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VII: Aqueous Solution Concentration, Stoichiometry LECTURE SLIDES Molarity Solution Stoichiometry Titration Calculations Dilution Problems Kotz & Treichel: Sections 5.8 -5.9

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Concentrations of Compounds in Aqueous Solutions (Chapter 5, Section 5.8, p. 213) Usually the reactions we run are done in aqueous solution, and therefore we need to add to our study of stoichiometry the concentration of compounds in aqueous solution. We will utilize a very useful quantity known as “molarity,” the number of moles of solute per liter of solution.

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Concentration (molarity) = # moles solute L solution If we placed 1.00 mol NaCl (58.4 g) in a 1 L volumetric flask, dissolved it in water, swirled to dissolve and diluted the solution to the 1.00 liter mark you would have a solution that contains 1.00 mol NaCl per liter of solution. This may be represented several ways: Concentration (molarity) = 1.00 mol NaCl / L soln = 1.00 M NaCl = [1.00] NaCl Chemists call this a “1.00 molar solution”

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Calculating Molar Amounts TYPICAL PROBLEMS: What is the molarity of a solution made by dissolving 25.0 g of BaCl 2 in sufficient water to make up a solution of 500.0 mL? How many g of BaCl 2 would be contained in 20.0 mL of this solution? How many mL of this solution would deliver 1.25 g of BaCl 2 ? How many mol of Cl - ions are contained in 10.00 ml of this solution?

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What is the molarity of a solution made by dissolving 25.0 g of BaCl 2 in sufficient water to make up a solution of 500.0 mL? 25.0 g BaCl 2 = ? mol/ L BaCl 2 (= ? M BaCl 2 ) 500.0 mL soln 1Ba = 1 X 137.33g = 137.33 2Cl = 2 X 35.45g = 70.90 208.23 g/mol Molar mass, BaCl 2 :

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Mass of solute Volume of soltn Molar mass, solute Conversion to L

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How many g of BaCl 2 would be contained in 20.0 mL of this solution? (.240 M BaCl 2 ) Question: 20.0 mL soln = ? g BaCl 2 Relationships: 1000 mL = 1 L 1 L soln =.240 mol BaCl 2 1 mol BaCl 2 = 208.23 g BaCl 2 20.0 mL soln = ? g BaCl 2 mL L mol g

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Molarity Molar Mass conversion

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How many mL of this solution would deliver 1.25 g of BaCl 2 ? 1.25 g BaCl 2 = ? mL soln.240 mol BaCl 2 = 1 L soln 208.23 g BaCl 2 = 1 mol BaCl 2 Molar Mass Molarity

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How many mol of Cl - ions are contained in 10.0 ml of this solution? 10.0 mL soln = ? Mol Cl -.240 mol BaCl 2 = 1000 mL soln 1 mol BaCl 2 = 2 mol Cl - Note: BaCl 2(aq) ---> Ba 2+ (aq) + 2 Cl - (aq)

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If 35.00 g CuSO 4 is dissolved in sufficient water to makeup 750. mL of an aqueous solution, a) what is the molarity of the solution? b) how many mL of the solution will deliver 10.0 g of CuSO 4 ? c) How many moles of sulfate ion (SO 4 2- ) will be delivered in 10.0 mL of the solution? 1 Cu = 1 X 63.55 = 63.55 1 S = 1 X 32.07 = 32.07 4 O = 4 X 16.00 = 64.00 159.62 g/mol GROUP WORK 7.1: Molarity Problems

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STOICHIOMETRY OF REACTIONS IN AQUEOUS SOLUTION: Chapter 5, Section 5.9 Let’s use our favorite reaction to add another dimension to calculating from balanced equations: How many ml of 3.00 M HCl solution would be required to react with 13.67 g of Fe 2 O 3 according to the following balanced equation: Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 36.46 g/mol 18.02 g/mol 162.20 g/mol 3.00 M 13.67 g ? mL

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Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 3.00 M 13.67 g ? mL Pathway: g Fe 2 O 3 ---> mol Fe 2 O 3 ---> mol HCl --- > mL soln 13.67 g Fe 2 O 3 = ? mL soln 1000 mL soln = 3.00 mol HCl 6 mol HCl = 1 mol Fe 2 O 3 159.70 g Fe 2 O 3 = 1 mol Fe 2 O 3 13.67 g Fe 2 O 3 = ? mL soltn

