Chapter Three Fe atoms 1 mol Fe When balancing a chemical equation, changing the subscripts changes the identity of the substance.
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1 3. The mole is the SI unit for the amount of a substance. A mole is equal in quantity to Avogadro s number ( ) of particles, or the formula mass in grams of a substance. 3.4 There are the same number of molecules in.5 moles of H O and.5 moles of H. 3.5 There are moles of iron atoms in 1 mole of Fe O 3. The stoichiometric equivalent between Fe and Fe O is mol Fe 1 mol Fe O 3. For the number of iron atoms in 1 mole of Fe O 3 : 1 mol Fe O mol Fe 3 1 mole FeO Fe atoms 1 mol Fe = atoms Fe 3.1 When balancing a chemical equation, changing the subscripts changes the identity of the substance There are three distinct empirical formulas represented AB, AB 3, and A 3 B 8. There are two molecules with the empirical formula AB 3 ; AB 3 and A B 6. There is one A 3 B 8, and there are two with the formula AB ; A 6 B 1 and A 3 B Student B is correct. Student A wrote a properly balanced equation. However, by changing the subscript for the product of the reaction from an implied one, NaCl, to a two, NaCl, this student has changed the identity of the product. When balancing chemical equations, never change the values of the subscripts given in the unbalanced equation :4, 1 mol C:4 mol H mol I molecules of I molecules I =.99 mole I 3.30 (a) atom C: 1 atom O mole C: 1 mole O (c) 1 atom C: atom H (d) 1 mole C: mole H mol O mol O = (4.5 mol CaCO 3 ) 1 mol CaCO3 = 1.8 mol O mol H atoms H atom H = (.31 mol C 3 H 8 ) 1 mol C3H8 1 mol H = atoms H 3.07 g S 3.48 (a) g S = (0.546 mol S) 1 mole S = 17.5 g S (c) g N = (3.9 mol N) g N 1 mole N = 46.1 g N 6.98 g N g Al = (8.11 mol Al) 1 mole N = 19 g Al 3.50 g Na = mol Na.99 g Na atoms Na atoms Na 1 mol Na 1 mol Cr 3.5 mol Cr = 85.7 g Cr = 1.65 mol Cr 5.00 g Cr = g Na 31
2 3.54 Note: all masses are in g/mole (a) Ca(NO 3 ) = 1Ca + N + 6O = (40.078) + ( ) + ( ) = g/mole = g/mol Pb(C H 5 ) 4 = 1Pb + 8C + 0H = (07.) + ( ) + ( ) = 33.4 g/mole (Since the mass of Pb is known exactly.) (c) Na SO 4 10H O = Na + 1S +14O + 0H = (.98977) ( ) + ( ) = g/mole = g/mol (d) Fe 4 [Fe(CN) 6 ] 3 = 7Fe + 18C + 18N = ( ) + ( ) + ( ) = g/mole = g/mol (e) Mg 3 (PO 4 ) = 3Mg + P + 8O = ( ) + ( ) + ( ) = g/mole = g/mol g ZnCl 3.56 (a) g ZnCl = (0.754 mol ZnCl ) 1 mol ZnCl = 103 g ZnCl 1 mol KIO g KIO μg KIO3 μg KIO 3 = (0.194 μmol KIO 3 ) 6 10 mol KIO μ 1 mol KIO g KIO3 = g KIO 3 1 mol POCl g POCl3 (c) g POCl 3 = (0.3 mmol POCl 3 ) 3 10 mmol POCl = g POCl 3 1 mol POCl 3 3 ( ) 13.1 g NH HPO (d) g (NH 4 ) HPO 4 = ( mol (NH 4 ) HPO 4 ) 1 mol ( NH4) HPO 4 = g (NH 4 ) HPO (a) 1 mole Ca(OH) mol Ca(OH) = (9.36 g Ca(OH) g Ca(OH) 1000 g PbSO4 1 mole PbSO4 mol PbSO 4 = (38. kg PbSO 4 ) = 16 mol PbSO 4 1 kg PbSO g PbSO4 1 mole H O (c) mol H O = (4.9 g H O ) g H O = 0.16 mol H O 1 g NaAuCl (d) mol NaAuCl 4 = 4.65 mg NaAuCl 4 1 mol NaAuCl mg NaAuCl g NaAuCl = mol NaAuCl (a) The molar mass of (CH 3 ) N H is 60.1 g/mol. 4.0 g C % C = 60.1 g (CH 3) NH 100% = 40.0% 8.06 g H % H = 60.1 g (CH 3) NH 100% = 13.4% 8.0 g N % N = 60.1 g (CH 3) NH 100% = 46.6% 4 4 3
