Unit 6: The Mole Mr. Blake 23 6.02 X 10 Review: Atomic Masses Elements occur in nature as mixtures of isotopes. Carbon = 98.89% 12C (6 p+, 6 n) 1.11% 13C (6p+, 7n) <0.01% 14C (6p+, 8n) Carbon’s atomic mass = 12.01 amu Atomic Weights are relative C: # and mass H: # and mass Mass Ratio 1 C = 12.0 amu 1 H = 1.0 amu 12 to 1 2 C = 24.0 amu 2 H = 2.0 amu 12 to 1 3 C = 36.0 amu 3 H = 3.0 amu 12 to 1 4 C = 48.0 amu 4 H = 4.0 amu 12 to 1 5 C = 60.0 amu 5 H = 5.0 amu 12 to 1 10 C = 120.0 amu 10 H = 10.0 amu 12 to 1 What is the mole? Not this kind of mole! A. What is the Mole? • A counting number (like a dozen). • 1 mol = 602,000,000,000,000,000,000,000 of anything. A large amount!!!! Similar Words • Pair: 1 pair of shoelaces = 2 shoelaces. • Dozen: 1 dozen oranges = 12 oranges. • Gross: 1 gross of spider rings = 144 rings. • Ream: 1 ream of paper = 500 sheets of paper. • Mole: 1 mole of Na atoms = 6.02 X 1023 Na atoms. The Mole • So 1 mole of any element has 6.02 X 1023 particles. • This is a really big number – It’s so big because atoms are very small! • Defined as the number of atoms in 12.0 grams of C-12. This is the standard! • 12.0 g of C-12 has 6.022 X 1023 atoms. The Mole • This number is named in honor of Avogadro Amedeo ______________ (1776 – 1856), who studied quantities of gases and discovered that no matter what the gas was, there were the same number of molecules present • 6.02 x 1023 is also called _______________________. Avogadro’s number (NA) I didn’t discover it. Its just named after me! Amadeo Avogadro Just How Big is a Mole? • Enough soft drink cans to cover the surface of the earth to a depth of over 200 miles. • If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles. • If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole. Everybody Knows Avogadro’s Number! But Where Did it Come From? • It was NOT just picked! It was measured. • One of the better methods of measuring this number was the Millikan Oil Drop Experiment. • Since then we have found even better ways of measuring using xray technology. The Mole • 1 dozen cookies = 12 cookies • 1 mole of cookies = 6.02 X 1023 cookies • 1 dozen cars = 12 cars • 1 mole of cars = 6.02 X 1023 cars • 1 dozen Al atoms = 12 Al atoms • 1 mole of Al atoms = 6.02 X 1023 atoms - Note that the NUMBER is always the same, but the MASS is very different! • Mole is abbreviated mol A Mole of Particles Contains 6.02 x 1023 particles 1 mole C = 6.02 x 1023 C atoms 1 mole H2O = 6.02 x 1023 H2O molecules 1 mole NaCl = 6.02 x 1023 NaCl “molecules” (technically, ionics are compounds not molecules so they are called formula units) 6.02 x 1023 Na+ ions and 6.02 x 1023 Cl– ions Learning Check Suppose we invented a new collection unit called a widget. One widget contains 8 objects. 1. How many paper clips in 1 widget? a) 1 b) 4 c) 8 2. How many oranges in 2.0 widgets? a) 4 b) 8 c) 16 3. How many widgets contain 40 gummy bears? a) 5 b) 10 c) 20 Avogadro’s Number as Conversion Factor 6.02 x 1023 particles 1 mole or 1 mole 6.02 x 1023 particles - Note that a particle could be an atom OR a molecule! Learning Check 1. Number of atoms in 0.500 mole of Al a) 500 Al atoms b) 6.02 x 1023 Al atoms c) 3.01 x 1023 Al atoms 2.Number atoms a) 1.0 b) 3.0 c) 1.1 of moles of S in 1.8 x 1024 S mole S atoms mole S atoms x 1048 mole S atoms B. Molar Mass • Mass of 1 mole of an element or compound. • Equal to the numerical value of the average atomic mass (get from periodic table) • Atomic mass tells the... – atomic mass units per atom (amu) – grams per mole (g/mol) • Round to 2 decimal places (hundredths) Molar Masses of Elements (Found in Periodic Table) 1 mole of C atoms = 12.01 g 1 mole of Mg atoms = 24.31 g 1 mole of Cu atoms = 63.55 g Carried to the hundredths place!! B. Molar Mass Examples • carbon 12.01 g/mol • aluminum 26.98 g/mol • zinc 65.39 g/mol Calculating Molecular Mass Calculate the molecular mass of magnesium carbonate, MgCO3. 