© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.1 Formation of Solutions Identify the kinds of intermolecular forces in each substance (Section 8.2). Substances with similar intermolecular forces tend to form solutions. Analysis Which of the following pairs of substances would you expect to form solutions? (a) Carbon tetrachloride (CCl 4 ) and hexane (C 6 H 14 ). (b) Octane (C 8 H 18 ) and methyl alcohol (CH 3 OH). Solution (a) Hexane contains only C — H and C — C bonds, which are nonpolar. Carbon tetrachloride contains polar C — Cl bonds, but they are distributed symmetrically in the tetrahedral molecule so that it too is nonpolar. The major intermolecular force for both compounds is London dispersion forces, so they will form a solution. (b) Octane contains only C — H and C — C bonds and so is nonpolar; the major intermolecular force is dispersion. Methyl alcohol contains polar C — O and O — H bonds; it is polar and forms hydrogen bonds. The intermolecular forces for the two substances are so dissimilar that they do not form a solution.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.2 Solubility of Gases: Effect of Temperature The solubility of O 2 (on the y-axis) can be determined by finding the appropriate temperature (on the x-axis) and extrapolating. The percent change is calculated as Analysis From the following graph of solubility versus temperature for O 2, estimate the concentration of dissolved oxygen in water at 25 °C and at 35 °C. By what percentage does the concentration of O 2 change?

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Continued From the graph we estimate that the solubility of O 2 at 25 °C is approximately 8.3 mg/L and at 35 °C is 7.0 mg/L. The percent change in solubility is Solution

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.3 Solubility of Gases: Henry’s Law According to Henry’s law, the solubility of the gas divided by its pressure is constant: Analysis At a partial pressure of oxygen in the atmosphere of 159 mmHg, the solubility of oxygen in blood is 0.44 g/100 mL. What is the solubility of oxygen in blood at 11,000 ft, where the partial pressure of O 2 is 56 mmHg? Of the four variables in this equation, we know P 1, C 1, and P 2, and we need to find C 2. Solution Ballpark Estimate The pressure drops by a factor of about 3 (from 159 mmHg to 56 mmHg). Since the ratio of solubility to pressure is constant, the solubility must also drop by a factor of 3 (from 0.44 g/100 mL to about 0.15 g/100 mL). STEP 1: Identify known information. We have values for P 1, C 1, and P 2. P 1 = 159 mmHg C 1 = 0.44 g/100 mL P 2 = 56 mmHg STEP 2: Identify answer and units. We are looking for the solubility of O 2 (C 2 ) at a partial pressure P 2. Solubility of O 2, C 2 = ?? g/100 mL

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Continued STEP 3: Identify conversion factors or equations. In this case, we restate Henry’s law to solve for C 2. Ballpark Check STEP 4: Solve. Substitute the known values into the equation and calculate C 2. The calculated answer matches our estimate.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.4 Mass Percent as Conversion Factor: Mass of Solution to Mass of Solute Analysis The percentage of gold in jewelry is typically reported in carats, with 24 carats representing 100% gold. A sample of 18-carat gold would contain 18 grams of gold in 24 grams of metal, which would equal a (m/m)% of 75%. Calculate the mass of gold in a 5.05 g ring that is 18-carat gold. Solution We are given a concentration and the total mass of the sample solution (the gold alloy in the ring), and we need to find the mass of gold by rearranging the equation for (m/m)% concentration. Ballpark Check The calculated answer is consistent with our estimate of 3.8 g gold. Ballpark Estimate A 75% (m/m) solution contains 75 g for every 100 g of solution, so 10 g contains 7.5 g. The mass of the ring is a little more than 5 g (or half of 10 g) so the amount of gold in the ring will be slightly more than half of 7.5 g, or ~ 3.8 g gold.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.5 Volume Percent as Conversion Factor: Volume of Solution to Volume of Solute Analysis How many milliliters of methyl alcohol are needed to prepare 75 mL of a 5.0% (v/v) solution? Ballpark Check The calculated answer is consistent with our estimate of between 3 and 4 mL. Solution We are given a solution volume (75 mL) and a concentration [5.0% (v/v), meaning 5.0 mL solute/100 mL solution]. The concentration acts as a conversion factor for finding the amount of methyl alcohol needed. Ballpark Estimate A 5% (v/v) solution contains 5 mL of solute in 100 mL of solution, so the amount of solute in 75 mL of solution must be about three-fourths of 5 mL, which means between 3 and 4 mL.