ffimffim J $oluflons Knowledge of the properties and uses of solutions is important in the study of chemistry. Many substances used in laboratories are much easier to storc and use in solution form. Many chemical reactions happen only when the reactants are in solution. J"l Solutes cnd Solvenfs Solutions are homogeneous mixtures-that is, solutions are uniform throughout the mixture on a molecular scale. The substance in solution with which the chemist is most concerned is called the solute, the "stuff" which is dissolved. The solvent is the substance that causes the solute to be dissolved and is the carrier for the solute. Most common solutions use water as the solvent and are called aqueous solutions. Solute Solvent Examples gas gas alr gas liquid ammonia solution, carbonated beverages, 02 in water gas solid hydrogen in palladium (an element) liquid liquid antifreeze, wine, beer liquid SOIid dental amalgam (mercury in silver) solid liquid salt water, sugar solutions solid solid metal alloys (silver in gold) J.2 Concenfrqfion of Solutions Whether you are cooking in the kitchen, making a garden spray or analyzing samples in a medical laboratory. solutions of known concentrations are being used. Rather than determine the mass of specific quantities of reactants for chemical reactions, it is more convenient to dissolve the chemicals to make solutions of known concentration. The chernicals may then be dispensed by measu ring specific volumes of solution. The concentration of a solution describes the amount of solute relative to the volume of solution. A solution of high concentration is called concentrated, while a solution of low concentration is said to be dilute. A solution may be diluted by increasing the amount of solvent in the solution. In order to determine the arnount of solute in a measured volume of solution, the concentration of the solution and the solution volume must be known. Concentrations of solutions are commonly rneasured in terms of molar concentration. The molar concentration of a solution is defined as the number of moles nf solute dissolved in a liter of solution. This definition is commonly expressed as the formula: molar concentration of solute = amount of solute in moles Of L; = volume of solution in liters n VL= mol The units for molar concentration are mol/L. When the single word concentration is used in the text, it is assumed thal molar concentration is meant. 2,i,6 Ljt-lr J Solutions J.3 Exercises Concentrqtion of Solutions L. Detine the followi*g terrns: a. solute b. solvent c. solution cl. concentration 2. What units are used" to measlrre molar concentratian? J"4 Solufion Problem'Solving As with problems in Units F and G, solution problems can be solved by either of two methods: by equations (Method r) or by the conversion-factor technique (Method 2). The examples and problems that follow show many applications of, and the convenience of, working with solutions. The examples shown will be solved by boih calculation methods. Method 1 Equation Method: only two formulas with their variations are needed to solve most solution problems (see Flct;nE I1). Start with the given amount and use the equations appropriate to determine the unknown quantity. Method 2 Conversion Factor Method: many people find it easier and faster to use molar -mass and molar concentration in such a way that the ratios allow the units to cancel. This way the multiple calculations involved in doing solution problems can be set up as one problem and the units can be used to double-check the accuracy of the setup (see Frcunr I2). FIcunn|1 EquationProblem-Solving Flowchart Equations {s) MASS M(s/mol) NM and C ! volume *llM of solution V moles Note: lf the Equation Method is used, the formula should be verified each time by substituting the correct units into the formula and making sure that the correct units are obtained in the answer. C I V molar concentration Cv P= [= T= Solutions