3 (c) (d) (e) The molar mass of CaCO 3 is g/mol g Ca % Ca = g CaCO3 100% = 40.0% 1.01 g C % C = g CaCO3 100% = 1.0% g O % O = g CaCO3 100% = 48.0% The molar mass of Fe(NO 3 ) 3 is 41.9 g/mol g Fe % Fe = 100% = 3.1% 41.9 g Fe NO ( ) 3 3 % N = 4.03 g N 41.9 g Fe( NO3 ) 3 100% = 17.4% % O = g O 41.9 g Fe( NO3 ) 3 100% = 59.5% The molar mass of C 3 H 8 is g/mol g C % C = 100% = 81.7% g C H g H % H = 100% = 18.3% g C3H8 The molar mass of Al (SO 4 ) 3 is 34. g/mol g Al % Al = 100% = 15.8% 34. g Al SO ( ) 4 3 % S = % O = 96. g S 34. g Al( SO4) g O 34. g Al( SO4) 3 100% = 100% = 8.1% 56.1% 3.68 % N in carbamazepine = % N in carbetapentane = 8.0 g N 36.9 g C15H1NO g N g C0H31NO 3 100% = 11.9% N 100% = 4.0% N Therefore, carbamazepine has a higher percentage of nitrogen (a) CH 3 O HSO 4 (c) C H 5 (d) BH 3 (e) C H 6 O mol C mol C = (0.43 g C) = mol C 1.01 g C 1 mol Cl mol Cl = (.50 g Cl) = mol Cl g Cl 1 mol F mol F = (1.34 g F) = mol F g F Now we divide each of these numbers of moles by the smallest of the three numbers, in order to obtain the simplest mole ratio among the three elements in the compound: 33
4 for C, moles / moles = 1.00 for Cl, moles / moles =.000 for F, moles / moles =.00 Chapter Three These relative mole amounts give us the empirical formula CCl F 3.84 Assume a 100 g sample: 1 mol C mol C = (63. g C) 1.01 g C = 5.6 mol C 1 mol H mol H = (5.6 g H) g H = 5. mol H 1 mol O mol O = (31.6 g O) g O = 1.98 mol O Now we divide each of these numbers of moles by the smallest of the three numbers, in order to obtain the simplest mole ratio among the three elements in the compound: for C, 5.6 moles / 1.98 moles =.66 = (8/3) for H, 5. moles / 1.98 moles =.64 = (8/3) for O, 1.98 moles / 1.98 moles = 1.00 = (3/3) These relative mole amounts give us the empirical formula C 8 H 8 O All of the carbon is converted to carbon dioxide so, g C = (.01 g CO ) 1 mol CO 1 mol C 1.01 g C g CO 1 mol CO 1 mol C = g C 1 mol C mol C = (0.549 g C) 1.01 g C = mol C All of the hydrogen is converted to H O, so g H = (0.87 g H O) 1 mol H O mol H g H 18.0 g HO 1 mol HO 1 mol H = g H 1 mol H mol H = (0.095 g H) = mol H g H The amount of O in the compound is determined by subtracting the mass of C and the mass of H from the sample. g O = 0.8 g g g = g 1 mol O mol O = (0.181 g O) g O = mol O The relative mole ratios are: for C, moles / moles = 4.04 for H, moles/ moles = 8.1 for O, moles / moles = 1.00 The relative mole amounts give the empirical formula C 4 H 8 O 3.90 (a) Formula mass = 1.1 g 34
