Chapter 16. Applications of Aqueous Equilibria 16.1 Buffer Solutions 16.2 Capacity and Preparation of Buffer Solutions 16.3 Acid-Base Titrations 16.4 Solubility Equilibria 16.5 Complexation Equilibria Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

16.1 Buffer Solutions Learning objective: Calculate the pH of a buffered solution Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

16.1 Buffer Solutions Buffered solutions – solutions which are resistant to change in pH upon addition of strong acid or base. Usually prepared from a conjugate acid-base pair - either a weak acid and its conjugate base or a weak base and its conjugate acid. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example A solution contains mol of solid sodium acetate dissolved in 1.00 L of M acetic acid. Determine the concentration of hydronium ions, acetate ions, and acetic acid. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example Determine if a solution prepared by mixing 5.0 mL of concentrated HCl (12 M) with 75 mL of 1.0 M sodium acetate is a buffer solution. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Molecular View of a Buffer Solution A buffer can protect the pH of a solution by reacting with both strong acids and strong bases, preventing large changes in [OH - ] and [H 3 O + ]. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example 16-3 Molecular View of a Buffer Solution The molecular picture at below represents a small portion of a buffer system. Solvent water molecules are omitted for clarity. Redraw the original figure to show the equilibrium condition that is established when (a) three hydroxide ions enter the region, and (b) seven hydronium ions enter the region. Include any water molecules that are part of the buffer chemistry. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

The Buffer Equation Also called the Henderson-Hasselbalch Equation The pH of the buffer solution is dependent more on pK a of the buffer than concentrations of acids and bases. As rule, this equation is only useful if HA and A - differ by less than a factor of 10. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example Buffer solutions with pH values around 10 are prepared using sodium carbonate (Na 2 CO 3 ) and sodium hydrogen carbonate (NaHCO 3 ). What is the pH of a solution prepared by dissolving 10.0 g of each of these two salts in enough water to make L of solution? Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example By how much does the pH of the buffer solution in Example 16 – 4 change on the addition of 3.50 mL of 6.0 M HCl? Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Learning objective: Explain how to prepare a buffered solution of known pH and capacity Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd Capacity and Preparation of Buffer Solutions

Buffer Capacity – the amount of added [H 3 O + ] and [OH - ] that the buffer solution can tolerate without exceeding a specified pH range. Technical definition: the amount of acid (or base) that when added to a buffer changes the pH by 1 unit. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example 16 – 6 Buffer Capacity Biochemists and molecular biologists use phosphate buffers to match physiological conditions. A buffer solution that contains H 2 PO 4 - as the weak acid and HPO 4 2- as the weak base has a pH value very close to 7.0. A biochemist prepares L of a buffer solution that contains M HPO 4 2- and M H 2 PO 4 -. What is the pH of this buffer solution? Is the buffering action of this solution destroyed by addition of 0.40 g NaOH? Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Common Buffer Systems Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example 16 – 7 Buffer Preparation What mass of sodium acetate (NaCH 3 CO 2, M = g/mol) and what volume of concentrated acetic acid (17.45 M) should be used to prepare 1.5 L of a buffer solution at pH = 5.00 that is M overall? Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example 16 – 8 Preparing a Buffer A technician wants to prepare a buffer solution at pH = 9.00 with an overall concentration of M. The technician has solutions of 1.00 M HCl and NaOH and bottles of all common salts. What regents should be used, and in what quantities, to prepare 1.00 L of a suitable buffer? Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

16.3 Acid-Base Titrations Learning objective: Calculate an acid or base concentration from titration data Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

16.3 Acid – Base Titrations 1. Strong Acid with a Strong Base 2. Weak Acid with a Strong Base 3. Weak Base with a Strong Acid Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Acid – Base Titrations Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. The “titrant”

Example 16-9 Acid – Base Titration Industrial wastewater often is contaminated with strong acids. Environmental regulations require that such wastewater be neutralized before it is returned to the environment. A 150-mL sample of wastewater was titrated with M sodium hydroxide, and mL of the base was required to reach the stoichiometric point. What was the molarity of hydronium ions in this sample of wastewater? Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

At the Stoichiometric Point… Just enough hydroxide ions have been added to react with all of the acidic protons present in solution. This allows us to be quantitative. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Standardization The concentration of the titrant must be accurately known for quantitative results. The titrant is therefore titrated against a stable, pure, weighable standard, often potassium hydrogen phthalate, KHC 8 H 4 O 4 : Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example Standardization A biochemist needed to standardize a solution of KOH. A sample of potassium hydrogen phthalate weighing g was dissolved in mL of water and a drop of indicator was added. The solution was then titrated with the KOH solution. The titration required mL of base to reach the stoichiometric point. Find the molarity of the KOH solution. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Titration of a Strong Acid by OH - Ions Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Titration of a Weak Acid by OH - Ions Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Titration of a Weak Acid by OH - Ions Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. 1. At the beginning, HA and H 2 O are the major species, so we use K a to determine the pH of the solution. 2. During the titration we are creating a buffer, so we use the buffer equation to determine pH. At the midpoint of the titration (when HA = A - ), pH = pK a 3. When nearly all the HA is reacted, the only major species are A - and water, and we use K b to determine pH. 4. After all HA molecules have reacted, the solution contains excess A - and OH -. Here we determine pH using the excess OH -.