24.31 g + 12.01 g + 3(16.00 g) = 84.32 g/mol Molar Mass of Molecules and Compounds A substance’s molecular mass (molecular weight) is the mass in grams of one mole of the compound. 1 mole Ca x 40.08 g/mol = 40.08 g/mol +2 moles Cl x 35.45 g/mol = 70.90 g/mol Therefore,the mass of the entire compound is… 1 mole of CaCl2 = 110.98 g/mol B. Molar Mass Examples • water – H2O – 2(1.01) + 16.00 = 18.02 g/mol • sodium chloride – NaCl – 22.99 + 35.45 = 58.44 g/mol B. Molar Mass Examples • sodium bicarbonate – NaHCO3 – 22.99 + 1.01 + 12.01 + 3(16.00) = 84.01 g/mol • sucrose – C12H22O11 – 12(12.01) + 22(1.01) + 11(16.00) = 342.34 g/mol C. Molar Conversions molar mass MASS 6.02 1023 MOLES IN GRAMS NUMBER OF PARTICLES (g/mol) (particles/mol) Calculations with Molar Mass molar mass Grams Moles Converting moles to grams Ex. #1 How many grams of lithium are in 3.50 moles of lithium? 3.50 mol Li 6.94 g Li 1 mol Li = 24.3 g Li Converting Moles and Grams Ex. #2 Aluminum is often used for the structure of light-weight bicycle frames. How many grams of Al are in 3.00 moles of Al? Goal: 3.00 moles Al ? g Al 1. Molar mass of Al 1 mole Al = 26.98 g Al 2. Conversion factors for Al 26.98 g Al 1 mol Al 3. Setup 3.00 moles Al Answer or x 1 mol Al 26.98 g Al 26.98 g Al 1 mole Al = 81.0 g Al Molar Conversion Examples 3. How many moles of carbon are in 26 g of carbon? 26 g C 1 mol C 12.01 g C = 2.2 mol C 4) How many molecules are in 2.50 moles of C12H22O11? 6.02 1023 2.50 mol molecules = 1.51 1024 1 mol molecules C12H22O11 Calculations molar mass Grams Avogadro’s number Moles particles Everything must go through Moles!!! Ex. #1 Find the mass of 2.1 1024 molecules of NaHCO3. 2.1 1024 molecules 1 mol 84.01 g 6.02 1023 1 mol molecules = 290 g NaHCO3 Ex. #2 How many atoms of Cu are present in 35.4 g of Cu? 35.4 g Cu 1 mol Cu 63.5 g Cu 6.02 X 1023 atoms Cu 1 mol Cu = 3.4 X 1023 atoms Cu V. Percent Composition: The percent by ______ in a compound. mass of each _________ element Mass of element x 100 % compositio n Mass of compound What is the % composition of Ba(CN)2 ? 1(137.33 g Ba) + 2(12.01 g C) + 2(14.01 g N) = 189.37 g Ba(CN)2 % Ba 137.33 g Ba x 100 72.52 % Ba 189.37 g Ba(CN)2 24.02 g C %C x 100 12.68 % C 189.37 g Ba(CN)2 28.02 g N %N x 100 14.80 % N 189.37 g Ba(CN)2 What is the % composition of Iron III sulfate, ___________? Fe2(SO4)3 2(55.85 g Fe) + 3(32.07 g S) + 12 (16.00 g O) = 399.91 g Fe2(SO4)3 2(55.85 g Fe) % Fe x 100 399.91 g Fe2(SO4)3 27.93 % Fe 3(32.07 g S) %S x 100 399.91 g Fe2(SO4)3 24.06 % S 12(16.00 g O) %O x 100 399.91 g Fe2(SO4)3 48.01 % O Percent Composition (Hydrates): 1. Ba(CN)2 ∙ 2 H2O is what % water by mass? 1(Ba) + 2(C) + 2(N) + 2(H2O) = 225.41 g Ba(CN)2 • 2 H2O 2(18.02 g H2O) % H2O x 100 225.41 g Ba(CN)2 2 H2O 15.99 % H2O Formulas •Empirical formula: the lowest whole number ratio of atoms in a compound. •Molecular formula: the true number of atoms of each element in the formula of a compound. molecular formula = (empirical formula)n [n = integer] molecular formula = C6H6 = (CH)6 empirical formula = CH Formulas (continued) Formulas for ionic compounds are ALWAYS empirical (lowest whole number ratio). Examples: NaCl MgCl2 Al2(SO4)3 K2CO3 Formulas (continued) Formulas for molecular compounds might be empirical (lowest whole number ratio). Molecular: H2O C6H12O6 C12H22O11 Empirical: H2O CH2O C12H22O11 Empirical Formula Determination 1. Base calculation on 100 grams of compound. 