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Molar Mass Balanced Equation Molarity

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Group Work 7.2: Solution Stoichiometry How many g of Fe 2 O 3 would react with 25.0 mL of 3.00 M HCl? Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 3.00 M ? g 25.0 mL mL mol HCl mol Fe 2 O 3 g Fe 2 O 3 25.0 mL soltn = ? g Fe 2 O 3

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Limiting Reagent, Solutions Suppose you mixed 20.00 mL of.250 M Pb(NO 3 ) 2 solution with 30.00 mL of.150 KI solution. How many g of PbI 2 precipitate might you theoretically obtain? Pb(NO 3 ) 2 (aq) + 2 KI (aq) ---> PbI 2 (s) + 2 KNO 3 (aq).250 M.150 M 461.0 g/mol 20.00 mL 30.00 mL ? g 1Pb = 1 X 207.2 = 207.2 2 I = 2 X 126.9 = 253.8 461.0 g/mol

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Pb(NO 3 ) 2 (aq) + 2 KI (aq) ---> PbI 2 (s) + 2 KNO 3 (aq).250 M.150 M 461.0 g/mol 20.00 mL 30.00 mL ? g Pathway: mL mol “A” mol “C” g “C” mL mol “B” mol “C” g “C” “A”“B”“C” Low number wins!

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Pb(NO 3 ) 2 (aq) + 2 KI (aq) ---> PbI 2 (s) + 2 KNO 3 (aq).250 M.150 M 461.0 g/mol 20.00 mL 30.00 mL ? g 20.00 ml soltn A.250 mol A 1 mol C 461.0 g C = 2.3050 g C 1000 mL 1 mol A 1 mol C = 2.30 g C 30.00 mL soltn B.150 mol B 1 mol C 461.0 g C = 1.037 g C 1000 mL 2 mol B 1 mol C = 1.04 g C

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How many mL of solution A,.250 M Pb(NO 3 ) 2, would be required to react with 30.00 mL of solution B,.150 M KI? Pb(NO 3 ) 2 (aq) + 2 KI (aq) ---> PbI 2 (s) + 2 KNO 3 (aq).250 M.150 M ? mL 30.00 mL Excess reagent: Pathway: mL “B” soltn mol “B” mol “A” mL “A” soltn 30.00 mL B soltn = ? mL A soltn

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Pb(NO 3 ) 2 (aq) + 2 KI (aq) ---> PbI 2 (s) + 2 KNO 3 (aq).250 M.150 M ? mL 30.00 mL 30.00 mL soltn.150 mol B 1 mol A 1000 mL soltn 1000 mL soltn 2 mol B.250 mol A = 9.00 mL soltn A Molarity equation Molarity

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Group Work 7.3: Solution Stoichiometry #2 How many mL of.150 M KI solution would be required to react with 20.00 mL of.250 M Pb(NO 3 ) 2 ? Pb(NO 3 ) 2 (aq) + 2 KI (aq) ---> PbI 2 (s) + 2 KNO 3 (aq).250 M.150 M 20.00 mL ? mL

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Summary 1. Molarity, M: useful description of a solution; gives number of moles of solute in 1 L of solution. Useful to convert mL of solution to moles of solute in equation situations. 2. Molarity of solution can also yield moles per liter of the ions produced when the solute ionizes in water, using the formula of the solute as conversion factor 3. Adds another way to calculate mass or moles from volume (compare to density, #grams of substance or solution in 1 mL or 1 cm 3 of solution or substance).

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TITRATION CALCULATIONS Titration: Procedure in which measured increments of one reactant are added to a known amount of a second reactant until some indicator signals that the reaction is complete. This point in the reaction is called “the equivalence point.” Indicators include many acid/base dyes, potentiometers, color change in one reagent...