5 73.6 g/mol 1.1 g/mol = The molecular formula is Na 1 Si 6 O 18 Formula mass = 10.0 g g/mol = g/mol The molecular formula is Na 3 P 3 O 9 (c) Formula mass = g 6.1 g/mol = g/mol The molecular formula is C H 6 O 3.94 From the information provided, the mass of sulfur is the difference between the total mass and the mass of antimony: g S = g compound g Sb = g S To determine the empirical formula, first convert the two masses to a number of moles. 1 mole S mol S = (0.645 g S) g S = mol S 1 mole Sb mol Sb = ( g Sb) g Sb = mol Sb Now, divide each of these values by the smaller quantity to determine the simplest mole ratio between the two elements: For Sb: moles/ moles = mol Sb For S: moles/ moles =.500 mol S Hence the empirical formula is Sb S 5, and the empirical mass is ( Sb) + (5 S) = g/mol. Since the molecular mass reported in the problem is the same as the calculated empirical mass, the empirical formula is the same as the molecular formula NO(g) + O (g) NO (g) 3.10 (a) SO + O SO 3 NaHCO 3 + H SO 4 Na SO 4 + H O + CO (c) P 4 O H O 4H 3 PO 4 (d) Fe O 3 + 3H Fe + 3H O (e) Al + 3H SO 4 Al (SO 4 ) 3 + 3H (a) CaO + HNO 3 Ca(NO 3 ) + H O Na CO 3 + Mg(NO 3 ) MgCO 3 + NaNO 3 (c) (NH 4 ) 3 PO 4 + 3NaOH Na 3 PO 4 + 3NH 3 + 3H O (d) LiHCO 3 + H SO 4 Li SO 4 + H O + CO (e) C 4 H 10 O + 6O 4CO + 5H O 35
6 3.108 (a) 5 mole O mol O = (6 mol C 8 H 18 ) = 80 mol O mole C8H18 (Note: This calculation is limited due to sig figs.) 16 mole CO mol CO = (0.5 mol C 8 H 18 ) = 4 mol CO mole C8H18 18 mole HO (c) mol H O = (8 mol C 8 H 18 ) mole C8H = 70 mol H O 18 5 mole O (d) mol O = ( 6.00 mol CO ) 16 mole CO = 9.38 mol O mole C8H18 mol C 8 H 18 = (6.00 mol CO ) 16 mole CO = mol C 8 H (a) 3 mol C 3 H 8 5 mol O 3.00 g O 1 mol C3H = 500 g O 8 1 mol O 0.1 mol C 3 H 8 3 mol CO g CO 1 mol C3H = 13 g CO 8 1 mol CO (c) 4 mol C 3 H 8 4 mol H O g H O 1 mol C3H = 300 g H O 8 1 mol HO 1 mol N H 7 mol H O 34.0 g H O g H O = (85 g N H 4 ) 3.05 g NH4 1 mol NH4 1 mol HO 4 = 6330 g H O (a) First determine the amount of C H 4 that would be required to react completely with the given amount of H O: 1000 g C g H O = 1.0 kg C H H4 1 mol CH4 1 mol HO 4 1 kg CH g CH4 1 mol CH g HO 1 kg HO = 0.64 kg H O 1 mol HO 1000 g HO Since only kg of H O are supplied, it is the limiting reactant. This can be confirmed by calculating the amount of C H 4 that would be required to react completely with all of the available H O: 1000 g HO 1 mol HO 1 mol CH4 g C H 4 = 0.01 kg H O 1 kg HO 18.0 g HO 1 mol HO 8.05 g CH4 1 kg CH4 1 mol CH g CH4 = kg C H g HO 1 mol HO g C H 5 OH = (0.010 kg H O) 1 kg HO 18.0 g HO 1 mol CH5OH g CH5OH = 6 g C H 5 OH 1 mol HO 1 mol CH5OH 36
7 3.1 (a) First calculate the number of moles of water that are needed to react completely with the given amount of PCl 5 : 4 mole HO mol H O = (0.360 mol PCl 5 ) 1 moles PCl5 = 1.44 mol H O Since this is less than the amount of water that is supplied, the limiting reactant must be PCl 5. This can be confirmed by the following calculation: 1 mol PCl5 mol PCl 5 = (.88 mol H O) 4 mol HO = 0.70 mol PCl 5 which also demonstrates that the limiting reactant is PCl 5. 5 mol HCl g HCl g HCl = (0.360 mol PCl 5 ) 1 mol PCl 5 1 mol HCl = 65.6 g HCl 3.16 Assume there is excess oxygen present and determine the theoretical yield of carbon dioxide. 1 mol CH3OH mol CO g CO g CO = (6.40 g CH OH) = 8.79 g CO 3.04 g CH3OH mol CH3OH 1 mol CO 6.1 g % yield = 100% = 69.6% 8.79g 3 37
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