2. Determine moles of each element in 100 grams of compound. 3. Divide each value of moles by the smallest of the values. 4. Multiply each number by an integer to obtain all whole numbers. Empirical Formula Determination Adipic acid contains 49.32% C, 43.84% O, and 6.85% H by mass. What is the empirical formula of adipic acid? (49.32g C) (1 mol C ) = 4.107 molC (12.01 gC ) (6.851gH)(1 molH ) = 6.78 molH (1.01 gH ) (43.84g O)( 1molO ) = 2.74 molO (16.00 gO ) Empirical Formula Determination (part 2) Divide each value of moles by the smallest of the values. 4.107 molC Carbon: = 1.50 2.74 molO 6.78 molH = 2.47 Hydrogen: 2.74 molO 2.74 molO = 1.00 Oxygen: 2.74 molO Empirical Formula Determination (part 3) Multiply each number by an integer to obtain all whole numbers. Carbon: 1.50 x 2 3 Hydrogen: 2.50 x 2 5 Empirical formula: C3H5O2 Oxygen: 1.00 x 2 2 Finding the Molecular Formula The empirical formula for adipic acid is C3H5O2. The molecular mass of adipic acid is 146 g/mol. What is the molecular formula of adipic acid? 1. Find the empirical mass of C3H5O2 3(12.01 g) + 5(1.01) + 2(16.00) = 73.08 g Finding the Molecular Formula The empirical formula for adipic acid is C3H5O2. The molecular mass of adipic acid is 146 g/mol. What is the molecular formula of adipic acid? 2. Divide the molecular mass by the mass given by the emipirical formula. 3(12.01 g) + 5(1.01) + 2(16.00) = 73.08 g 146 2 73 Finding the Molecular Formula The empirical formula for adipic acid is C3H5O2. The molecular mass of adipic acid is 146 g/mol. What is the molecular formula of adipic acid? 3. Multiply the empirical formula by this number to get the molecular formula. 3(12.01 g) + 5(1.01) + 2(16.00) = 73.08 g 146 =2 73 (C3H5O2) x 2 = C6H10O4 Hydrates ionic H2O trapped in A. An _______ compound that has _______ the crystal lattice structure. Hydrated salt 1. ________________: A compound with water (i.e. BaI2 •2 H2O). 2. __________________: A compound without water (i.e. Anhydrous salt BaI2). B. Determination of a hydrate: H 2O 1. Determine the mass of ________. 2. Determine the mass of the _________________. anhydrous salt 3. Find the __________ of water and anhydrous salt. moles 4. Find the mol ratio. X= mol H2O mol anhydrous salt * Whole number C. Example: 1. A barium iodide hydrate is heated in a crucible. Determine the formula of the hydrate given the following data: Before heating: 10.407 g BaI2 • X H2O (Hydrated Salt) _ 9.520 g BaI After heating: (Anhydrous Salt) ____________ 2 Step 1: Mass of water? 0.887 g H2O Step 2: Mass of Anhydrous salt? 9.520 g BaI 2 Step 3: Calculate the mol of the water & the anhydrous salt. 0.887 g H2O 1 mol H2O = 0.0492 mol H2O 18.02 g H2O 9.520 g BaI2 1 mol BaI2 = 0.0243 mol BaI2 391.13 g BaI2 Step 4: Calculate the number of waters. mol H 2O 0.0492 mol H 2O = x = 2 mol anhydrous salt = 0.0243 mol BaI2 Step 5: BaI2• 2 H2O 2. Data: Before heating: 5.20 g ZnSO3 • X H2O (Hydrated _ 2.60 g H2O salt) ____________ After heating: 2.60 g ZnSO3 Step 1: Mass of water? (Anhydrous salt) Step 2: Mass of Anhydrous salt? 2.60 g ZnSO3 Step 3: Calculate the mol of the water & the anhydrous salt. 2.60 g H2O 1 mol H2O = 0.144 mol H2O 18.02 g H2O 2.60 g ZnSO3 1 mol ZnSO3 145.43 g ZnSO3 = 0.0179 mol ZnSO3 Step 4: Calculate the number of waters. mol H2O 0.144 mol