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Titrations are run with buret and Erlenmeyer flasks as seen on the CD ROM or demo just observed... Two types of problems are typically encountered: Standardizing an acid or a base solution (determining the exact molar concentration of an acid or base solution) Determining amount of acidic or basic material in a sample ( or other substances detectable by some indicator)

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Ex 5.13 type: Standardizing an acid solution: Suppose a pure, dry sample of Na 2 CO 3 weighing 0.379 g is dissolved in water and titrated to the equivalence point with 35.65 mL of HCl solution. What is the molarity of the HCl solution? Na 2 CO 3(aq) + 2HCl (aq) -----> 2 NaCl (aq) + H 2 O + CO 2(g) 105.99 g/mol 35.65 mL soln 0.379 g M= ? = #mol HCl / L soltn 2 Na = 2 X 22.99 = 45.98 1 C = 1 X 12.01 = 12.01 3 O = 3 X 16.00 = 48.00 105.99 g/mol

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Calculations for Standardization 1) Calculate moles of solute from balanced equation, using information about known reagent 2) Calculate M, using volume of solution required for titration of known to equivalence point

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Na 2 CO 3(aq) + 2HCl (aq) -----> 2 NaCl (aq) + H 2 O + CO 2(g) 105.99 g/mol 35.65 mL soln 0.379 g M=? = Mol HCl / L soltn Step One: Calculate Moles of HCl from equation.379 g Na 2 CO 3 = ? moles HCl

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M, HCl soln = ? = # mol HCl = L soln.00715 mol HCl 1000 mL =.201 mol HCl =.201 M HCl 35.65 mL soltn 1 L L soltn Na 2 CO 3(aq) + 2HCl (aq) -----> 2 NaCl (aq) + H 2 O + CO 2(g) 105.99 g/mol 35.65 mL soln 0.379 g.00715 mol M=? Step Two: Calculate molarity: Calculated in Step One

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Group Work 7.4: Suppose a pure, dry sample of Na 2 CO 3 weighing 0.437 g is dissolved in water and titrated to the equivalence point with 39.85 mL of HCl solution. What is the molarity of the HCl solution? Na 2 CO 3(aq) + 2HCl (aq) -----> 2 NaCl (aq) + H 2 O + CO 2(g) 105.99 g/mol 39.85 mL soln 0.437 g M= ? = #mol HCl / L soltn #1: Find moles of HCl from g Na 2 CO 3 #2: Find Molarity (moles HCl / volume soltn)

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Standardization of a Base: Let’s use the 0.201 M HCl which we standardized in the first problem to determine the exact molar concentration of a sodium hydroxide solution (“standardize the base”!): Problem: If titrating 25.00 mL of NaOH to a phenolphthalein endpoint required 31.25 mL of.201 M HCl, what is the molar concentration of the base?

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If titrating 25.00 mL of NaOH to a phenolphthalein endpoint required 31.25 mL of.201 M HCl, what is the molar concentration of the base? NaOH(aq) + HCl(aq) ---> H 2 O(l) + NaCl(aq) 25.00 mL 31.25 mL M=?.201 M Steps: 1) calculate moles NaOH reacted 2) calculate M, moles NaOH/ volume soln

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NaOH(aq) + HCl(aq) ---> H 2 O(l) + NaCl(aq) 25.00 mL 31.25 mL M=?.201 M Step 1) 31.25 mL HCl soln = ? mol NaOH Step 2) Calculate molarity:

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A 30.0 mL sample of vinegar requires 39.35 mL of.843 M NaOH solution for titration to the equivalence point. What is the molar concentration of the acetic acid in vinegar? CH 3 CO 2 H(aq) + NaOH(aq) ----> H 2 O + NaCH 3 CO 2 (aq) 30.0 mL 39.35mL.843 M M=?mol CH 3 CO 2 H /L Step 1) solve for moles, CH 3 CO 2 H Step 2) solve for M CH 3 CO 2 H Group Work 7.5

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Let’s do another base solution, standardizing it with Potassium acid phthalate, KHC 8 H 4 O 4, a popular solid for this purpose. (Structure, next slide!) It reacts with strong bases according to the following net ionic equation: KHC 8 H 4 O 4 (aq) + NaOH (aq) ------> H 2 O (l) + KNaC 8 H 4 O 4 (aq)