UNtr J 2l*7 Flcunr 12 c*nversion f-actor Prohlem-$olving Flowchart R"atios Molar Concentration # mol L : = ffiol 1L volume 1L mol of solution # mol moles Molar Mass rnol g #o lmol v-t4 *v v ldeal Gas Law PV = nRT molar concentration 1 mol '-. tTlol #g = P= VT Cqlculqring Concentrqtion frcm Moles ond Volume If 0.S00 mol of table salt, NaCl, is dissolved to give 500. mL of a laboratory solution, what is the molar concentration of the solution? In this case the definition for molar concentration is used: c = !v - o'9oomol 0.500 L = 1.80 mol L Cqlculoring Concenlrotion from Moss ond Volume An antacid solution may be prepared by dissolving 15.0 g of sodium bicarbonate (baking soda) in sufficient water to make 250. mL of solution. Determine the molar concentration of the antacid solution. Method t: nru"Hco3 m M C n V Methodz: C :: 1s.adNaHCO. x 1sP4 :0.1zemor 84.01g/mol 0,179 mol -r, 0.250 L 1 mol NaHCOu 84.0t9(t-taUCO* 1 X o"25oL = mol L a.714ry NaHCou Regardless of what method you choose, be sure to follow the step-wise sequence shown on the flowchart. Colculofing lVloss from Volume ond Concenfrsflon This type of calculation is most commonly used by chemists and technicians in preparing solutions of known concentration" What mass of washing soda, IrlarCO3 . L0 HrO, is necessary to make 400. mL of 0.b00 mol/L solution? 24.'j Unm J Solutions Methocl l: nna2co316Frzo = Cv = 0'500 Y - mNa2co3toFi2o = nM = x 2S6'19 -gryd = Meihod 2r rn61sr663r0!-rzo 0'200 rya( 57.2 = 0.4a0]- " O.40OE = 0'200 mol gof Na2CO3'10HzO *+P " '::# = 57"2gof Na2CO3'10H2O Colculoting Volume from Mqss ond Concentrqfion Soclium hydroride. conmonlv kno'uvn as caustic soda, has many uses in the laboratory and in industry. What volume of 0.600 mol/L NaOH can be prepared frorn 4.8 g of solute? Methodl: nNusH = fi = o'12 Por n ^#fu,=o.12mol o.2o L of solution c = o.oooffi1r/L = n, lvfethocl2: VNaoH = 4.8.4iNaoH * .S** VNaoH= 1L 40.00paNaOH 0.600po|-NaOH J.5 Exercises Solufion Problem-Solving 1. Copper(Il) sulfate, an important copper salt, is used in copper electroplating cells, and to kill algae in swimming pools and water tesen,oirs. What is the molar concentration of an electroplating solution in which 1.50 mol of copper(Il) sulfate are dissolved in enough water to make 2.00 L of solution? 2. Whenll.0gofglacial(pure)aceticacidisdissolvedinwatertomake2S0.mLof vinegar solution, what is the moiar concentration of the vinegar? 3. Sociium bicarbonate is used medicinallv to counteract excess stomach acidity. How many rnoles of solid sodium bicarbonirte would be needed to make 100. mL of a 0.660 mol/L solutiou suitabie for use as an antacid'l 4. A toilet howl cleaner may be prepared b)'mixing sodium bicarbonate (baking soda) and socliurn hydroxide (lye). What mass of sodium bicarbonate must be added to a 2.50 L borvl to obtain a necessary 0.150 mol/L solution? 5. Sodium phosphate may be used to rernove scale deposits from a car radiator. What volume of a 0.075 mol/L solution rvould contain the necessary 1.10 mol of sodium phosphate to remove the radiator scales? Sclutions UNm J 249 \ 7I t2 SOLUTIONS CONCENTRATION OF SOLUTIONS 11 ,12 Concentration of Solutions ol The concentrationola solution describes the amount o{ solute relative to the volume of solution. A solution be may A solution is called dilule. high concentration is called concentrated, while a solution of low concenlration dituted by increasing the amount of solvent in the solution. ln orderto determine the amount of solute in a measured volume of solution, the concenlration of the solution of and lhe solution volume must also be known. Concentrations ol solutions are commonly measured in terms dissolved ot solute moles number of ined as the is def molar concentration. The molar concentralion of a solution in a litre of solution. This definition is commonly expressed as a formula. amount of solute in moles volume of solution in litres molar concentration solute