4. Magnesium has three natural isotopes with the following masses and natural abundances:


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1 Exercise #1 Atomic Masses 1. The average mass of pennies minted after 1982 is 2.50 g and the average mass of pennies minted before 1982 is 3.00 g. In a sample that contains 90.0% new and 10.0% old pennies, what is the overall average mass of pennies in this sample? 2. A mass spectrometer computed the atomic mass ratio of fluorine to carbon12 as to1. If the atomic mass of carbon12 is 12 amu (exactly), determine the atomic mass of fluorine in amu. 3. Natural boron is composed of two isotopes: 19.78% boron10 (atomic mass = amu) and 80.22% boron11 (atomic mass = amu). What is the average atomic mass of naturally occurring boron? 4. Magnesium has three natural isotopes with the following masses and natural abundances: 24 Mg: abundance = 79.00%; atomic mass = amu; 25 Mg: abundance = 10.00%; atomic mass = amu; 26 Mg: abundance = 11.00%; atomic mass = amu. Calculate the average atomic mass of naturally occurring magnesium. 5. Chlorine has two naturally occurring isotopes with the following atomic masses: 35 Cl = amu and 37 Cl = amu. If the average atomic mass of chlorine is amu, calculate the percent abundances of isotopes 35 Cl and 37 Cl in nature? 1
2 Exercise #2 Counting by Mass 1. (a) What is the mass of one silicon atom in amu and in grams? (b) What is the total mass of one trillion silicon atoms in amu and in grams? (c) What is the total mass of x silicon atoms in amu and in grams. (Give the answers in 4 significant figures) (d) How many silicon atoms are present in a 5.00g sample of pure silicon? Can a sample of silicon weigh 5.00 amu? Why or why not. 2. The atomic mass of carbon is amu and the atomic mass of silicon is amu. What mass of carbon contains as many carbon atoms as there are silicon atoms in 5.00 g of silicon? 3. The atomic mass of carbon is amu and the atomic mass of silicon is amu. (a) What mass of silicon contains the same number of atoms as 2.42 g of carbon? (b) How many atoms are present in each sample? (1 amu = x g) 4. There are approximately 5.5 millions red blood cells per cubic inch in a healthy adult and an average adult has approximately 5.0 L of blood. (a) How many red blood cells (RBC) does an average adult have? (b) If a person donates 1.0 pint of whole blood per visit to the Red Cross, how many RBC does he/she give away? (c) Suppose that the blood of an average adult male contains a total of 2.8 g of iron. How many iron atoms are present in each RBC? (d) The red blood cells contain protein known as hemoglobin, which gives the cells the red color. This red color is due to the heme group in the protein that requires the present of iron (Fe) to give it its characteristic red color. If there are four Fe atoms per hemoglobin molecule, what is the average number of hemoglobin molecules per RBC? (1 inch = 2.54 cm; 1 pint = 473 ml) 2
3 Exercise #3 Percent Composition and Empirical Formula 1. A sample of sodium carbonate was found to contain g sodium, 3.00 g carbon, and g oxygen. (a) Calculate the percent composition (by mass) of sodium carbonate. (b) Determine the empirical formula of sodium carbonate. 2. When g of finely divided iron is burned and completely converted into its oxide, g of a reddish brown oxide is obtained. (a) Determine the empirical formula of the oxide. (b) Write a balanced equation for the reaction of iron and molecular oxygen based on this empirical formula. 3. One of the chlorofluorocarbon (CFC) compounds used in the refrigeration unit has the following compositions: 18.07% Carbon, 28.59% Fluorine, and 53.34% Chlorine, by mass. (a) Determine the empirical formula of the compound. (b) What is the molecular formula of the compound if the molecular mass is 133 amu? 4. A compound is composed of carbon, hydrogen, nitrogen and oxygen. When a g sample of the compound is completely combusted, it yields g of CO 2 and g of H 2 O. In a separate analysis to determine nitrogen, g of the compound is found to produce g of N 2. (a) Calculate the mass percent of each element in the compound. (b) Determine the empirical formula of the compound. (c) If the compound has a molar mass of 134 g/mol, what is the molecular formula? 3
