Concentration of Solutions

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1 CHAPTER 4 Concentration of Solutions There are three principal ways to express solution concentration in chemistry percentage by mass, molarity, and molality. The following table compares these three ways of stating solution concentration. Examining the method of preparation of the three types may help you understand the differences among them. Symbol Meaning How to prepare Percentage % Grams solute 5%: Dissolve 5 g of per 00 g of solute in 95 g solution solvent. Molarity M Moles solute 5 M: Dissolve 5 mol per liter of of solute in solvent solution and add solvent to make L of solution. Molality m Moles solute 5 m: Dissolve 5 mol per kilogram of solute in kg of solvent of solvent. PERCENTAGE CONCENTRATION You will find percentages of solutes stated on the labels of many commercial products, such as household cleaners, liquid pesticide solutions, and shampoos. If your sink becomes clogged, you might buy a bottle of drain opener whose label states that it is a.4% sodium hydroxide solution. This means that the bottle contains.4 g of NaOH for every 00 g of solution. Computing percentage concentration is very much like computing percentage composition (see Chapter 6). Both involve finding the percentage of a single component of a multicomponent system. In each type of percentage calculation, the mass of the important component (in percentage concentration, the solute) is divided by the total mass of the system and multiplied by 00 to yield a percentage. In percentage concentration, the solute is the important component, and the total mass of the system is the mass of the solute plus the mass of the solvent. of 3

2 General Plan for Solving Percentage Concentration Problems solvent solute 3 solution Percentage concentration mass of solute mass of solution 00 4 Percentage concentration by mass SAMPLE PROBLEM What is the percentage by mass of a solution made by dissolving 0.49 g of potassium sulfate in.70 g of water? SOLUTION. ANALYZE What is given in the the mass of solvent, and the mass problem? of solute, K SO 4 What are you asked to find? the concentration of the solution expressed as a percentage by mass Items solvent Data.70 g H O solute 0.49 g K SO 4 Concentration (% by mass)? %. PLAN What step is needed to Divide the mass of solute by the calculate the concentration mass of the solution and multiply of the solution as a by 00. percentage by mass? of 3

3 water K SO 4 3 K SO 4 solution percentage solute mass concentration 00 solution mass 4 Percentage K SO 4 by mass given g K SO 4 00 percentage concentration g K SO 4 g H O given given 3. COMPUTE percentage concentration 0.49 g K SO g K SO 4.70 g H O % K SO 4 4. EVALUATE Are the units correct? Yes; the number of significant fig- ures is correct because the data had a minimum of two significant figures. Is the number of significant figures correct? Is the answer reasonable? Yes; percentage K SO 4 was required. Yes; the computation can be approximated as 0.5/ %. PRACTICE. What is the percentage concentration of 75.0 g of ethanol dissolved in g of water? ans: 3.0% ethanol. A chemist dissolves 3.50 g of potassium iodate and 6.3 g of potassium hydroxide in g of water. What is the percentage ans: 0.430% KIO 3 concentration of each solute in the solution? 0.765% KOH 3. A student wants to make a 5.00% solution of rubidium chloride using g of the substance. What mass of water will be needed to make the solution? ans: 7.6 g H O 4. What mass of lithium nitrate would have to be dissolved in 30.0 g of water in order to make an 8.0% solution? ans: 6.59 g LiNO 3 3 of 3

4 MOLARITY Molarity is the most common way to express concentration in chemistry. Molarity is the number of moles of solute per liter of solution and is given as a number followed by a capital M. A M solution of nitric acid contains mol of HNO 3 per liter of solution. As you know, substances react in mole ratios. Knowing the molar concentration of a solution allows you to measure a number of moles of a dissolved substance by measuring the volume of solution. General Plan for Solving Molarity Problems solute Convert using the molar mass of the solute. Amount of solute in mol moles solute M liter solution 4 Molar concentration, M 3 Volume of solution in L SAMPLE PROBLEM What is the molarity of a solution prepared by dissolving g of potassium hydroxide in some water and then diluting the solution to a volume of ml? SOLUTION. ANALYZE What is given in the problem? What are you asked to find? the mass of the solute, KOH, and the final volume of the solution the concentration of the solution expressed as molarity 4 of 3