N tv or t V in ALCHEM, assume that The units lor molar concentration are mol/L. when the single word concentration is used molar concentration is meant. Solution Problems the many applications of and the convenience of The examples and problems which follow serve to illustrate need be used to answer most solution problems; va'riations) (with their formulas working with solutions. Only two i.e., n=n n sndc= m_ Y Type 1: Calculating Concentration lrom Moles and Volume lf 0.900 mol of table salt, NaCl, is dissolved to give 500 mL of a laboratory solution, what is the molar concentration of the solution? ,^ NaCl n \-, v 0.900 mol 0500 L = 1 .80 mol/ L G fhe molar concentration of the table salt solution is 1.80 mol/L Type 2: Calculating Concentration lrom Mass and Volume An antacid solution may be. prepared by dissolving 15.0 g of sodium bicarbonate (baking soda) in sufficient /yater lo make 250 mL of solution. Determine the molar concentration of the antacid solution n= Na HCO, n m m Na HCO, 15 og A.17 9 mol = a.250 L 0.1 79 mol = ffit The antacid solution v 0.716 mol/L 0.716 mol/L Type 3: Calculaling Moles from Volume and Concenlration potassium permanganate, KMnoo, due to its oxidizing properties is an effective disinfectant. How many moles cf KMnOo are in a 2.00 L of disintectant solution that is 0.0025 mol/L KMnO. ? (Note: One should be aware of the other properties of KMn(J4 Detore uslng it directly as a disinfectant') n=Cv KMnOo = = 0.0025 moll L x 2.00 L 0.0050 mol The number of moles of KMnOa required is 0.0050 Calculaior Nole: - ti Gi;g; iitcirtitor for a two step problem, round off the answer lor the lirst step to lhe correct number of si9nilicant digits. Fle-enter the first-step answer into the calculator to do the second step. When done this way the rounded off tinal answer should agreq with the answer that the teacher has' t3 SOLUTIONS SOLUTION PROBLEMS l2 , Type 1: Concentration from Moles and Volume 1. Copper(ll) sulfate, an important copper salt, is used in copper electroplating cells, and to kill algae in swimming pools and water reservoirs. What is the molar concentration of an electroplating solution in which 1.50 mol of copper(ll) sulfate are dissolved in water to make 2.00 L of solution? 2. What is the molar concentration of a solution in which 0.240 mol of washing soda, NarCOs'1OHeO, is dis- 3. lron(ll) sullate finds use in fixing colors in dyeing and in making ink. solved in water to make 480.mL of a solution for softening wash water. What is the molar concentration of an ink solulion that contains 0.210 mol of iron(ll) sulfate dissolved to form 840.mL ol solution? I Remedial Problems 4. Since a saturated solution of calcium chloride does not f reeze until -55 "C, calcium chloride can be used to melt ice on roads and walks. What is the molar concentration of a saturated solution in which 35.5 mol of CaCl, is dissolved in water to make 5.00 L of solution? 5. Sulfuric acid is an important laboratory reagent as well as a very important industrial chemical. One ol its many industrial uses is an electrolyte in lead storage (car) batleries. Calculate the molar concentration of a battery acid solution which contains 9.25 mol of form 1.80 L of solution. il Ha SO4 dissolved to t2 SOLUTIONS SOLUTION PROBLEMS l4 $, - Type 2: Concenlration lrom Mass and Volume 1 . A given sample of household ammonia contains 156 g of NHa(o) dissolved in water to form 2.00 L of solution. What is the molar concentration ot the household am:-nonia'Sillulion? 2. When 3. What is the molar concentration of 500.mL of a solution that contains 12.7 g of swimming pool chlorinator, 1 1 .0 g of glacial (pure) acetic acid is dissolved in water to make 250rmL of vinega r solution , what is the molar concentration of the vinegar? Ca(OCl)r? 6, Remedial Problems 4. Asolution forwaterproofing concrete may be prepared by dissolving 2006 of ammonium stearate in water to make 5.00 L of solution. Determine the molar concentration of the solution. 