4 Exercise #4 Reaction Stoichiometry 1. Ammonia is produced from nitrogen and hydrogen gases according to the following equation: N 2(g) + 3H 2(g) 2NH 3(g) (a) How many molecules of H 2 will react with 25 N 2 molecules? (b) How many NH 3 molecules of are produced from 25 N 2 molecules if all of N 2 molecules are completely reacted? (c) How many N 2 molecules will react with 60 H 2 molecules? How many NH 3 molecules are produced when all of H 2 molecules have been reacted? (d) If 25 N 2 molecules are reacted with 60 H 2 molecules, which molecules will be completely consumed? How many NH 3 molecules are produced when one of the reactants has been completely consumed? Which molecules will be in excess and how many of these molecules are unreacted? (e) If 3.00 moles of nitrogen gas is reacted with 7.50 moles of hydrogen gas, how many moles of ammonia are produced? Are both reactants completely consumed? If not, which of the reactants is in excess and by how much? (f) How many grams of hydrogen gas are required to react with g of nitrogen? How many grams of ammonia will be produced if all of N 2 were completely reacted and H 2 were in excess? (g) How many grams of nitrogen gas will react with 27.0 g of H 2? How many grams of NH 3 will be produced if all of H 2 were completely reacted and N 2 were in excess? (h) (i) How many grams of NH 3 will be produced if the reaction mixture is composed of g of N 2 and 27.0 g of H 2, and the yield is 100%? (ii) Which reactant, H 2 or N 2, will be completely consumed? (iii) How many grams of the excess reactant are unreacted? (iv) If the reaction actually produces 125 g of NH 3, what is the percent yield? 2. Balance the following equation that represents the complete combustion of octane in gasoline. C 8 H 18 (l) + O 2 (g) CO 2 (g) + H 2 O(g); (a) What is the minimum number of moles of O 2 required to react completely with 1.00 L of octane (C 8 H 18 )? (b) How many kilograms of CO 2 will be produced when 1.00 L of octane is completely reacted and the reaction has 100% yield? (Assume density = g/ml) 4
5 3. In a reaction to produce ammonia, the reactor is charged with N 2 and H 2 gases at the rates of 804 g and 195 g per minute, respectively. The reactor temperature is maintained at 225 o C. (a) Which substance is the limiting reactant? (b) What is the rate (in g/min) for the production of ammonia if the reactor is operating at 100% efficiency? (c) How many kilograms of ammonia will be produced in 1.00 hour under this condition? (d) If the actual hourly production of NH 3 is 54.1 kg, calculate the percentage yield. 4. Hydrogen fluoride is prepared by the reaction of calcium fluoride with concentrated sulfuric acid according to the following equation: CaF 2 (s) + H 2 SO 4 (l) CaSO 4 (s) + 2 HF(g) (a) In a particular reaction, 98.5 g of calcium fluoride was reacted with 138 g of concentrated sulfuric acid. How many grams of HF were formed if the yield is 100%? (b) If the reaction produced 46.0 grams of HF, what is the percentage yield? (Concentrated sulfuric acid is 98.0%, by mass, in H 2 SO 4 ) 5. The following reaction is used to produce methanol: CO(g) + 2 H 2 (g) CH 3 OH(l); (a) How many grams of CO and H 2, respectively, are required to produce 1.00 gallon of methanol if the reaction has a 100% yield? (1 gall = L; density of methanol = g/ml) (b) How many grams of each reactant are needed if the reaction has 93.0% yield? (Note: more reactant would be needed to produce the same amount of product if the yield is less than 100%.) 5
6 Answers: Exercise #1: g; amu; amu; amu; % 35 Cl and 24.24% 37 Cl; Exercise #2: 1. (a) Mass of a silicon atom = amu; x g; (b) x amu; x g; (c) x amu; g; (d) 1.07 x atoms; None the mass is less than an atomic mass g Carbon; 3. (a) 5.66 g Si; (b) 1.2 x atoms of each 4. (a) 1.7 x 10 9 RBC; (b) 1.6 x 10 8 RBC; (c) 1.8 x Featoms per RBC; (d) 4.5 x hemoglobin molecules per RBC; Exercise #3: 1. (a) 43.40% Na; 11.32% C, and 45.28% O; (b) Empirical formula = Na 2 CO 3 ; 2. Empirical formula = Fe 2 O 3 ; 4Fe + 3O 2 2Fe 2 O 3 ; 3. Empirical formula = CClF; molecular formula = C 2 Cl 2 F 2 ; 4. (a) 26.85% C; 4.51% H; 20.9% N, and 47.7% O; (b) Empirical formula = C 3 H 6 N 2 O 4 ; (c) Molecular formula = C 3 H 6 N 2 O 4 Exercise #4: 1. (a) 75 H 2 molecules; (b) 50 NH 3 molecules; (c) 20 N 2 molecules; 40 NH 3 molecules; (d) 40 NH 3 molecules; 5 N 2 molecules will be unreacted; (e) 5.00 mol of NH 3 ; No; N 2 is in excess by 0.50 mol; (f) 25.7 g of H 2 ; 145 g of NH 3 produced; (g) 125 g of N 2 ; 152 g of NH 3 produced; (h) (i) 145 g of NH 3 produced; (ii) N 2 is completely consumed; (iii) 1.3 g of H 2 is unreacted; (iv) Percent yield = 86.2%; 2. (a) 75.7 mol of O 2 ; (b) 2.13 x 10 3 g of CO 2 ; 3. (a) N 2 is the limiting reactant; (b) Rate of NH 3 production = 977 g per minute; (c) 58.6 kg per hour; (d) Percent yield = 92.3% 4. (a) Expected yield = 50.5 g HF; (b) percent yield = 91.3% 5. (a) 2.61 x 10 3 g CO and 376 g H 2 are needed; (b) 2.81 x 10 3 and 405 g of H 2 would be needed; 6
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