Composition of Substances and Solutions

1. Composition of Substances and Solutions • Atomic Mass and Formula Mass; • The Mole & Molar Mass; • Percent Composition of Compounds; • Determination of Empirical & Molecular Formulas; • Molarity • Other Units for Solution Concentrations

2. Atomic Masses • Absolute masses of atoms cannot be obtained – too small to measure the mass directly; • Atomic mass is expressed as relative mass – masses relative to a chosen standard or reference. • Carbon-12: chosen as reference; assigned an atomic mass of 12 u exactly; • Masses of other atoms are relative to that of carbon-12 atom; • Relative atomic masses are determined using mass spectrophotometer;

3. A Schematic Diagram of Mass Spectrophotometer

4. Isotope Mass of CO2

5. Mass Spectrum of Chlorine:1) Indicate 2 isotopes of chlorine, with relative masses of 35 u and 37 u;2) Cl-35 more abundant (~75%) than Cl-37 (~25%)

6. Mass Spectrum of Isotopes of MercuryHow many isotopes? What are their relative masses?

7. Calculation of Relative Atomic Masses Example-1: An atomic mass spectrum gives atomic mass ratio of oxygen atom to carbon-12 as 1.3329:1. If the atomic mass of carbon-12 is exactly 12 u, what is the atomic mass of oxygen? Atomic mass of oxygen = 1.3329 x 12 u = 15.995 u

8. Calculation of Average Atomic Masses Example-2: Chlorine is composed of two stable naturally occurring isotopes: chlorine-35 (mass = 34.9689 u;abundance = 75.76%) and chlorine-37 (mass = 36.9659 u; abundance = 24.24%). Calculate the average atomic mass of chlorine? Atomic mass of chlorine = (34.9689 u x0.7576) + (36.9659 u x0.2424) = 35.45 u(as given in the periodic table)

9. Calculation of Average Atomic Masses • Example-3: Copper is composed of two naturally occurring isotopes: copper-63 (mass = 62.93 u; abundance = 69.09%) and copper-65 (mass = 64.93 u; abundance = 30.91%;). Average relative atomic mass of copper: = (62.93 u x0.6909) + (64.93 u x0.3091) = 63.55 u(as given in the periodic table)

10. Exercise #1: Relative Atomic Mass A mass spectrophotometer computed the atomic mass ratio of fluorine to carbon-12 as 1.5832-to-1. If the atomic mass of carbon-12 is 12 u (exactly), what is the atomic mass of fluorine in u? (Answer: 18.998 u)

11. Exercise #2: Average Atomic Mass Natural boron is composed of two isotopes: boron-10 (mass = 10.0129 u; abundance = 19.78%) and boron-11 (mass = 11.0093 u; abundance = 80.22%). Calculate the relative average atomic mass of boron? (Answer: 10.81 u)

12. Mole Quantity • The Mole: A quantity that contains the Avogadro’s number of items; Avogadro’s number = 6.022 x 1023 12 g of carbon-12 isotope contains 6.022 x 1023 C-12 atoms. 1 mole of C-12 = 12 g 1 mole of carbon = 12.01 g (C-13 included)

13. Gram-Atomic Mass • Gram-atomic mass = atomic mass expressed in grams - implies mass of 1 mole of an element; • Gram-atomic mass = mass of an element that contains the Avogadro’s number (6.022 x 1023) of atoms of that element. • 12.01 g of carbon contains 6.022 x 1023 carbon atoms; • 16.00 g oxygen contains 6.022 x 1023 oxygen atoms; • 28.09 g silicon contains 6.022 x 1023 Si atoms; • Gram-atomic mass =Molar mass of element

14. Atomic Mass & Molar Mass • Examples: Gram-atomic mass Element Atomic mass (Molar mass) Carbon 12.01 u 12.01 g/mol Oxygen 16.00 u 16.00 g/mol Aluminum 26.98 u 26.98 g/mol Silicon 28.09 u 28.09 g/mol Gold 197.0 u 197.0 g/mol