5 Items Data solute g KOH Moles of solute? mol KOH Molar mass of solute* 56. g/mol Volume of solution ml Concentration (molarity)? M * determined from the periodic table. PLAN What steps are needed to calculate the concentration of the solution as molarity? KOH multiply by the inverted molar mass of KOH Determine the amount in moles of solute; calculate the moles per liter of solution. Volume of KOH solution in ml multiply by the conversion factor L 000 ml Amount of KOH in mol moles solute M liter solution 4 Molarity of KOH solution 3 Volume of KOH solution in L molar mass of KOH given mol KOH mol KOH g KOH 56. g KOH given L ml solution L solution 000 ml calculated above mol KOH M solution L solution calculated above 3. COMPUTE mol KOH g KOH 56. g KOH L ml solution 000 ml mol KOH L solution 5 of 3

6 4. EVALUATE Are the units correct? Yes; the number of significant fig- ures is correct because the data had a minimum of four significant figures. Is the number of significant figures correct? Is the answer reasonable? PRACTICE mol KOH L solution.35 M Yes; units canceled to give moles KOH per liter of solution. Yes; note that mol is approximately /3 mol and L is / L. Thus, the calculation can be estimated as (/3)/(/) 4/3, which is very close to the result.. Determine the molarity of a solution prepared by dissolving 4.6 g of citric acid, C 3 H 5 O(COOH) 3, in water and then diluting the resulting solution to ml.. What is the molarity of a salt solution made by dissolving 80.0 mg of NaCl in.00 ml of water? Assume the final volume is the same as the volume of the water. 3. What is the molarity of a solution that contains g of acetic acid, CH 3 COOH, dissolved in enough acetone to make ml of solution? ans: 0.06 M ans:.40 M ans: M SAMPLE PROBLEM 3 An analytical chemist wants to make ml of a 6.00 M solution of sodium hydroxide. What mass of NaOH will the chemist need to make this solution? SOLUTION. ANALYZE What is given in the problem? What are you asked to find? the identity of the solute, the total volume of solution, and the molarity of the solution the mass of solute to dissolve 6 of 3

7 Items solute Molar mass of solute Moles of solute Volume of solution Concentration (molarity) Data? g NaOH g/mol? mol NaOH ml 6.00 M. PLAN What steps are needed to calculate the mass of solute needed? 3. COMPUTE Molarity of NaOH solution Determine the amount in moles needed for the solution required, and convert to grams by multiplying by the molar mass of the solute. Volume of NaOH solution in L multiply by the conversion L factor 000 ml Volume of NaOH solution in ml given L ml solution L solution 000 ml Amount of NaOH in mol multiply by the molar mass of NaOH NaOH given mol NaOH L solution L ml solution L solution 000 ml 6.00 mol NaOH g NaOH L solution L solution mol NaOH 80. g NaOH 4. EVALUATE Are the units correct? calculated above Yes; the number of significant fig- ures is correct because the data had a minimum of three significant figures. Is the number of significant figures correct? molar mass of NaOH g NaOH g NaOH L solution mol NaOH Yes; units canceled to give grams of NaOH. 7 of 3