5. L A car battery terminal protective coating can be prepared by dissolving 240.0 g of sodium silicate (water glass) in water to make 250rmL ol solution. What is the molar concentration of the solution? t6 SOLUTIONS SOLUTION PROBLEMS t2 1 .: * G Type 3: Moles lrom Volume and Concentration counteract excess stomach aciditY sodium bicarbonate is used medicinally to mol/ L solution needed to make 100uml of a 0.660 Howmanymolesofsolidsodiumbicarbonatewouldbe suitabre lor use as an antacid? ' * , { 2 . \ A usef ul tile and household cleaner is sodium PhosPhate Find the number of moles of Na, POo for use at home. 3. (TSP) ' in2.00Lofa0'100mol/L Nag POo m A rust stain remover may be prepared by d issolving Potassiu prepared (aq) cleaning solution Pe rsulf persulfate are there in 500rffiL of a How many moles of potassium removing rust ila ins? O ate '242 ( K2 SO5 ) in wate r. mol/ L solution suitable for Remedial Problems reagent, finds considerable use in cleaning 4..Hydrochloricacidinadditiontobeinganimportantlaboratory before painting and inpttparingarticlesforgalvanizing'tinning rust off iron and steer, in etching concrete or electroPlating. in 75'0 mL of 0.100 mollL hydrochloric acid cleaning Find the number of mores of hydrogen chloride solutton. 5. from which many and industrial uses' lt also is the source common salt, NaCl, has numerous domestic derived', are Naclo and Narsoo N;Hco;, Narco., valuable sodium compounos such as r.raoH, HowmanymolesofNaClareneededtoprepare500,mLofSaturated5'30mol/Lsolulion? G SOLUTIONS SOLUTION PROBLEMS l2 l9 e Type 4: Calculaling Mass from Volume and Concentration What mass c{ washing soda, NarCOr.1OHrO, is necessary to make 400 mL of a 0.0500 solution? =Cv = 0.0500 mol /L x 0.400 L n Na, CO, .1 0H, O N", CO, .1 0H, mol/L =nM O The mass ol washing soda required is 5.72 g. Type 5: Calculating Volume from Moles and Concentration Vinegar is a dilute solution of acetic acid, 1.60 mol of acetic acid? cHrcooH. what volume of 0.800 mol/L v-ineg-ar solution conlalns _-!_ u cH3cooH = o'8oo 'too*"' mol/L 2.00 L = I The volume of vinegar necessary is 2.00 L. Type 6: Calculating Volume lrom Mass and Concentralion Sodium hydroxide, commonlv known as caustic soda, has many uses in the laboratory and in industry. What volume of 0.600 mol/L NaOH can be repared from 4.8 g ol solule? n=m NaoH M t, v NaoH t g 40.00 = A.12 mol g/ mol n C 0.600 moV The volume 4'8 = L of NaOH(uq; that can be prepared is 0.20 L. t10 SOLUTIONS SOLUTION PROBLEMS 12 ,13 $ Type 4z Mass f rorn Volume and Concentration (lye)' bicarbonate (baking soda) and sodium hydroxide A toilet bowl cleaner may be prepared by mixing sodium 1.' What mass of sodium bicarbonate must be added to 0.1 L; a 2.50 L bowl to obtain a necessary 50 mol/ L solution? molar along with the baking soda in ouestion 1 if the What mass of lye (NaOH) must be added to the bowl concentration of the lye must be 0.0/5 mol lL? Remedial Problems under in water and its concentrated solution is sold commercially 3 .r Sodium silicate, N a, Si03 , is verY soluble the half and phosphate sodium of mass equal with an the name of water glass' Sodium silicate may be used for dishes and laundry' mass of sodium metaPhosPhate to prepare a water softener 10.0 L of a 0.00500 mol/L water softening solution? What mass of sodium silicate is necessary to prepare 4. A hydrate ol sodium thiosulfate known as hypo(NarSrO.'SHzO) is used as $ a fixer in photography because it readily dissolves silver compounds' Show the calculations and list the steps' Describe how to prepare 100rmL of a 0.120 mol/L hyposolution. 6, SOLUTIONS SOLUTION PROBLEMS |.2,13 0 111 Type 5: Volume from Moles and Concentration 1. Sodium phosphate may be used to remove scale deposits from a car radialor. What volume of a 0.075 mol/L solution would conlain the necessary 1.10 mol of sodium phosphate to 'emove the radiator scales? 