16. Molecular Mass and Molar Mass • Molecular mass = mass of one molecule (in u); • Molar mass = mass of one mole of element or compound (in g/mol) = sum of atomic masses; • Examples: Molecular MassMolar Mass (g/mol) N2 28.02 u 28.02 H2O 18.02 u 18.02 C8H18 114.22 u 114.22 C12H22H11 342.30 u 342.30

17. Calculating Molar Mass • Calculating the molar mass of sucrose, C12H22O11: (12 x 12.01 g) + (22 x 1.008 g) + (11 x 16.00 g) = 342.3 g/mole • Molar mass of ammonium phosphate, (NH4)3PO4: {(3 x 14.01) + (12 x 1.008) + (1 x 30.97) + (4 x 16.00)}g/mol = 149.10 g/mol

18. Percent Composition of a Compound • Composition of ammonium phosphate, (NH4)3PO4: • Molar mass of (NH4)3PO4 = 149.10 g/mol; Mass percent of N = (42.03 g/149.10 g) x 100% = 28.19% Mass percent of H = (12.10 g/149.10 g) x 100% = 8.12% Mass percent of P = (30.97 g/149.10 g) x 100% = 20.77% Mass percent of O = (64.00 g/149.14 g) x 100% = 42.92% Total percent (by mass) = 100%

19. Formula of Compounds • Empirical Formula A formula that shows a simple number of atoms or a simple whole number ratio of moles of atoms. Examples: MgO, Cu2S, CH2O, Al2C3O9. etc. • Molecular Formula A formula that shows the actual number of atoms of each type in a molecule. Examples: C4H10, C6H6, C6H12O6, N2H4, P4O10, etc.

20. Empirical Formula #1 • 1) Determination of empirical formula from mass of elements in a sample of compound. Example: When 2.00 g of phosphorus is completely combusted, it yields 4.58 g of an oxide of phosphorus. Calculate the empirical formula of the phosphorus oxide. • Solution: Calculate moles of P and O in sample and obtain a simple mole ratio; Mole of P = 2.00 g P x (1 mol/30.97 g) = 0.0646 mol P; Mole of O = (4.58 g – 2.00 g) x (1 mol/16.00 g) = 0.161 mol O; Dividing by mole of P (0.161 mol O/0.0646 mol P), yields a mole ratio = 2.5/1 or 5/2 Simple whole # mole ratio = 5 mol O : 2 mol P; • Empirical formula = P2O5

21. Empirical Formula #2 • 2) Determination of empirical formula from % composition: Example: A compound containing carbon, hydrogen, and oxygen has the following composition (by mass percent): 68.12% C, 13.73% H, and 18.15% O, Determine its empirical formula. • Solution: Use mass percent to calculate mole and mole ratio of C:H:O • Mole of C = 68.12 g x (1 mol C/12.01 g) = 5.672 mol C • Mole of H = 13.73 g x (1 mol H/1.008 g) = 13.62 mol H • Mole of O = 18.15 g x (1 mol O/16.00 g) = 1.134 mol O Divide throughout by the smallest mole (in this case, mole of O): 5.672 mol C/1.134 = 5; 13.62 mol H/1.134 = 12; 1.134 mol O/1.134 = 1; Empirical formula = C5H12O

22. Empirical Formula #3 • 3) Determination of empirical formula from data of combustion reaction: Example: A compound is composed of carbon, hydrogen, and oxygen. When 2.32 g of this compound is burned in excess of oxygen, it produces 5.28 g of CO2 gas and 2.16 g of water. Calculate the composition (in mass percent) of the compound and determine its empirical formula. • Solution: • Find mass of C, H, and O in the sample and then calculate their mass percent: Mass of C = 5.28 g CO2 x (12.01 g C/44.01 g CO2) = 1.44 g Mass % of C = (1.44 g C/2.32 g sample) x 100% = 62.1% Mass of H = 2.16 g H2O x (2 x 1.008 g/18.02 g H2O) = 0.242 g Mass % of H = (0.242 g H/2.32 g sample) x 100% = 10.4% Mass of O = 2.32 g sample – 1.44 g C – 0.24 g H = 0.64 g Mass % of O = 100 – 62.1% C – 10.4% H = 27.5% • Composition by mass % = 62.1% C; 10.4% H, and 27.5% O; • (next page)