8 Is the answer reasonable? Yes; the calculation can be estimated as (3/4) (6)(40) (3/4) PRACTICE. What mass of glucose, C 6 H O 6, would be required to prepare L of a 0.5 M solution? ans: g. What mass of magnesium bromide would be required to prepare 70. ml of a M aqueous solution? ans:.4 g 3. What mass of ammonium chloride is dissolved in 300. ml of a M solution? ans: 4.0 g MOLALITY Molality is the amount in moles of solute per kilogram of solvent and is given by a number followed by an italic lowercase m. A 5 m aqueous solution of glucose contains 5 mol of C 6 H O 6 per kilogram of water. Molal concentration is important primarily in working with colligative properties of solutions, which you will do in Chapter 6. General Plan for Solving Molality Problems solute 3 solvent Convert using the molar mass of the solute. Convert using the equation kg 000 g. Amount of solute in mol m mol solute kg solvent 4 solvent in kg 5 Molal concentration, m 8 of 3

9 SAMPLE PROBLEM 4 Determine the molal concentration of a solution containing 8.3 g of ethylene glycol, HOCH CH OH, dissolved in 66 g of water. the mass of ethylene glycol dis- solved, and the mass of the solvent, water SOLUTION. ANALYZE What is given in the problem? What are you asked to find? Items solute Molar mass of solute Moles of solute solvent Concentration (molality). PLAN What steps are needed to calculate the molal concentration of the ethylene glycol solution? the molal concentration of the solution Data 8.3 g ethylene glycol 6.08 g/mol ethylene glycol? mol ethylene glycol 66 g H O? m Determine the amount of solute in moles and the mass of solvent in kilograms; calculate the moles of solute per kilogram of solvent. C multiply by the inverted molar mass of C Amount of C in mol moles C O m kg H O 5 Molality of C solution 3 H O multiply by the conversion factor kg 000 g 4 H O in kg molar mass of C given mol C mol C g C 6.08 g C 9 of 3

10 given kg g H O kg H O 000 g calculated above mol C m C solution kg H O calculated above 3. COMPUTE 8.3 g C mol C 6.08 g C.3 mol C 4. EVALUATE Are the units correct? Yes; units canceled to give moles C per kilogram of solvent. Yes; the number of significant fig- ures is correct because the data had a minimum of three significant figures. Yes; because.3 mol is approximately 4/3 mol and 0.66 kg is approximately /6 kg, the calculation can be estimated as (4/3)/(/6) 4/3 8, which is very close to the result. Is the number of significant figures correct? Is the answer reasonable? 66 g H O kg 000 g 0.66 kg H O.3 mol C 0.66 kg H O 7.89 m PRACTICE. Determine the molality of a solution of 560 g of acetone, CH 3 COCH 3, in 60 g of water.. What is the molality of a solution of.9 g of fructose, C 6 H O 6, in 3.0 g of water? 3. How many moles of -butanol, CH 3 CHOHCH CH 3, must be dissolved in 5 g of ethanol in order to produce a.0 m -butanol solution? What mass of -butanol is this? ans: 6 m ans:.3 m ans:.50 mol -butanol g -butanol 0 of 3

11 ADDITIONAL PROBLEMS. Complete the table below by determining the missing quantity in each example. All solutions are aqueous. Any quantity that is not applicable to a given solution is marked NA. Mass Quantity Quantity of solute of solution of solvent Solution made used made used a..0% KMnO 4? g KMnO g? g H O b M BaCl? g BaCl.750 L NA c. 6.0 m glycerol,? g glycerol NA g H O HOCH CHOHCH OH d.? M K Cr O 7.7 g 650. ml NA K Cr O 7 e.? m CaCl 88 g CaCl NA.04 kg H O f M NaCl? g NaCl 5.0 ml NA g..00 m glucose,? g glucose? g solution.50 kg H O C 6 H O 6. How many moles of H SO 4 are in.50 L of a 4.5 M aqueous solution? 3. Determine the molal concentration of 7.5 g of linoleic acid, C 8 H 3, in 55 g of hexane, C 6 H You have a solution that is 6.% sodium thiosulfate, Na S O 3,by mass. a. What mass of sodium thiosulfate is in 80.0 g of solution? b. How many moles of sodium thiosulfate are in 80.0 g of solution? c. If 80.0 g of the sodium thiosulfate solution is diluted to 50.0 ml with water, what is the molarity of the resulting solution? 5. What mass of anhydrous cobalt(ii) chloride would be needed in order to make ml of a 4.00 M cobalt(ii) chloride solution? 6. A student wants to make a 0.50 M aqueous solution of silver nitrate, AgNO 3 and has a bottle containing.7 g of silver nitrate. What should be the final volume of the solution? 7. What mass of urea, NH CONH, must be dissolved in 50 g of water in order to prepare a.50 m solution? 8. What mass of barium nitrate is dissolved in.9 ml of a 3.38 M solution? of 3

