KNOW, calculations based on….. CHAPTER 3 Mole Molar Mass Avogadro’s Number Calculations - mass, mole, particle - mass % - determining formulas Emperical/Molecular - Molarity (mols/L) - Dilution Stoichiometry Limiting Reagent KNOW, calculations based on….. Formulas Balance Eqn Subst Mass TERMS: formula/molar/molecular weight or mass - sum total of all atoms in chem formula - CaCl2; 1 Ca + 2 Cl = 1(40.1) + 2(35.5) = 111.1 g/mol states: (s) - (l) - (g) - (aq)

FORMULA--MOLECULAR WEIGHT The sum of the Atomic Weights of all atoms present in one formula unit or molecule Formula Wt: ionic cmpd Molecular Wt: covalent molecule

What is the formula weight of sodium carbonate, PROBLEM What is the formula weight of sodium carbonate, Na2CO3. This is an industrial chemical used in making glass. Also, equivalent to 1mole of a substance SOLUTION 2 * 23.0 = 46.0 2 Na 1 C 3 O 1 * 12.0 = 12.0 3 * 16.0 = 48.0 + 106.0 g 3

What is the % composition of chloroform, CHCl3, anesthetic? PROBLEM SOLUTION 1 C 1 H 3 Cl 1 * 12.0 = 12.0 1 * 1.0 = 1.0 3 * 35.5 = 106.5 1. Identify # each element 2. Calculate formula weight + 119.5 g 3. Calculate % Composition by each element

% Composition + 100.0 %

MOLES Mole: A collection of objects A collection of Avogadro’s number of objects Avogadro’s number 6.02 * 1023 Atoms Particles Ions Cations Anions Molecules Formula Units MOLES mass = 1 mole Multiply by Divide by MASS

Given mass, find moles How many moles are in 345.6 g NaNO3 ? Step 1: find formula wt. of NaNO3 1 Na = 23.0 g 1 N = 14.0 g 3 O = 3 * 16.0 = 48.0 g 1 mole of NaNO3 = 85.0 g Step 2 : Find # of moles Use factor-label method 4.07 moles NaNO3

How many grams are in 0.6 moles N2O ? Given moles, find mass How many grams are in 0.6 moles N2O ? Step 1: find molecular wt. of N2O 2 N = 2 * 14.0 = 28.0 g 1 O = 16.0 g 1 mole of N2O = 44.0 g Step 2 : Find mass Use factor-label method 26.4 g N2O 8

Given moles, find # molecules Divide by MOLES NUMBER of PARTICLES by Multiply Avogadro’s Number 6.02*1023 Given moles, find # molecules How many molecules are in 1.6 moles oxygen? Step 1: Recognize that mass does not apply here. But Avogadro’s # is used Step 2 : Find # molecules Use factor-label method 9.63 * 1023 molecules O2 9

Given # atoms, find moles How many moles are in 3.01 *1012 atoms of Chromium? Step 1: Recognize that mass does not apply here. But Avogadro’s # is used Step 2 : Find # moles Use factor-label method 5.00 * 10-12 mols Cr 10

There is not a direct relationship between MASS and PARTICLES MOLES 6.02*1023 mass = 1 mole Multiply by Divide by Avogadro’s Number Multiply by Divide by MASS NUMBER of PARTICLES There is not a direct relationship between MASS and PARTICLES 11

2 Step Conversion Problem Will need to use MASS at some point in the problem Given # formula units, find grams How many grams are in 1.208 * 1024 formula units AgCl ? Step 1: find formula wt. of AgCl 1 Ag = 107.9 g 1 Cl = 35.5 g 1 mole of AgCl = 143.4 g Step 2 : Find moles Step 3 : Find mass Use factor-label method 288 g AgCl Converts formula units to MOLES Converts moles to MASS 12

2 Step Conversion Problem Will need to use MASS at some point in the problem Given grams, find # atoms How many atoms are in 128.0 grams of Mercury ? Step 1: find molar mass of Hg 1 mole of Hg = 200.6 g Step 2 : Find moles Step 3 : Find atoms Use factor-label method 3.84*1023 atoms Hg Converts mass to MOLES Converts moles to ATOMS 13

EMPERICAL FORMULA Problem: Determine the formula for a cmpd that is 26.6% potassium, 35.4% chromium, and 38.1% oxygen. Solution: step1) assume, using 100 g sample, thus the percentages can be used as your masses for each diff. element 26.6% -- 26.6 g K 35.4% --- 35.4 g Cr 38.1% --- 38.1 g O step 2) convert your masses to moles of each diff. element Determine Formulas Convert mols of parts into whole # subscripts STEPS 1. Determinemolefraction for each element 2. Divide each subscript by the smallest value 3. If not all # are whole #, find smallest factor to multiple all subscripts by to obtain a whole # 14

step 3) Divide each value by the smallest “mole” number from step 2 step 4) calculate whole # subscripts Potassium Dichromate 15

MOLECULAR FORMULA Problem: An unknown substance containing 82.7% carbon and 17.4% hydrogen has a molar mass of 58.2 grams. Find the molecular formula. Solution: step1) assume, using 100 g sample, thus the percentages can be used as your masses for each diff. element 82.7% -- 82.7 g C 17.4% --- 17.4 g H step 2) convert your masses to moles of each diff. element 16

step 3) Divide each value by the smallest “mole” number from step 2 step 4) calculate whole # subscripts step 5) Find formula wt. of C2H5 and the ratio to the molar mass C2H5: C = 2 * 12.0 = 24.0 g H = 5 * 1.0 = 5.0 g 29.0 g step 6) Determine the molecular formula There are 2 empirical formula units 2(C2H5) = C4H10 C4H10 = 4(12.0) + 10(1.0) = 58.0 g 17