23. Empirical Formula #3 • Deriving empirical formula from % composition: • Calculate mole and simple mole ratio from mass percent: Mole of C = 62.1 g C x (1 mol/12.01 g) = 5.17 mol Mole of H = 10.4 g H x (1 mol/1.008 g) = 10.3 mol Mole of O = 27.5 g O x (1 mol/16.00 g) = 1.72 mol • Dividing throughout by smallest mole of O yield a simple ratio: 5.17 mol C/1.72 = 3 mol C; 10.3 mol H/1.72 = 6 mol H; 1.72 mol O/1.72 = 1 mol O; • Simple mole ratio: 3 mol C : 6 mol H : 1 mol O • Empirical formula: C3H6O

24. Molecular Formula • Molecular formula is derived from empirical formula and molecular mass, which is obtained independently • Empirical formula = CxHyOz; molecular formula = (CxHyOz)n, where n = (molecular mass/empirical formula mass) • Example: A compound has an empirical formula C3H6O; its molecular mass is 116.2 u. What is the molecular formula? • Solution: Empirical formula mass = (2 x 12.01 u) + (6 x 1.008 u) + 16.00 u = 58.1 u Molecular formula = (C3H6O)n; where n = (116.2 u/58.1 u) = 2 Incorrect molecular formula = (C3H6O)2; • Correct molecular formula = C6H12O2

25. Exercise #3: Determination of Formulas A 2.50-gram sample of phosphorus is completely burned in air and yields 5.71 g of product that is composed of only phosphorus and oxygen. In a separate analysis, the compound was found to have molar mass of 284 g/mol. (a) What is the empirical formula of the compound? (b) What is its molecular formula? (c) Write an equation for the combustion of phosphorus. (Answer: (a) P2O5; (b) P4O10; (c) 4P + 5 O2P4O10)

26. Solution Concentrations • The concentration of a solution may be expressed in: • Molarity, mass percent, volume percent, mass-volume percent, ppm & ppb

27. Solution Concentrations • Mass-volume percentage: • Parts per million (ppm): • Parts per billion (ppb):

28. Molar Concentration • Example: 4.0 g of sodium hydroxide, NaOH, is dissolved in enough water to make a 100.-mL of solution. Calculate the molarity of NaOH. Mole of NaOH = 4.0 g NaOH x (1 mole/40.0 g) • = 0.10 mole Molarity of NaOH = 0.10 mol/0.100 L = 1.0 M

29. Calculation of Solute Mass in Solution • Example: How many grams of NaOH are present in 35.0 mL of 6.0 M NaOH solution? • Mole of NaOH = (6.0 mol/L) x 35.0 mL x (1 L/1000 mL) • = 0.21 mol • Mass of NaOH = 0.21 mol x (40.0 g/mol) • = 8.4 g NaOH

30. Preparing of Solutions from Pure Solids • From the volume (in liters) and molarity of solution, calculate the mole and mass of solute needed; • Weigh the mass of pure solute accurately; • Transfer solute into a volumetric flask of appropriate size; • Add deionized water to the volumetric flask, well below the narrow neck, and shake well to dissolve the solute. • When completely dissolved, add more distilled water to fill the flask to the mark and mix the solution well.

31. Preparing Solution from Solid • Example: Explain how you would prepare 1.00 L of 0.500 M NaCl solution. • Calculate mass of NaCl needed: Mole of NaCl = 1.00 L x (0.500 mol/L) = 0.500 mol Mass of NaCl = 0.500 mol x (58.44 g/mol) = 29.2 g • Preparing the solution: Weigh 29.2 g of NaCl accurately and transfer into 1-liter volumetric flask. Fill the flask half way with distilled water, shake well until all solid has dissolved. Fill the flask to the 1-liter mark with more distilled water and mix the solution well by inverting the flask back and forth several times.

32. Preparing Solution from Stock • Calculate volume of stock solution needed using the formula: MiVi = MfVf (i = initial; f = final) • Measure accurately the volume of stock solution and carefully transfer to a volumetric flask of appropriate size; • Dilute stock solution with distilled water to the required volume (or to the “mark” on volumetric flask) • Mix solution well. (Note: if diluting concentrated acid, place some distilled water in the flask, add the concentrated acid, and then add more distilled water to the required volume.)