2. A perspiration stain remover may be prepared from sodium perborate trihydrate (NaBOr.HzOz.3HrO). Jalculale the volume of 0.600 mol/L perspiration stain remover that would be prepared lrom 0.300 mol ot sodium perborate trihydrate. Remedial Problems 3. Awatersolution of sodium hydroxide, known as caustic soda, is useful for dissolving grease and matter of plant and animal origin. Oalculate the volume of 0.100 mol/L caustic soda solution that contains 3.ti0 mol of sodium hydroxide I 4. silver nitrate is used extensively in making photographic plates and films. What volume of 0.320 mol/L silver nitrate solution would contain 0.24O mol of silver nitrate? 5. Sodium bicarbonate is used in baking as baktng soda, or as one of the componenls of baking powder. Describe how to prepare 0.821 mol/L saturated solution of sodium bicarbonate using bicarbonate. ft 1 .64 mol ol sol6 sodium 112 soLuTloNS 12,13 SOLUTION PROBLEMS Concentratlon Type 6: Volume lrom Mass and of sodium hYPochlorite; e'g' ' l.ChlorinebleachinitssolutionlormusuallyissoldasaSto6percentsolution as in Clorox and Purex' g of NaOCI solution would contain 119.2 How many ritres of 0.800 mol/L 2. ? hardened with Paint' very efficient cleaner for old brushes a makes phosphate A sorution o{ sodium POn ? f rom 126 g of Nas creaning solution can be Dre0ared brush mor/L 0.700 of what vorume $, with a protective coating of conprevented by painting the terminals - Remedial Problems 3.Corrosionofbatteryterminalscanbe centrated sodium silicate, Ndzsio3 . 240"9 ol sodium silicate solution can be prepared from What volume of 8'20 lnollL coating 4. ? cleaned of household utensils can be economically other,nonaluminum and pans lrying Pots, kettles, lye (NaOH)' materials Oy using a solution ol grease anO OaxeO-Jn'tooO Describehowtopreparea0.l00mol/Llyesolutionusingl0.0golsolidNaoH'showcalculationsandlisl the stePs. @ 12, 13 t SOLUTIONS AN OVERVIEW SOLUTION PROBLEMS t13 - 1. A dilute salution of sodium bicarbonate can be used as a soothing eyewash. disolved what is the molar concentration of an eyewash solution which has 3.57 mmol ol sodium bicarbonate in water to make 240'mL ol solution? 2. remover' Sodium bisullite and oxalic acid dissolved in water makes an effeclive radiator rust NaHSO., is dissolved in What is the molar concentration ol a solution in which 1206 ol sodium bisulfite, waler to form 8.00 L of a rust removing solution? 3. grease from engines An all-round cleaning agent, sodium phosphate, is excellent lor removing and mechanical Parts. cleaning solution Find thenumber ol moles of sodium phosphate in 8.00 L of a 0.0125 mol/L 4. I certain organic impurOne ol the many industrial uses of sulfuric acid employs sulfuric acid for removing ities lrom Petroleum. What volume of 2.50 mol/L H2SO! solution would contain 2.00 mol of sulfuric acid? 5. its soluSodium hydroxide (commonly known as caustic soda or lye) is used as a cleaning agent because plant origin' and animal tions readily dissolves grease and other matter of What mass ol sodium hydroxide is required to prepare 400.mL of a 0.2(X) mol/L cleaning solution? 6. A calcium chloride solution may be used as a grass killer' What volume of a 1.0 mol/L calcium chloride grass killing solution could be prepared lrom 1.00 kg of calcium chloride? 7 . Ammonium carbonate is a suitable replacement for the aqueous solution of ammonia as a household cleaning agent because it yields ammonia readily. Describe how lo prepare 1.00 L of a 0.450 mollL solution of ammonium carbonate. show calculations and list the five steps followed in preparing the solution. t l4 I SOLUTIONS DILUTION Most solutions bought lor laboratories are bought in concentrated form. Some solutions are concentrated form in the laboratory for later use. The bought or prepared solutions are then solutions of known concenlralion as required. d orF, r ) When a solution is diluted, only lhe amounl of solvent is increased. Therefore, the number of