mol; (b) g/mol; (c) g/mol The molecular mass of water is amu. What is the mass of Avogadro s number of water molecules?

7 Example Exercise 9.5 Mole Calculations II What is the mass in grams of atoms of sulfur? Strategy Plan Step 1: What unit is asked for in the answer? Step 2: What given value is related to the answer? Step 3: What unit factor(s) should we apply? By definition, 1 mol S = atoms S, and the molar mass from the periodic table is g S = 1 mol S; the two pairs of unit factors are shown in Step 3. Unit Analysis Map

8 Example Exercise 9.5 Continued Mole Calculations II We apply the unit factor 1 mol S/ atoms S to cancel atoms S cancel mol S :, and g S/1 mol S to What is the mass of formula units of lead(ii) sulfide, PbS? Answer: 30.8 g PbS Sulfur occurs naturally as S 8 molecules. What is the mass of Avogadro s number of S 8 molecules?

9 Example Exercise 9.6 Mole Calculations II How many O 2 molecules are present in g of oxygen gas? Strategy Plan Step 1: What unit is asked for in the answer? Step 2: What given value is related to the answer? Step 3: What unit factor(s) should we apply? The molar mass from the periodic table is g O 2 = 1 mol O 2, and by definition, 1 mol O 2 = molecules O 2. Thus, the two pairs of unit factors are shown in Step 3. Unit Analysis Map

10 Example Exercise 9.6 Continued Mole Calculations II We apply the unit factor 1 mol O 2 /32.00 g O 2 to cancel g O 2 cancel moles O 2. Thus,, and molecules O 2 /1 mol O 2 to How many formula units of lithium fluoride are found in g LiF? Answer: formula units LiF Ozone occurs naturally as O 3 molecules. What is the mass of Avogadro s number of ozone molecules?

11 Example Exercise 9.7 Mass of a Molecule Calculate the mass in grams for a single molecule of carbon dioxide, CO 2 (given that MM = g/mol). Strategy Plan Step 1: What unit is asked for in the answer? Step 2: What given value is related to the answer? Step 3: What unit factor(s) should we apply? By definition, 1 mol CO 2 = molecules. Thus, the unit factors are shown in Step 3. Unit Analysis Map

12 Example Exercise 9.7 Continued Mass of a Molecule We apply the unit factor 1 mol CO 2 / molecules CO 2 to cancel mol CO 2. Calculate the mass in grams for a single molecule of carbon monoxide, CO. Answer: g/molecule What is the mass of a carbon monoxide molecule expressed in amu?

13 Example Exercise 9.8 Density of a Gas at STP Calculate the density of ammonia gas, NH 3, at STP. (MM = g/mol) Strategy Plan Step 1: What unit is asked for in the answer? Step 2: What given value is related to the answer? Step 3: What unit factor(s) should we apply? From the molar volume of a gas at STP, 1 mol = 22.4 L; thus, the unit factors are 1 mol/22.4 L, and 22.4 L/1 mol. Unit Analysis Map

14 Example Exercise 9.8 Continued Density of a Gas at STP We apply the unit factor 1 mol /22.4 L to cancel moles the denominator., which appears in If we filled a balloon with ammonia gas (0.761 g/l), the balloon would float in air (1.29 g/l). Similarly, a less dense liquid floats on a more dense liquid; for example, gasoline (0.7 g/ml) floats on water (1.0 g/ml). Calculate the density of hydrogen sulfide gas, H 2 S, at STP. Answer: 1.52 g/l Why does the balloon filled with helium gas rise, while the balloon filled with nitrogen gas does not?

15 Example Exercise 9.9 Molar Mass of a Gas A fire extinguisher releases 1.96 g of an unknown gas that occupies 1.00 L at STP. What is the molar mass (g/mol) of the unknown gas? Strategy Plan Step 1: What unit is asked for in the answer? Step 2: What given value is related to the answer? Step 3: What unit factor(s) should we apply? From the molar volume of a gas at STP, 1 mol = 22.4 L; thus, the unit factors are 1 mol/22.4 L, and 22.4 L/1 mol. Unit Analysis Map

16 Example Exercise 9.9 Continued Molar Mass of a Gas We apply the unit factor 1 mol/22.4 L to cancel liters, which appears in the denominator. Because the unknown gas is from a fire extinguisher, we suspect that it is carbon dioxide. By summing the molar mass for CO 2 (44.01 g/mol), we help confirm that the unknown gas is carbon dioxide. Boron trifluoride gas is used in the manufacture of computer chips. Given that g of the gas occupies 497 ml at STP, what is the molar mass of boron fluoride gas? Answer: 67.8 g/mol What is the volume of one mole of any gas at STP?

17 Example Exercise 9.10 Mole Calculations III What is the mass of 3.36 L of ozone gas, O3, at STP? Strategy Plan Step 1: What unit is asked for in the answer? Step 2: What given value is related to the answer? Step 3: What unit factor(s) should we apply? From the molar volume of a gas at STP, 1 mol O 3 = 22.4 L O 3. The molar mass from the periodic table is g O 3 = 1 mol O 3. Thus, the two pairs of unit factors are shown in Step 3. Unit Analysis Map

18 Example Exercise 9.10 Mole Calculations III Continued We apply the unit factor 1 mol O 3 /22.4 L O 3 to cancel L O 3 cancel moles O 3,, and g O 3 /1 mol O 3 to What volume is occupied by g of methane gas, CH 4, at STP? Answer: L CH 4 (174 ml) How many molecules of ozone are in one mole of gas?