33. Preparing Solution from Stock • Example: Explain how you would prepare 1.0 L of 3.0 M H2SO4 solution from concentrated H2SO4, which is 18 M. • Calculate volume of concentrated H2SO4 needed: Vol. of conc. H2SO4 = (1.0 L x 3.0 M/18 M) = 0.17 L = 170 mL • Preparing the solution: Place some distilled water in the 1-liter volumetric flask (that would fill the flask to about a quarter full). Measure accurately 170 mL of conc. H2SO4 and transfer carefully to the volumetric flask that already contains some distilled water. Then fill the flask to the 1-liter mark with more distilled water and mix the solution well by inverting the flask back and forth several times.

34. Percent by Mass • Example: • A sugar solution contains 25.0 g of sugar dissolved in 100.0 g of water. What is the mass percent of sugar in solution? • Percent sugar = {25.0 g/(25.0 g + 100.0 g)} x 100% • = 20.0% (by mass)

35. Calculation of Mass from Percent • Example: Seawater contains 3.5% (by mass) of NaCl. How many grams of sodium chloride can be obtained from 5.00 gallons of seawater? (1 gall. = 3.785 L; assume density of seawater = 1.00 g/mL) Mass of seawater = 5.00 gall x (3785 mL/gall.) x (1.00 g/mL) = 18925 g; Mass of NaCl = 18925 g sw x (3.5/100) = 662 g

36. Percent by Volume • Example: A solution is prepared by mixing 150. mL of methanol, 100. mL of acetone, and 250. mL of water. What is the volume percent of methanol and acetone in solution? Percent methanol = (150. mL/500. mL) x 100% • = 30.0% (by volume) Percent acetone = (100. mL/500. mL) x 100% = 20.0% (by volume)

37. Mass-Volume Percentage • Ratio of mass solute (in g) to volume of solution (in mL) x 100%; • Examples: (1) 0.9 g of NaCl in 100 mL of solution = (0.9 g/100 mL) x 100% = 0.9% (w/v) (2) 55 g glucose in 1 L (1000 mL) of solution = (54 g/1000 mL) x 100% = 5.4% (w/v)

38. ppm and ppb • ppm = parts per million = • ppb = parts per billion = • 85 mg of glucose in 1 L of solution = 85 ppm; • 15 mg of Pb in 1 L of solution = 15 ppb; (Assuming 1 L of solution = 1 kg, which is true for aqueous solution at very low concentration, and 1 kg = 106 mg and 1 kg = 109mg)

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40. Chemical Equation #1 • Description of reaction: Iron reacts with oxygen gas and forms solid iron(III) oxide: • Identity: reactants = iron (Fe) and oxygen gas (O2); product = iron(III) oxide • Chemical equation: Fe(s) + O2(g) Fe2O3(s) • Balanced equation: 4Fe(s) + 3 O2(g) 2Fe2O3(s)

41. Chemical Equation #2 • Description of reaction: Phosphorus reacts with oxygen gas to form solid tetraphosphorus decoxide. Equation: P(s) + O2(g) P4O10(s) Balanced eqn.: 4P(s) + 5 O2(g) P4O10(s)

42. Chemical Equation #3 • Description of reaction: Propane gas (C3H8) is burned in air (excess of oxygen) to form carbon dioxide gas and water vapor; • Identity: reactants = C3H8(g) and O2(g); products = CO2(g) and H2O(g); • Equation: C3H8(g) + O2(g)CO2(g) + H2O(g); • Balanced equation: C3H8(g) + 5 O2(g) 3CO2(g) + 4H2O(g)

43. Chemical Equation 4 • Description of reaction: Ammonia gas (NH3) reacts with oxygen gas to form nitrogen monoxide gas and water vapor; • Equation: NH3(g) + O2(g)NO(g) + H2O(g); • Balancing the equation: 2NH3(g) + 5/2 O2(g) 2NO(g) + 3H2O(g); • Multiply throughout by 2 to get rid of the fraction: • 4NH3(g) + 5 O2(g) 4NO(g) + 6H2O(g);

44. Balancing Chemical Equations Rules for balancing equations: • Use smallest integer coefficients in front of each reactants and products as necessary; coefficient “1” need not be indicated; • The formula of the substances in the equation MUST NOT be changed. Helpful steps in balancing equations: • Begin with the compound that contains the most atoms or types of atoms. • Balance elements that appear only once on each side of the arrow. • Next balance elements that appear more than once on either side. • Balance free elements last. • Finally, check that smallest whole number coefficients are used.