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Solution Worked Example 9.6 Solution Concentration: Mass/Volume Percent Analysis A solution of heparin sodium, an anticoagulant for blood, contains 1.8 g of heparin sodium dissolved to make a final volume of 15 mL of solution. What is the mass/volume percent concentration of this solution? Mass/volume percent concentration is defined as the mass of the solute in grams divided by the volume of solution in milliliters and multiplied by 100%. Ballpark Estimate The mass of solute (1.8 g) is smaller than the volume of solvent (15 mL) by a little less than a factor of 10. The weight/volume percent should thus be a little greater than 10%. Ballpark Check The calculated (m/v)% is reasonably close to our original estimate of 10%.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.7 Mass/Volume Percent as Conversion Factor: Volume to Mass How many grams of NaCl are needed to prepare 250 mL of a 1.5% (m/v) saline solution? Solution Analysis We are given a concentration and a volume, and we need to find the mass of solute by rearranging the equation for (m/v)% concentration. Ballpark Estimate The desired (m/v)% value, 1.5%, is between 1 and 2%. For a volume of 250 mL, we would need 2.5 g of solute for a 1% (m/v) solution and 5.0 g of solute for a 2% solution. Thus, for our 1.5% solution, we need a mass midway between 2.5 and 5.0 g, or about 3.8 g.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Continued Ballpark Check Worked Example 9.7 Mass/Volume Percent as Conversion Factor: Volume to Mass The calculated answer matches our estimate.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Ballpark Estimate A concentration of 100 ppb means there are –9 g (1 10 –7 g) of solute in 1 g of solution. In 400 g of solution, we should have 400 times this amount, or –7 = 4 10 –5 g. Worked Example 9.8 ppm as Conversion Factor: Mass of Solution to Mass of Solute The maximum allowable concentration of chloroform, CHCl 3, in drinking water is 100 ppb. What is the maximum amount (in grams) of chloroform allowed in a glass containing 400 g (400 mL) of water? Solution Analysis We are given a solution amount (400 g) and a concentration (100 ppb). This concentration of 100 ppb means This equation can be rearranged to find the mass of solute.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.8 ppm as Conversion Factor: Mass of Solution to Mass of Solute Continued Ballpark Check The calculated answer matches our estimate.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.9 Solution Concentration: Molarity What is the molarity of a solution made by dissolving g of sulfuric acid (H 2 SO 4 ) in water and diluting to a final volume of 50.0 mL? The molar mass of H 2 SO 4 is 98.1 g/mol. Solution Analysis Molarity is defined as moles of solute per liter of solution: M = mol/L. Thus, we must first find the number of moles of sulfuric acid by doing a mass to mole conversion, and then divide the number of moles by the volume of the solution. Ballpark Estimate The molar mass of sulfuric acid is about 100 g/mol, so g is roughly mol. The volume of the solution is 50.0 mL, or 0.05 L, so we have about mol of acid in 0.05 L of solution, which is a concentration of about 0.5 M. STEP 1: Identify known information. We know the mass of sulfuric acid and the final volume of solution. STEP 2: Identify answer including units. We need to find the molarity (M) in units of moles per liter.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.9 Solution Concentration: Molarity Continued Ballpark Check STEP 3: Identify conversion factors and equations. We know both the amount of solute and the volume of solution, but first we must make two conversions: convert mass of H 2 SO 4 to moles of H 2 SO 4, using molar mass as a conversion factor, and convert volume from milliliters to liters. STEP 4: Solve. Substitute the moles of solute and volume of solution into the molarity expression. The calculated answer is close to our estimate, which was 0.5 M.