H2O x =8 mol anhydrous salt 0.0179 mol ZnSO 3 Step 5: ZnSO3 • 8 H2O IQ #2 Using your knowledge of mole calculations and unit conversions, determine how many atoms there are in 1 gallon of gasoline. Assume that the molecular formula for gasoline is C6H14 and that the density of gasoline is approximately 0.85 grams/mL. Using a conversion factor of 3785 mL per gallon, we can determine that the mass of gasoline in one gallon is 3785 mL x 0.8500 g/mL = 3217 grams. Because the molar mass of C6H14 is 86 g/mole, there are 3217 / 86 moles of gasoline molecules, or 37.4 moles of molecules present. Multiplying 37.4 x 20 (the number of atoms per mole of gasoline), there are 748 moles of atoms. Finally, multiplying 748 moles of atoms by 6.02 x 1023 atoms/mole, we can find that there are 4.50 x 1026 atoms present in the sample. CHEMICAL REACTIONS Reactants: Zn + I2 Product: Zn I2 Chemical Equations • Their Job: Depict the kind of reactants and products and their relative amounts in a reaction. 4 Al (s) + 3 O2 (g) ---> 2 Al2O3 (s) • The numbers in the front are called coefficients stoichiometric ____________. • The letters (s), (g), and (l) are the physical states of compounds. Introduction – Chemical reactions occur when bonds between the outermost parts of atoms are formed or broken. – Chemical reactions involve changes in matter, the making of new materials with new properties, and energy changes. – Symbols represent elements, formulas describe compounds, chemical equations describe a chemical reaction. Parts of a Reaction Equation – Chemical equations show the conversion of reactants (the molecules shown on the left of the arrow) into products (the molecules shown on the right of the arrow). • A “+” sign separates molecules on the same side • The arrow is read as “yields” • Example C + O2 CO2 • This reads “carbon plus oxygen react to yield carbon dioxide” • The charcoal used in a grill is basically carbon. The carbon reacts with oxygen to yield carbon dioxide. The chemical equation for this reaction, C + O2 CO2, contains the same information as the English sentence but has quantitative meaning as well. Chemical Equations Because of the principle of the conservation of matter, an equation must be balanced. It must have the same number of atoms of the same kind on both sides. Lavoisier, 1788 Symbols Used in Equations (s) • Solid ___ • Liquid (l) (g) • Gas ___ • Aqueous solution (aq) H2SO4 • Catalyst • Escaping gas () • Change of temperature () Balancing Equations – When balancing a chemical reaction you may add coefficients in front of the compounds to balance the reaction, but you may not change the subscripts. – Changing the subscripts changes the compound. – Subscripts are determined by the valence electrons (charges for ionic or sharing for covalent) Subscripts vs. Coefficients • The subscripts tell you how many atoms of a particular element are in a compound. The coefficient tells you about the quantity, or number, of molecules of the compound. Chemical Equations 4 Al(s) + 3 O2(g) ---> 2 Al2O3(s) This equation means: 4 Al atoms + 3 O2 molecules ---produces---> 2 molecules of Al2O3 AND/OR 4 moles of Al + 3 moles of O2 ---produces---> 2 moles of Al2O3 Steps to Balancing Equations There are four basic steps to balancing a chemical equation. 1.Write the correct formula for the reactants and the products. DO NOT TRY TO BALANCE IT YET! DO NOT CHANGE THE FORMULAS! 