Sample Exercise 3.10 Converting Grams to Moles Calculate the number of moles of glucose (C6H12O6) in 5.380 g of C6H12O6. Solution Analyze We are given the number of grams of a substance and its chemical formula and asked to calculate the number of moles. Plan The molar mass of a substance provides the factor for converting grams to moles. The molar mass of C6H12O6 is 180.0 g/mol (Sample Exercise 3.9). Solve Using 1 mol C6H12O6=180.0 g C6H12O6 to write the appropriate conversion factor, we have Check Because 5.380 g is less than the molar mass, a reasonable answer is less than one mole. The units of our answer (mol) are appropriate. The original data had four significant figures, so our answer has four significant figures. How many moles of sodium bicarbonate (NaHCO3) are in 508 g of NaHCO3? Answer: 6.05 mol NaHCO3 Practice Exercise

Sample Exercise 3.11 Converting Moles to Grams Calculate the mass, in grams, of 0.433 mol of calcium nitrate. Solution Analyze We are given the number of moles and the name of a substance and asked to calculate the number of grams in the sample. Plan To convert moles to grams, we need the molar mass, which we can calculate using the chemical formula and atomic weights. Solve Because the calcium ion is Ca2+ and the nitrate ion is NO3–, calcium nitrate is Ca(NO3)2. Adding the atomic weights of the elements in the compound gives a formula weight of 164.1 amu. Using 1 mol Ca(NO3)2 = 164.1 g Ca(NO3)2 to write the appropriate conversion factor, we have Check The number of moles is less than 1, so the number of grams must be less than the molar mass, 164.1 g. Using rounded numbers to estimate, we have 0.5  150 = 75 g. The magnitude of our answer is reasonable. Both the units (g) and the number of significant figures (3) are correct. What is the mass, in grams, of (a) 6.33 mol of NaHCO3 and (b) 3.0  10–5 mol of sulfuric acid? Answer: (a) 532 g, (b) 2.9  10–3 g Practice Exercise

TERMS Solution A homogeneous mixture of 2 or more pure substances Solute The substance that is dissolved in solution Solvent The substance that does the dissolving

MOLARITY --CONCENTRATION mols liter M Label moles of solute liter of solution [H+] [OH-] Concentration of ACID Symbol Concentration of BASE Brackets indicate CONCENTRATION

DILUTION A single solution (homogeneous mixture) of a known concentration needs to be diluted to a lower concentration. This is accomplished by adding a known quantity of water (distilled) to the original solution volume. The terms used indicate: Mo; Vo Initial – Original -- Beginning M1; V1; Mi; Vi concentration & volume Md; Vd Final – Diluted -- Ending M2; V2; Mf; Vf concentration & volume Equation: M1 * V1 = M2 * V2

290.0 mL of a 0.560 M Fe(OH)3 solution is required to make a 0.250 M solution by dilution. What is the final volume. Step #1: Identify the parts for equation M1 = 0.560 M V1 = 290.0 M2 = 0.250 M V2 = X ml 650 ml Step #2: Set up and solve equation (0.560 M) (290.0 mL) = (X ml) (0.250 M) 0.250 M Notice: Dilution problems are not volume specific

1.25 L of H2O is added to 750 ml of 0.75 M HCl solution. What is the resulting molarity? Step #1: Identify parts for equation M1 = 0.75 M V1 = 750 ml M2 = X V2 = 2.0 L So, final vol. is amount Start + Added or 2000.0 ml or 0.75 L Step #2: Set up & solve equation 1.25 L is added to …. (0.75 M) (0.75 L) = (X) (2.0 L) 2.0 L OR 0.28 M

Given mass & volume, find molarity Determine the M of 752.0 g Barium Chloride in 575 ml of solution. Step 1: Need to change 575 ml to 0.575 L Step 2: Find formula wt. of CMPD. BaCl2 = 208.3 g/mol Step 3 : Find moles of CMPD. 752.0 g * 1 mol . 1 208.3 g 3.6 moles Step 4 : Find molarity of solution M = 3.6 moles 0.575 L 6.3 M

Given molarity & volume, find moles & mass How many moles of NaCl are in 36.7 ml of a 0.256 M solution? Step 1: Need to change 36.7 ml to 0.0367 L Step 2: Convert M label to mols/L 0.256 mols 1 L Using given concentration & volume, find moles Step 3 : Find moles of NaCl 0.0094 or 9.4*10-3 moles NaCl

Continuing, next we need to find the MASS of NaCl in0 .0094 moles Step 1: find formula wt. of NaCl 58.5 g /mol Step 2 : Find mass 0.55 g NaCl MOLES MASS Multiply by Divide

DILUTION MOLARITY PRACTICE PROBLEMS 1. What is the molarity of a solution containing 2.50 moles of KNO3 dissolved in 5.00 L? 2. How many moles of KCl are present in 100.0 mL of 0.125 M solution? DILUTION 1. What is the molarity of 50.0 mL of a 0.50 M NaOH solution after it has been diluted to 300.0 mL? 2. If 300.0 mL of water is added to 400.0 mL of a 0.400 M Na2CrO4 solution, what is the molarity of the resulting solution?