Section 3 10C, 10D Main Ideas Molarity is moles of solute per liter of solution Molality is moles of solute per kilogram of solvent 10C calculate the concentration of solutions in units of molarity; 10D use molarity to calculate the dilutions of solutions Concentration of Solutions Key Terms concentration molarity molality The concentration of a solution is a measure of the amount of solute in a given amount of solvent or solution Some medications are solutions of drugs a one - teaspoon dose at the correct concentration might cure the patient, while the same dose in the wrong concentration might kill the patient In this section, we introduce two different ways of expressing the concentrations of solutions: molarity and molality Sometimes, solutions are referred to as dilute or concentrated, but these are not very definite terms Dilute just means that there is a relatively small amount of solute in a solvent Concentrated, on the other hand, means that there is a relatively large amount of solute in a solvent Note that these terms are unrelated to the degree to which a solution is saturated A saturated solution of a substance that is not very soluble might be very dilute G NLINE Chemistry Solution Dilution Main Idea 10c, 10d Molarity is moles of solute per liter of solution Molarity is the number of moles of solute in one liter of solution For example, a one-molar solution of sodium hydroxide, NaH, contains one mole of NaH in every liter of solution The symbol for molarity is M, and the concentration of a one-molar solution of sodium hydroxide is written as 1 M NaH ne mole of NaH has a mass of 400 g If this quantity of NaH is dissolved in enough water to make exactly 100 L of solution, the solution is a 100 M solution If 00 g of NaH, which is 0500 mol, is dissolved in enough water to make 100 L of solution, a 0500 M NaH solution is produced This relationship between molarity, moles, and volume may be expressed in the following ways Molarity (M) molarity = _ amount of solute (mol) volume of solution (L) = 0500 mol NaH = 0500 M NaH 100 L If we diluted 1 L of the 0500 M NaH solution to L, we could find the new concentration simply by using the ratio M 1 V 1 = M V Here, M 1 and V 1 are the molarity and volume of the original solution, and M and V are the molarity and volume of the new solution We solve for M as follows: (0500 M)(1 L) = 050 M ( L) 404 Chapter 1
Solutions are often diluted just before use, because those of greater molarity take up less lab space Chemists can have solutions of greater molarity and lower volume in stock and then dilute them to ones of higher volume and lower molarity for use Note that a 1 M solution is not made by adding 1 mol of solute to 1 L of solvent Instead, 1 mol of solute is first dissolved in less than 1 L of solvent The resulting solution is carefully diluted with more solvent to bring the total volume to 1 L, as shown in Figure 31 Figure 31 Preparing a 05000 M Solution The preparation of a 05000 M solution of CuS 4 5H starts with calculating the mass of solute needed 1 3 Start by calculating the mass of CuS 4 5H needed Making a liter of this solution requires 05000 mol of solute Convert the moles to mass by multiplying by the molar mass of CuS 4 5H This mass is calculated to be 149 g Add some solvent to the solute to dissolve it, and then pour it into a 10-L volumetric flask Rinse the weighing beaker with more solvent to remove all the solute, and pour the rinse into the flask Add water until the volume of the solution nears the neck of the flask 4 5 6 7 Put the stopper in the flask, and swirl the solution thoroughly Carefully fill the flask to the 10-L mark with water Restopper the flask, and invert it at least 10 times to ensure complete mixing The resulting solution has 05000 mol of solute dissolved in 1000 L of solution, which is a 05000 M concentration Solutions 405