moles of solute: in lhe initial (concentrated) solution is equal to the number of moles of solute in lhe finat(diluted) solution. i - initial f =final ni = nS Civi = CFI Sincen = Cv The above equation may be used to solve several types of dilution problems. Example 1: Concentraled commercial hydrochloric acid is prepared by dissolving hydrogen chloride gas in water. The molar concentration of concenlrated hvdrochloric acid is 12.4 mol/L. what volume of concentrated {38olo) hydrochloric acid must a laboratory technician use in order to prepare 2.00 L of 0.250 mol/L HCt13q;? Civi = CFt 12.4 moUL x vi = 0.250 mol/L x 2.00 L v; =0.250 mol/L x 2.00 =L o'0403 L ir,.4 r"r/LThe volume of concentrated hydrochloric acid required is 40.3 mL. Example 2: concentrated (glacial) acetic acid is 99.5% pure and has a concentration ol 17.4 mol/1. What is the molar concentration of a 5olo vinegar solution prepare-d from concentrated acetic acid if 200 mL of concentrated acetic acid is diluted to fill a 4.00 L container of vin-egar? Civi = Cflf 17 0.870 rnoll L .4 mol/L x 0 .20O L = l7 .4 mol I L x 0.200 4.00 Cr x 4.00 L L Cg L Ihe molar concentration of the vinegar solution is 0.BZO mot/L. Molar Concentration of Some Concentrated Solutions irt ;:'.::i t'.i.::r' UCllaq) H3 PO4 (aq) HNO3 (aq) CH, COOH(rq) H2 SO4 (aq) N H. (aq) 3\o/o 8 5o/o 690/o 99.5 o/o 17 I 4 "/o tT .O mol/ L 28 1 o/o 12.4 moll L I 4 .t mot/ L 15.4 mol/L .4 mol/ L 4.8 mol/ L QA SOLUTIONS DILUTION PROBLEMS l4 ThefollowingtwopagesofdilutionproblemswereadaptedfromjnformationobtainedlromTheFormulaBook Robert C' Weast' tne CRC Handboii iici"*itstry and Phvsics edited by by Norman Stark and liom l.oneoftheusesofmethanol,cH3oH(alsoknownaSmethy]alcohol,woodalcoholandmethylhydrate)' of tn pure form methanol has a molar concentration in diluted form is a windshield *asn")-antlrreeze. 24'7 mollL 10'0 mol/L chemistry and Physics a srudent preoared 8'0 L ol was necesJslng a table rrom rhe cRc Handbook ol methanol ol volume What antltreeze goo7t tor-30"1;' aqueous methanol as windshielO wasnei a"ry to prepare the antifreeze solution? 2.Aconcenlrated(19.1mol/L)sodiumhydroxidesolution(alsoknownascausticsoda)whendilutedhaswide spread use as a cleaner and disinfectant' jar cleaner used by a commercial firm if 10.L of concenwhat is the molar concentration of a bottle and 400'L? trated caustic soda solution is diluted to s 3 Concentratedammonia(NH.13q;)solutionispreparedbydissolvingammoniagasinwater.Themolarcon. 14'8 mol/L centration ol concentrated ammonta is ol (cautionl is required by a consumer to prepare 5'0 L whar volume of concentrated aqueous ammonia 0.70 mol/L household ammonia? 4 Pure C, Hs OH , ethanol ', is 17.2 many cleaners. and in mollL. ln diluted lorm ethanol is present in all alcoholic beverages pure ethanol De diluted in order to prepa re To what volume must 10.0 mL of 1 0 .3 mol/ L ethanol type-cleaning solution? 01 14 c Remedial SOLUTIONS DILUTION PROBLEMS 121 Remedial Problems 1' Household ammonia solution (0.70 mol/L) may be diluted to prepare a goll club cleaning solution (0.14 mol/L) or a comb and halrbrush cleaning sotution (0.021 mol/L). What volume of household ammonia is required lo prepare 250,mL of solution? a comb and hairbrush cleaning 2. It 60.0 L of a 2.50 mol/L toxlc substance wer6 poured into a pond to glve a final volume at 5.00 x 103 L, what would be the flnal concentration? I 3' To what llnalvolume must tho 60.0 L ol 2.50 final concentration 1.00 x mol/L soluilon ln the prevlous probtem be diluted to make the concentratlon for most toxic substances)? 10* mol/L. (a fairlv sale 4. Commercial concentration sulfuric acid is 17.6 mol/L. lf 1.50 L of 2.00 mol I L Hz SOn (aq) is required in a laboratory, how many millilitres of concentrated sulfuric acid may be used? (when preparirig acid solutions concentrated acid must be added to the water not vice versa). e. f
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