45. Stoichiometry • Stoichiometry = the quantitative relationships between one reactant to another, or between a reactant and products in a chemical reaction. • Interpreting balanced equations: Example: C3H8(g) + 5 O2(g) 3CO2(g) + 4H2O(g); • The equation implies that: 1 C3H8 molecule reacts with 5 O2 molecules to produce 3 CO2 molecules and 4 H2O molecules; OR 1 mole of C3H8 reacts with 5 moles of O2 to produce 3 moles of CO2 and 4 moles of H2O.

46. Stoichiometric Calculations Mole-to-mole relationship: • Example: In the following reaction, if 6.0 moles of octane, C8H18, is completely combusted in excess of oxygen gas, how many moles of CO2 and H2O, respectively, will be formed? How many moles of O2 does it consumed? Reaction: 2C8H18(l) + 25 O2(g)  16CO2(g) + 18H2O(g) Calculations: • Mole CO2 formed = 6.0 mol C8H18 x (16 mol CO2/2mol C8H18) = 48 moles • Mole H2O formed = 6.0 mol C8H18 x (18 mol H2O/2mol C8H18) = 54 moles • Mole O2 consumed = 6.0 mol C8H18 x (25 mol O2/2mol C8H18) = 75 moles

47. Stoichiometric Calculations Mass-to-mole-to-mole-to-mass relationship: • Example-1: In the following reaction, if 690 g of octane, C8H18, is completely combusted in excess of oxygen gas, how many grams of CO2 are formed? Reaction: 2C8H18(l) + 25 O2(g) 16CO2(g) + 18H2O(g) Calculation-1: • Moles C8H18 reacted = 690 g C8H18 x (1 mol/114.2 g) = 6.0 moles • Moles CO2 formed = 6.0 mol C8H18 x (16 mol CO2/2 mol C8H18) • = 48 moles CO2 • Mass of CO2 formed = 48 mol CO2 x (44.01 g/mol) = 2.1 x 103 g

48. Stoichiometric Calculations Mass-to-mole-to-mole-to-mass relationship: • Example-2: In the following reaction, if 690 g of octane, C8H18, is completely combusted in excess of oxygen gas, how many grams of H2O are formed? Reaction: 2C8H18(l) + 25 O2(g) 16CO2(g) + 18H2O(g) Calculation-2: • Moles C8H18 reacted = 690 g C8H18 x (1 mol/114.2 g) = 6.0 moles • Moles H2O formed = 6.0 mol C8H18 x (18 mol H2O/2 mol C8H18) • = 54 moles CO2 • Mass of H2O formed = 54 mol H2O x (18.02 g/mol) = 970 g

49. Stoichiometric Calculations Mass-to-mole-to-mole-to-mass relationship: • Example-3: In the following reaction, if 690 g of octane, C8H18, is completely combusted in excess of oxygen gas, how many grams of oxygen gas are consumed? Reaction: 2C8H18(l) + 25 O2(g) 16CO2(g) + 18H2O(g) Calculation-3: • Moles C8H18 reacted = 690 g C8H18 x (1 mol/114.2 g) = 6.0 moles • Moles O2 consumed = 6.0 mol C8H18 x (25 mol O2/2 mol C8H18) • = 75 moles O2 • Mass of H2O formed = 75 mol O2 x (32.00 g/mol) = 2.4 x 103 g

50. Stoichiometry Involving Limiting Reactant • Limiting reactant one that got completely consumed in a chemical reaction before the other reactants. Product yields depend on the amount of limiting reactant