19 Example Exercise 9.11 Mole Calculations III How many molecules of hydrogen gas, H 2, occupy L at STP? Strategy Plan Step 1: What unit is asked for in the answer? Step 2: What given value is related to the answer? Step 3: What unit factor(s) should we apply? From the molar volume of a gas at STP, 1 mol H 2 = 22.4 L H 2 and by definition, 1 mol H 2 = molecules H 2. Thus, the two pairs of unit factors are shown in Step 3. Unit Analysis Map

20 Example Exercise 9.11 Continued Mole Calculations III We apply the unit factor 1 mol H 2 /22.4 L H 2 to cancel L H 2, and molecules H 2 /1 mol H 2 to cancel moles 77H 2. Thus, What is the volume occupied by atoms of helium gas, He, at STP? Answer: L He (124 ml) What is the mass of one mole of hydrogen gas?

21 Example Exercise 9.12 Percent Composition of a Substance TNT (trinitrotoluene) is a white crystalline substance that explodes at 240 C. Calculate the percent composition of TNT, C 7 H 5 (NO 2 ) 3. Let s calculate the percent composition assuming there is 1 mol of TNT. For compounds with parentheses, it is necessary to count the number of atoms of each element carefully. That is, 1 mol of C 7 H 5 (NO 2 ) 3 contains 7 mol of C atoms, 5 mol of H atoms, 3 mol of NO 2 (that is, 3 mol N atoms and 6 mol of O atoms). We begin the calculation by finding the molar mass of C 7 H 5 (NO 2 ) 3 as follows: Now, let s compare the mass of each element to the total molar mass of the compound, that is, g. The percent composition of TNT reveals that the explosive is mostly oxygen by mass. When we sum the individual percentages ( = 99.99%), we verify our calculation and, find that the total is approximately 100%.

22 Example Exercise 9.12 Continued Percent Composition of a Substance EDTA (ethylenediaminetetraacetic acid) is used as a food preservative and in the treatment of metallic lead poisoning. Calculate the percent composition of EDTA, C 10 H 16 N 2 O 8. Answers: 41.09% C, 5.53% H, 9.587% N, and 43.79% O If an analysis of sugar, C x H y O z, gave 40.0% C and 6.7% H, what is the percent oxygen? Answers: See Appendix G.

23 Example Exercise 9.13 Empirical Formula from Mass Composition In a laboratory experiment, g of scandium was heated and allowed to react with oxygen from the air. The resulting product oxide had a mass of g. Now, let s find the empirical formula for scandium oxide, Sc? O?. The empirical formula is the simplest whole-number ratio of scandium and oxygen in the compound scandium oxide. This ratio is experimentally determined from the moles of each reactant. The moles of scandium are calculated as follows: The moles of oxygen are calculated after first subtracting the mass of Sc from the product, Sc? O? : The moles of oxygen are calculated from the mass of oxygen that reacted: The mole ratio in scandium oxide is Sc O To simplify the ratio and obtain small whole numbers, we divide by the smaller number: Since the calculated ratio is not close to whole numbers, we cannot round off the experimental ratio Sc 1.00 O However, we can double the ratio to obtain whole numbers, that is, Sc 2.00 O Thus, the empirical formula is Sc 2 O 3.

24 Example Exercise 9.13 Continued Empirical Formula from Mass Composition Iron can react with chlorine gas to give two different compounds, FeCl 2 and FeCl 3. If g of metallic iron reacts with chlorine gas to yield g of iron chloride, which iron compound is produced in the experiment? Answer: FeCl 3 If mol of yellow powder sulfur reacts with mol of oxygen gas, what is the empirical formula of the sulfur oxide?

25 Example Exercise 9.14 Empirical Formula from Percent Composition Glycine is an amino acid found in protein. An analysis of glycine gave the following data: 32.0% carbon, 6.7% hydrogen, 18.7% nitrogen, and 42.6% oxygen. Calculate the empirical formula of the amino acid. If we assume a 100 g sample, then the percentage of each element equals its mass in 100 g of glycine, that is, 32.0 g C, 6.7 g H, 18.7 g N, and 42.6 g O. We can determine the empirical formula as follows: The mole ratio of the elements in the amino acid is C 2.66 H 6.6 N 1.33 O We can find a small whole-number ratio by dividing by the smallest number: Simplifying, we find that the empirical formula for the amino acid glycine is C 2 H 5 NO 2.

26 Example Exercise 9.14 Continued Empirical Formula from Percent Composition Calculate the empirical formula for caffeine given the following percent composition: 49.5% C, 5.15% H, 28.9% N, and 16.5% O. Answer: C 4 H 5 N 2 O If mol of yellow powder sulfur reacts with mol of oxygen gas, what is the empirical formula of the sulfur oxide?

27 Example Exercise 9.15 Molecular Formula from Empirical Formula The empirical formula for fructose, or fruit sugar, is CH 2 O. If the molar mass of fructose is 180 g/mol, find the actual molecular formula for the sugar. We can indicate the molecular formula of fructose as (CH2O)n. The molar mass of the empirical formula CH 2 O is 12 g C + 2(1 g H) + 16 g O = 30 g/mol. Thus, the number of multiples of the empirical formula is Thus, the molecular formula of fructose is (CH 2 O) 6 or C 6 H 12 O 6. Ethylene dibromide was used as a grain pesticide until it was banned. Calculate (a) the empirical formula and (b) the molecular formula for ethylene dibromide given its approximate molar mass of 190 g/mol and its percent composition: 12.7% C, 2.1% H, and 85.1% Br. Answers: (a) CH 2 Br; (b) C 2 H 4 Br 2 If the molecular formula of hydrogen peroxide is H 2 O 2, what is the empirical formula?

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