10C Calculating with Molarity Sample Problem A You have 350 L of solution that contains 900 g of sodium chloride, NaCl What is the molarity of that solution? G NLINE Learn It! Video Solve It! Cards Analyze Given: solute mass = 900 g NaCl solution volume = 350 L molarity of NaCl solution Molarity is the number of moles of solute per liter of solution The solute is described in the problem by mass, not the amount in moles You need one conversion (grams to moles of solute) using the inverted molar mass of NaCl to arrive at your answer grams of solute number of moles of solute molarity g NaCl _ mol NaCl = mol NaCl g NaCl _ amount of solute (mol) = molarity of solution (M) V solution (L) Solve You will need the molar mass of NaCl NaCl = 5844 g/mol 900 g NaCl 1 mol NaCl = 154 mol NaCl 5844 g NaCl 154 mol NaCl = 0440 M NaCl 350 L of solution CHECK YUR WRK Because each factor involved is limited to three significant digits, the answer should have three significant digits which it does The units cancel correctly to give the desired moles of solute per liter of solution, which is molarity 10D Calculating with Molarity Sample Problem B You have 08 L of a 05 M HCl solution How many moles of HCl does this solution contain? Analyze Given: volume of solution = 08 L concentration of solution = 05 M HCl moles of HCl in a given volume G NLINE Learn It! Video The molarity indicates the moles of solute that are in one liter of solution Given the volume of the solution, the number of moles of solute can then be found concentration (mol of HCl/L of solution) volume (L of solution) = mol of HCl Continued 406 Chapter 1
Calculating with Molarity (continued) Solve 05 mol HCl 08 L of solution = 04 mol HCl 10 L of solution CHECK YUR WRK The answer is correctly given to one significant digit The units cancel correctly to give the desired unit, mol There should be less than 05 mol HCl, because less than 1 L of solution was used 10D Calculating with Molarity Sample Problem C A 34 g sample of potassium chromate is needed to carry out a reaction in aqueous solution of silver chromate All you have on hand is 5 L of a 60 M K solution What volume of the solution is needed to give you the 34 g K needed for the reaction? Analyze Given: volume of solution = 5 L concentration of solution = 60 M K mass of solute = 34 g K volume of K solution in L The molarity indicates the moles of solute that are in 1 L of solution Given the mass of solute needed, the amount in moles of solute can then be found Use the molarity and the amount, in moles, of K to determine the volume of K that will provide 34 g grams of solute moles solute moles solute and molarity liters of solution needed Solve To get the moles of solute, you ll need to calculate the molar mass of K 1 mol K = 194 g K 34 g K 1 mol K = 010 mol K 194 g K Cr 4 Use the molarity of the solution to convert Since you know 60 mol of K is in 1 L of solution, you will need: 010 mol K _ 1 L 60 mol = = 000 L of K solution CHECK YUR WRK The answer is correctly given to two significant digits The units cancel correctly to give the desired unit, liters of solution Answers in Appendix E 1 What is the molarity of a solution composed of 585 g of potassium iodide, KI, dissolved in enough water to make 015 L of solution? How many moles of H S 4 are present in 0500 L of a 0150 M H S 4 solution? 3 What volume of 300 M NaCl is needed for a reaction that requires 1463 g of NaCl? Solutions 407
Main Idea Molality is moles of solute per kilogram of solvent Molality is the concentration of a solution expressed in moles of solute per kilogram of solvent A solution that contains 1 mol of solute, sodium hydroxide, NaH, for example, dissolved in exactly 1 kg of solvent is a one-molal solution The symbol for molality is m, and the concentration of this solution is written as 1 m NaH ne mole of NaH has a molar mass of 400 g, so 400 g of NaH dissolved in 1 kg of water results in a one-molal NaH solution If 00 g of NaH, which is 0500 mol of NaH, is dissolved in exactly 1 kg of water, the concentration of the solution is 0500 m NaH molality (m) molality = moles solute mass of solvent (kg) 0500 mol NaH = 0500 m NaH 100 kg H If 800 g of sodium hydroxide, which