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.10 Molarity as Conversion Factor: Molarity to Mass A blood concentration of M ethyl alcohol (EtOH) is sufficient to induce a coma. At this concentration, what is the total mass of alcohol (in grams) in an adult male whose total blood volume is 5.6 L? The molar mass of ethyl alcohol is 46.0 g/mol. (Refer to the flow diagram in Figure 9.7 to identify which conversions are needed.) Solution Analysis We are given a molarity (0.065 M) and a volume (5.6 L), which allows us to calculate the number of moles of alcohol in the blood. A mole to mass conversion then gives the mass of alcohol.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.11 Molarity as Conversion Factor: Molarity to Volume In our stomachs, gastric juice that is about 0.1 M in HCl aids in digestion. How many milliliters of gastric juice will react completely with an antacid tablet that contains 500 mg of magnesium hydroxide? The molar mass of Mg(OH) 2 is 58.3 g/mol, and the balanced equation is Solution Analysis We are given the molarity of HCl and need to find the volume. We first convert the mass of Mg(OH) 2 to moles and then use the coefficients in the balanced equation to find the moles of HCl that will react. Once we have the moles of HCl and the molarity in moles per liter, we can find the volume.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.12 Dilution of Solutions: Concentration What is the final concentration if 75 mL of a 3.5 M glucose solution is diluted to a volume of 450 mL? Solution Analysis The number of moles of solute is constant, so M c V c = M d V d Of the four variables in this equation, we know the initial concentration M c (3.5 M), the initial volume V c (75 mL), and the final volume V d (450 mL), and we need to find the final concentration M d. Ballpark Estimate The volume increases by a factor of 6, from 75 mL to 450 mL, so the concentration must decrease by a factor of 6, from 3.5 M to about 0.6 M. Solving the above equation for M d and substituting in the known values gives Ballpark Check The calculated answer is close to our estimate of 0.6 M.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.13 Dilution of Solutions: Volume Aqueous NaOH can be purchased at a concentration of 1.0 M. How would you use this concentrated solution to prepare 750 mL of 0.32 M NaOH? Solution Analysis The number of moles of solute is constant, so M c V c = M d V d Ballpark Estimate We want the solution concentration to decrease by a factor of about 3, from 1.0 M to 0.32 M, which means we need to dilute the 1.0 M solution by a factor of 3. This means the final volume must be about three times greater than the initial volume. Because our final volume is to be 750 mL, we must start with an initial volume of about 250 mL. Ballpark Check The calculated answer (240 mL) is reasonably close to our estimate of 250 mL. Of the four variables in this equation, we know the initial concentration M c (1.0 M), the final volume V d (750 mL), and the final concentration M d (0.32 M), and we need to find the initial volume V c. Solving the above equation for V 1 and substituting in the known values gives To prepare the desired solution, dilute 240 mL of 1.0 M NaOH with water to make a final volume of 750 mL.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Ballpark Estimate The molar mass of calcium is g/mol, and the calcium ion carries a charge of 2+. Thus, 1 g-Eq of Ca 2+ equals about 20 g/Eq or 20 mg/mEq. This means that the 5.0 mEq of Ca 2+ ions in 1.00 L of blood corresponds to a mass of 5.0 mEq Ca mg/mEq = 100 mg Ca 2+. Worked Example 9.14 Equivalents as Conversion Factors: Volume to Mass The normal concentration of Ca 2+ in blood is 5.0 mEq/L. How many milligrams of Ca 2+ are in 1.00 L of blood? Solution Analysis We are given a volume and a concentration in milliequivalents per liter, and we need to find an amount in milligrams. Thus, we need to calculate the gramequivalent for Ca 2+ and then use concentration as a conversion factor between volume and mass, as indicated in the following flow diagram: Ballpark Check The calculated answer (100 mg of Ca 2+ in 1.00 L of blood) matches our estimate.