12 9. Describe what you would do to prepare 00.0 g of a 3.5% solution of ammonium sulfate in water. 0. What mass of anhydrous calcium chloride should be dissolved in g of water in order to produce a 0.8 m solution?. How many moles of ammonia are in 0.50 L of a 5.00 M aqueous ammonia solution? If this solution were diluted to.000 L, what would be the molarity of the resulting solution?. What is the molar mass of a solute if 6.0 g of the solute in 5 g of water produce a 5.3 m solution? 3. A saline solution is 0.9% NaCl. What masses of NaCl and water would be required to prepare 50. L of this saline solution? Assume that the density of water is.000 g/ml and that the NaCl does not add to the volume of the solution. 4. A student weighs an empty beaker on a balance and finds its mass to be g. The student weighs the beaker again after adding water and finds the new mass to be 5. g. A mass of 4.08 g of glucose is then dissolved in the water. What is the percentage concentration of glucose in the solution? 5. The density of ethyl acetate at 0 C is 0.90 g/ml. What volume of ethyl acetate at 0 C would be required to prepare a.0% solution of cellulose nitrate using 5 g of cellulose nitrate? 6. Aqueous cadmium chloride reacts with sodium sulfide to produce bright-yellow cadmium sulfide. Write the balanced equation for this reaction and answer the following questions. a. How many moles of CdCl are in ml of a 3.9 M solution? b. If the solution in (a) reacted with excess sodium sulfide, how many moles of CdS would be formed? c. What mass of CdS would be formed? 7. What mass of H SO 4 is contained in ml of a 5.85 M solution of sulfuric acid? 8. A truck carrying.5 kl of 6.83 M aqueous hydrochloric acid used to clean brick and masonry has overturned. The authorities plan to neutralize the acid with sodium carbonate. How many moles of HCl will have to be neutralized? 9. A chemist wants to produce.00 g of barium sulfate by reacting a M BaCl solution with excess H SO 4, as shown in the reaction below. What volume of the BaCl solution should be used? BaCl H SO 4 : BaSO 4 HCl of 3

13 0. Many substances are hydrates. Whenever you make a solution, it is important to know whether or not the solute you are using is a hydrate and, if it is a hydrate, how many molecules of water are present per formula unit of the substance. This water must be taken into account when weighing out the solute. Something else to remember when making aqueous solutions from hydrates is that once the hydrate is dissolved, the water of hydration is considered to be part of the solvent. A common hydrate used in the chemistry laboratory is copper sulfate pentahydrate, CuSO 4 5H O. Describe how you would make each of the following solutions using CuSO 4 5H O. Specify masses and volumes as needed. a. 00. g of a 6.00% solution of CuSO 4 b..00 L of a M solution of CuSO 4 c. a 3.5 m solution of CuSO 4 in.0 kg of water. What mass of calcium chloride hexahydrate is required in order to make ml of a.50 M solution?. What mass of the amino acid arginine, C 6 H 4 N 4, would be required to make.50 L of a M solution? 3. How much water would you have to add to.40 kg of nickel(ii) sulfate hexahydrate in order to prepare a 5.00% solution? 4. What mass of potassium aluminum sulfate dodecahydrate, KAl(SO 4 ) H O, would be needed to prepare g of a 5.00% KAl(SO 4 ) solution? What mass of water would be added to make this solution? 3 of 3

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