is 00 mol, is dissolved in 1 kg of water, a 00 m solution of NaH is produced The molality of any solution can be found by dividing the number of moles of solute by the mass in kilograms of the solvent in which it is dissolved Note that if the amount of solvent is expressed in grams, the mass of solvent must be converted to kilograms by multiplying by the following conversion factor: _ 1 kg 1000 g Figure 3 shows how a 05000 m solution of CuS 4 5H is prepared, in contrast with the 05000 M solution in Figure 31 Figure 3 Preparation of a 05000 m Solution The preparation of a 05000 m solution of CuS 4 5H also starts with the calculation of the mass of solute needed 1 3 4 Calculate the mass of CuS 4 5H needed Making this solution will require 05000 mol of CuS 4 5H per kilogram of solvent (1000 g) This mass is calculated to be 149 g Add 1000 kg of solvent to the solute in the beaker Because the solvent is water, 1000 kg will equal 1000 ml Mix thoroughly The resulting solution has 05000 mol of solute dissolved in 1000 kg of solvent 408 Chapter 1
Concentrations are expressed as molalities when studying properties of solutions related to vapor pressure and freezing point and boiling point changes Mo lal ity is used because it does not change with changes in temperature Below is a comparison of the equations for molarity and molality Molarity (M) amount of A (mol) molarity = _ volume of solution (L) Molality (m) amount of A (mol) molality = mass of solvent (kg) G NLINE Calculating with Molality Sample Problem D A solution was prepared by dissolving 171 g of sucrose (table sugar, C 1 ) in 15 g of water Find the molal concentration of this solution Solve It! Cards Analyze Given: solute mass = 171 g C 1 solvent mass = 15 g H molal concentration of C 1 To find molality, you need moles of solute and kilograms of solvent The given grams of sucrose must be converted to moles The mass in grams of solvent must be converted to kilograms mol C 1 = _ g C 1 molar mass C 1 kg H = g H _ 1 kg 1000 g molality C 1 = mol C 1 kg H Solve Use the periodic table to compute the molar mass of C 1 C 1 = 3434 g/mol 171 g C 1 1 mol C 1 = 00500 mol C 3434 g C 1 1 11 15 g H _ 1000 g/kg = 015 kg H _ 00500 mol C 1 = 0400 m C 015 kg H 1 CHECK YUR WRK The answer is correctly given to three significant digits The unit mol solute/kg solvent is correct for molality Solutions 409
Calculating with Molality Sample Problem E A solution of iodine, I, in carbon tetrachloride, CCl 4, is used when iodine is needed for certain chemical tests How much iodine must be added to prepare a 0480 m solution of iodine in CCl 4 if 1000 g of CCl 4 is used? Analyze Given: molality of solution = 0480 m I mass of solvent = 1000 g CCl 4 mass of solute Your first step should be to convert the grams of solvent to kilograms The molality gives you the moles of solute, which can be converted to the grams of solute using the molar mass of I Solve Use the periodic table to compute the molar mass of I I = 538 g/mol 1000 g CCl 4 1 kg 1000 g CCl = 0100 kg CCl 4 4 01000 kg 0480 mol I = 00480 mol I 1 kg 00480 mol I _ 5380 g I = 1 g I mol I CHECK YUR WRK The answer has three significant digits and the units for mass of I 1 What is the molality of acetone in a solution composed of 55 g of acetone, (CH 3 ) C, dissolved in 00 g of water? What quantity, in grams, of methanol, CH 3 H, is required to prepare a 044 m solution in 400 g of water? Section 3 Formative ASSESSMENT Reviewing Main Ideas 1 What quantity represents the ratio of the number of moles of solute for a given volume of solution? We dissolve 500 grams of sugar, C 1, in water to make 1000 L of solution What is the concentration of this solution expressed as a molarity? 10C Critical Thinking 3 ANALYZING DATA You evaporate all of the water from 100 ml of NaCl solution and obtain 113 grams of NaCl What was the molarity of the NaCl solution? 4 RELATING IDEAS Suppose you know the molarity of a solution What additional information would you need to calculate the molality of the solution? 410 Chapter 1