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Ballpark Estimate The boiling point will increase about 0.5 °C for every 1 mol of ions in 1 kg of water. Since 0.75 mol of KBr produce 1.5 mol of ions, the boiling point should increase by (1.5 mol ions) (0.5 °C/mol ions) = 0.75 °C. Worked Example 9.15 Properties of Solutions: Boiling Point Elevation What is the boiling point of a solution of 0.75 mol of KBr in 1.0 kg of water? Solution Analysis The boiling point increases 0.51 ° C for each mole of solute per kilogram of water. Since KBr is a strong electrolyte, there are 2 moles of ions (K + and Br – ) for every 1 mole of KBr that dissolves. Ballpark Check The 0.77 °C increase is consistent with our estimate of 0.75 °C. The normal boiling point of pure water is 100 °C, so the boiling point of the solution increases to °C.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.16 Properties of Solutions: Freezing Point Depression Solution Analysis The freezing point decreases by 1.86 °C for each mole of solute dissolved in 1 kg of water. We can use the decrease in freezing point (2.5 °C) to find the amount of solute per kg of water. Ballpark Estimate The freezing point will decrease by about 1.9 °C for every 1 mol of solute particles in 1 kg of water. To lower the freezing point by 2.5 °C (about 30% more) will require about 30% more solute, or 1.3 mol. Ballpark Check The calculated answer agrees with our estimate of 1.3 mol/kg. We can rearrange this expression to The cells of a tomato contain mostly an aqueous solution of sugar and other substances. If a typical tomato freezes at –2.5 °C, what is the concentration of dissolved particles in the tomato cells (in moles of particles per kg of water)?

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.17 Properties of Solutions: Osmolarity The solution of glucose commonly used intravenously has a concentration of 5.0% (m/v) glucose. What is the osmolarity of this solution? The molar mass of glucose is 180 g/mol. Solution Analysis Since glucose is a molecular substance that does not give ions in solution, the osmolarity of the solution is the same as the molarity. Recall from Section 9.7 that a solution of 5.0% (m/v) glucose has a concentration of 5.0 g glucose per 100 mL of solution, which is equivalent to 50 g per liter of solution. Thus, finding the molar concentration of glucose requires a mass to mole conversion. Ballpark Estimate One liter of solution contains 50 g of glucose (MW = 180 g/mol). Thus, 50 g of glucose is equal to a little more than 0.25 mol, so a solution concentration of 50 g/L is equal to about 0.25 osmol, or 0.25 M. STEP 1: Identify known information. We know the (m/v)% concentration of the glucose solution. STEP 2: Identify answer and units. We are looking for osmolarity, which in this case is equal to the molarity of the solution because glucose is a molecular substance and does not dissociate into ions. Osmolarity = Molarity = ?? mol/liter

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.17 Properties of Solutions: Osmolarity Continued Ballpark Check The calculated osmolarity is reasonably close to our estimate of 0.25 osmol. STEP 3: Identify conversion factors. The (m/v)% concentration is defined as grams of solute per 100 mL of solution, and molarity is defined as moles of solute per liter of solution. We will need to convert from milliliters to liters and then use molar mass to convert grams of glucose to moles of glucose. STEP 4: Solve. Starting with the (m/v)% glucose concentration, we first find the number of grams of glucose in 1 L of solution and then convert to moles of glucose per liter.

© 2013 Pearson Education, Inc. Fundamentals of General, Organic, and Biological Chemistry, 7e John McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson Worked Example 9.18 Properties of Solutions: Osmolarity What mass of NaCl is needed to make 1.50 L of a osmol solution? The molar mass of NaCl is g/mol. Solution Analysis Since NaCl is an ionic substance that produces 2 mol of ions (Na +, Cl – ) when it dissociates, the osmolarity of the solution is twice the molarity. From the volume and the osmolarity we can determine the moles of NaCl needed and then perform a mole to mass conversion. STEP 1: Identify known information. We know the volume and the osmolarity of the final NaCl solution. STEP 2: Identify answer and units. We are looking for the mass of NaCl. STEP 3: Identify conversion factors. Starting with osmolarity in the form (moles NaCl/L), we can use volume to determine the number of moles of solute. We can then use molar mass for the mole to mass conversion. STEP 4: Solve. Use the appropriate conversions, remembering that NaCl produces two ions per formula unit, to find the mass of NaCl.