2.Find the number of atoms for each element on the left side. Compare those against the number of the atoms of the same element on the right side. 3.Determine where to place coefficients in front of formulas so that the left side has the same number of atoms as the right side for EACH element in order to balance the equation. 4.Check your answer to see if: – The numbers of atoms on both sides of the equation are now balanced. – The coefficients are in the lowest possible whole number ratios. (reduced) Some Suggestions to Help You • Take one element at a time, working left to right except for H and O. Save H for next to last, and O until last. • If everything balances except for O, and there is no way to balance O with a whole number, double all the coefficients and try again. (Because O is diatomic as an element) • (Shortcut) Polyatomic ions that appear on both sides of the equation should be balanced as independent units Balancing Equations 2 H2(g) + ___ O2(g) ---> ___ 2 H2O(l) ___ What Happened to the Other Oxygen Atom????? This equation is not balanced! Now, follow your rules for balancing equations and see if you can do it! IQ 2 Rewrite these word equations as balanced chemical equations 1) Hydrogen + sulfur hydrogen sulfide 2) Iron III chloride + calcium hydroxide iron III hydroxide + calcium chloride 3) Heating copper (II) sulfide in the presence of oxygen gas produces pure copper and sulfur dioxide gas. Balancing Equations ___ 2 Al(s) + ___ 3 Br2(l) ---> ___ Al2Br6(s) Balancing Equations Since we can’t have a fraction Take the number you need and for a coefficient, we must Need 11 Oxygen atoms but 5 11/2). ____C + (i.e. _____ O2(g) ----> put it over 3H 8(g) 2 multiply it come out byinmultiplying they only pairs! How all of 2.2O(g) _____CO (g) + _____ 4by H canthe we3coefficients fix 2this? 11 2 =11 ____B H (g) + _____ O2(g) ----> 1 ? 4 10 2 10 2 B2O3(g) + _____ 4 ___ H2O(g) 5 Learning Check! Sodium phosphate + iron (III) oxide sodium oxide + iron (III) phosphate Na3PO4 + _____ Fe2O3 ----> ____ Na2O + _____ FePO4 Algebraic Method Consider: Ca3(PO4)2 + H2SO4 CaSO4 + H3PO4 1. Assign letters to unknown coefficients: A Ca3(PO4)2 + B H2SO4 C CaSO4 + D H3PO4 2. Make a grid indicating the appearance of element (or ion) in each species of the equation. Use a whole number and the coefficient “letter” to indicate each appearance. Ca 3a + 0 = c + 0 PO4 2a + 0 = 0 + d H 0 + 2b = 0 + 3d SO4 0 + b = c + 0 3. Reduce each equation: Ca PO4 H SO4 3a = c 2a = d 2b = 3d b = c 4. Assume a = 1; solve for coefficients: A= 1 C= 3 D = 2 B = 3 5. Write equation with coefficients: Ca3(PO4)2 + 3 H2SO4 3 CaSO4 +2 H3PO4 Example: A B C Na2CO3 + C + Sb2S3 Na: 2a = 2e C: a + b = f O: 3a = 2f Sb: 2c = d S: 3c = e a = 1 e = 1 f = 3/2 c = 1/3 d = 2/3 b = 1/2 6Na2CO3 + 3 C + 2 Sb2S3 D E F Sb + Na2S + CO2 x 6 A = 6 E = 6 F = 9 C = 2 D =4 B = 3 4 Sb + 6 Na2S + 9 CO2 Topics for Unit #5 • • • • The Mole & Quantifying Substances (ch. 10) Avagadro’s Number (ch. 10) Chemical Equations & Balancing (ch. 11) Empircal vs. Molecular Formulas (ch. 11) Introductory Questions #1 1) How do you measure matter if there’s a lot of it there? Name the three ways suggested in the text (pg. 287) 2) What is the mass of 90 average-sized apples if 1 dozen of apples has a mass of 2.0 kg? 3) How many representative parts do you find in one mole? 4) Magnesium is a light metal used in the manufacture of aircraft, automobile wheels, tools, and garden furniture. How many moles of magnesium is 1.25 x1023 atoms of magnesium? (see practice problem 10.2 on pg 291) IQ#1-answers 1. Count the items, determine the mass, & Volume 2. We know: 1 dozen apples = 2.0 Kg # of apples = 90 12 apples = 1 dozen **Dimensional analysis: 90 apples x 1 doz. apples x 2.0 kg 12 apples 1 doz apples = 15 kg 3. 