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KHC 8 H 4 O 4 (aq) + NaOH (aq) ---> H 2 O (l) + K NaC 8 H 4 O 4 (aq) 204.22 g/mol.896 g 16.95 mL M=? mol NaOH /L 1K = 1 X 39.10 = 39.10 8C = 8 X 12.01 = 96.08 5H = 5 X 1.008 = 5.04 4O = 4 X 16.00 = 64.00 204.22 g/mol If a.896 g sample of potassium acid phthalate is dissolved in water and titrated to the equivalence point with 16.95 mL of NaOH solution, what is the molarity of the NaOH soln? Group Work 7.6

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“Redox” titration You wish to determine the weight percent of copper in a copper containing alloy. After dissolving a sample of an alloy in acid, an excess of KI is added, and the Cu 2+ and I - ions undergo the reaction: 2Cu 2+ (aq) + 5 I - (aq) -----> 2 CuI(s) + I 3 - (aq) The I 3 - which is produced in this reaction is titrated with sodium thiosulfate according to the equation: I 3 - (aq) + 2 S 2 O 3 2- (aq) -----> S 4 O 6 2- (aq) + 3 I - (aq) If 26.32 mL of 0.101 M Na 2 S 2 O 3 is required for titration to the equivalence point, what is the wt % of Cu in.251 g alloy?

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2Cu 2+ (aq) + 5 I - (aq) -----> 2 CuI(s) + I 3 - (aq) 63.55 g/mol produced 0.251 g alloy by reaction g Cu =? % Cu, alloy=? I 3 - (aq) + 2 S 2 O 3 2- (aq) -----> S 4 O 6 2- (aq) + 3 I - (aq) ? mol 26.32 mL.101 M Na 2 S 2 O 3

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I 3 - (aq) + 2 S 2 O 3 2- (aq) -----> S 4 O 6 2- (aq) + 3 I - (aq) ? mol 26.32 mL.101 M Na 2 S 2 O 3

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2Cu 2+ (aq) + 5 I - (aq) -----> 2 CuI(s) + I 3 - (aq) 63.55 g/mol g=?.00133 mol % Cu, alloy=? 0.251 g alloy % Cu, alloy=? = 1.69 g Cu X 100 = 67.3% 0.251 g alloy

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DILUTION PROBLEMS Suppose you would like to make up a more “dilute” solution (less moles/L) from a more “concentrated” one (more moles /L). This is how you might proceed: a) figure out how many total moles of solute you want in the desired volume of the dilute solution b) figure out what volume of the more concentrated solution will deliver this number of moles c) measure out the concentrated solution and add water to make up the desired volume of the dilute solution. (DEMO!)

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Describe how you might makeup 750. mL of 1.00 M H 2 SO 4 from a concentrated sulfuric acid solution which is 12.0 M H 2 SO 4. a) Calculate desired number of moles in dilute soln: b) Calculate volume of concentrated solution which will contain this number of moles:

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c) Measure out 62.5 mL of the concentrated soln and carefully add it to sufficient water to make up 750. mL of solution. NEVER ADD WATER TO CONCENTRATED ACIDS; ALWAYS ADD CON ACIDS TO WATER, SLOWLY...

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Formula for Dilution Problems: Since we can calculate moles as follows: mL X # moles = moles of solute 1000 mL and since: moles, con soln = moles, dil soln We can say: mL, con X M, con = mL, dil X M, dil and do the last problem “the easy way”:

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Describe how you might makeup 750. mL of 1.00 M H 2 SO 4 from a concentrated sulfuric acid solution which is 12.0 M H 2 SO 4. mL, con X M, con = mL, dil X M, dil ? mL X 12.0 M H 2 SO 4 = 750. mL X 1.00 M H 2 SO 4 mL con = 750 mL dil X 1.00 M H 2 SO 4 12.0 M H 2 SO 4 mL con = 62.5 mL Punch line the same: measure out 62.5 mL con acid and dilute to 750. mL.

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Group Work 7.7: Dilution Problem How many mL of 2.35 M AgNO 3 solution are required to makeup 2.00 L of.100 M AgNO 3 solution? Describe how you would makeup this new solution. mL con X M con = mL dil X M dil ? 2.35 M 2.00L.100 M

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