1 mol = 6.02 x 1023 parts IQ#1-answers cont’d 4. Count the items, determine the mass, & Volume **We know: # of atoms present = 1.25 x1023 Mg atoms 1 mol Mg = 6.02 x1023 atoms Mg Conversion: # atoms → # moles Use Dimensional analysis: 1.25 x1023 atoms Mg x 1 mol Mg = 0.208 mol Mg 23 6.02 x10 atoms Mg Answers to Homework Practice Problems #1-5 1) 5.0 kg 2) 672 seeds 3) 4.65 mol Si 4) 0.360 mol Br2 5) 2.75 x1024 atoms 6) 7.72 mol NO2 (pg. 289) (pg. 289) (pg. 291) (pg. 291) (pg. 292) (pg. 292) Introductory Questions #2 1. Using your periodic table determine the molecular mass of ammonium nitrate and Potassium permanganate. 2. Which compound has higher molar mass ammonium nitrate or Potassium permanganate? Show your work. 3. If I had 38.5 g of potassium permanganate and 58.6g of ammonium nitrate which do I have more of? Convert each into the number ofmoles present to compare. Homework • Do Quest. #7-13 from “The Mole Worksheet I” • Practice problems: pg. 296 #7 & 8 pg. 298 #16 & 17 pg. 299 #18 & 19 Read/Review Percent Composition Pgs 305-307 *Do Practice problems #34 & 35 on pg. 307 Introductory Questions #3 1. Which of the following substances has more molecules/compounds present? Be sure to show all calculations and work. 242.38g Heptanitrogen pentoxide 85.56g Aluminum arsenate 154.28g hydrogen perioxide 2. How much would 1000 atoms of magnesium weigh in grams? 3. Determine the % composition of barium perchlorate. Assignments to Check/Review • • • • • % Composition Worksheet answers Chemistry WS II: % Comp & Empirical Formulas Practice Problems from text: #36 & 37 (pg.310) Hydrate Formula----Worksheet Today’s Handout Lect/Disc: Chemical Reactions & equation writing **Homework: Hydrate Formula WS Chemical Equation Worksheet Signs of a Chemical Reaction • Evolution of heat and light • Formation of a gas • Formation of a precipitate • Color change B.Law of Conservation of Mass • Mass is neither created nor destroyed in a chemical reaction • Total mass stays the same • Atoms can only rearrange 4 H 36 g 2 O 4g 32 g 4 H 2 O C. Chemical Equations A+B C+D REACTANTS PRODUCTS Chemical Symbols Writing Equations 2H2(g) + O2(g) 2H2O(g) • Identify the substances involved. • Use symbols to show: – How many? - coefficient – Of what? - chemical formula – In what state? - physical state • Remember the diatomic elements. D. Writing Equations Two atoms of aluminum react with three units of aqueous copper(II) chloride to produce three atoms of copper and two units of aqueous aluminum chloride. • How many? • Of what? • In what state? 2 Al (s) +3 CuCl2 (aq) 3 Cu(s)+ 2AlCl3 (aq) E. Describing Equations • Describing Coefficients: – individual atom = “atom” – covalent substance = “molecule” – ionic substance = “unit” 3CO2 3 molecules of carbon dioxide 2Mg 2 atoms of magnesium 4MgO 4 units of magnesium oxide E. Describing Equations Zn(s) + 2HCl(aq) ZnCl2(aq) + H2(g) • How many? • Of what? • In what state? One atom of solid zinc reacts with two molecules of aqueous hydrochloric acid one unit to produce of aqueous zinc chloride and one molecule of hydrogen gas. Unit 5 HW Packet 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Book Notes (15 total) 10-1 practice problems #1-4* Page 315 #50-56, 58-59 Moles, Molecules, and Grams WS Percent Composition WS p. 315 # 63-68 Percent Comp., Emp. Formula WS Writing Complete Equations WS Balancing Chemical Equations WS Balancing Equations: Algebraic Technique WS Unit 5 Sample Test