A flow chart summarizes the major species in solution and the pH calculations for the four key regions of a weak acid titration. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example 16 – 11 pH at the Stoichiometric Point What is the pH at the stoichiometric point of the titration of L of M acetic acid with 2.50 M KOH solution? Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Titration of a Weak Base by H 3 O + Ions Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Titration of a Weak Base by H 3 O + Ions Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. 1. At the beginning, B and H 2 O are the major species, so we can use K b to determine the pH of the solution. 2. During the titration we are creating a buffer, so we use the buffer equation to determine pH. At the midpoint of the titration (when B = BH + ), pH = pK a 3. When nearly all the B is reacted, the only major species are BH + and water, and we use K a to determine pH. 4. After all B molecules have reacted, the solution contains excess BH and H 3 O +. Here we determine pH using the excess H 3 O +.

Example 16 – 12 Titration of a Weak Base Ephedrine, a weak base, is the active ingredient in many commercial decongestants. To analyze a sample of ephedrine dissolved in L of water, a chemist carries out a titration with M HCl, monitoring the pH continuously. The data obtained in this titration are shown in Figure 16 – 6. Calculate K b for ephedrine and determine the pH of the solution at the stoichiometric point. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Titration of Polyprotic Acids Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. H2AH2A H 2 A, HA  HA  HA , A 2  A2A2 A 2 , OH 

Example 16 – 14 Drawing a Titration Curve Sulphurous Acid, H 2 SO 3, has two acidic hydrogen atoms, with pK a values of 1.85 (K a = 1.40 x ) and 7.20 (K a = 6.3 x ). Construct a titration curve for the titration of 125 mL of M sulphurous acid with M NaOH. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Indicators Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Common Indicators Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example 16 – 15 Selecting an Indicator A student wants to titrate a solution of ammonia whose approximate concentration is M. What indicator would be appropriate? Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

16.4 Solubility Equilibria Learning objective: Use the concepts of K sp and the common-ion effect to calculate solution concentrations Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

16.4 Solubility Equilibria Insoluble compounds: solubility is less than 0.01 mol of dissolved material per liter of solution, K sp << 1 Slightly soluble: < K sp < Soluble: K sp > Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example 16 – 16 Solubility Products Gypsum is a relatively soft rock made of calcium sulphate. Rainwater percolates through gypsum, dissolves some of the rock, and eventually becomes saturated with Ca 2+ ions and SO 4 2- ions. A geochemist takes a sample of groundwater from a cave and finds that it contains 8.4 x M SO 4 2- and 5.8 x M Ca 2+. Use the data to determine the solubility product constant of calcium sulphate. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example 16 – 17 Calculating K sp When solid PbI 2 is added to pure water at 25 o C, the salt dissolves until the concentration of Pb 2+ reaches 1.35 x M. After this concentration is reached, excess solid remains undissolved. What is the K sp for this salt? Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example 16 – 18 Solubility Calculations Cadmium is an extremely toxic metal that finds its way into the aqueous environment as a result of some human activities. A major cause of cadmium pollution is zinc mining and processing, because natural deposits of ZnS ores usually also contain CdS. During the processing of these ores, highly insoluble cadmium sulphide (K sp = 7.9 x ) may be converted into considerably less insoluble cadmium hydroxide (K sp = 7.2 x ). What mass of Cd(OH) 2 will dissolve in 1.00 x 10 2 L of an aqueous solution? Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Precipitation Equilibria Let’s examine the reaction quotient, Q  If Q = K sp, the system is at equilibrium, and the solution is saturated.  If Q < K sp, the system is not at equilibrium and the solution is not saturated.  If Q > K sp, the system is not at equilibrium and the solution is supersaturated. If a solution is not at equilibrium, the reaction will shift either left or right until it is at equilibrium. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example 16 – 19 Precipitation Reactions As illustrated in Example 16 – 18, wastewater resulting from metal processing often contains significant amounts of toxic heavy metal ions that must be removed before the water can be returned to the environment. One method uses sodium hydroxide solution to precipitate insoluble metal hydroxides. Suppose that 1.0 x 10 2 L of wastewater containing 1.2 x M Cd 2+ is treated with 1.0 L of 6.0 M NaOH solution. What is the residual concentration of Cd 2+ after treatment, and what mass of Cd(OH) 2 precipitates? Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

The Common Ion Effect Common ion effect – adding a “common ion” to a saturated solution e.g. Cd(OH) 2 (s) Ý Cd +2 (aq) + 2 OH - (aq) If we add Cd +2 or OH -, the common ion effect would cause the reaction to shift to the left according to le Chatelier’s principle. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Common-Ion Effect Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example 16 – 20 The Common Ion Effect The concentration of chloride ion in seawater is around 0.55 M. To compare the solubility of Pb 2+ in freshwater vs. seawater, calculate the solubility in g/L of PbCl 2 in pure water and in 0.55 M NaCl. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Solubility and pH Effects Let’s examine the solubility of calcium carbonate CaCO 3 (s) Ý Ca 2+ (aq) + CO 3 2- (aq) K sp = 3.8 x The carbonate also hydrolyzes: CO 3 2- (aq) + H 2 O (l) Ý HCO 3 - (aq) + OH - (aq) K b =2.1 x What if we added some strong acid to a solution of calcium carbonate? H 3 O + (aq) + OH - (aq) Ý 2 H 2 O (l) K = 1.0 x Now, if we add all the reactions together CaCO 3 (s) + H 3 O + (aq) Ý HCO 3 - (aq) + Ca 2+ (aq) + H 2 O (l) Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Solubility and pH Effects CaCO 3 (s) + H 3 O + (aq) Ý HCO 3 - (aq) + Ca 2+ (aq) + H 2 O (l) i.e. CaCO 3 is 10 orders of magnitude more soluble in acidic solution! Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example 16 – 21 The most acid rain on record has pH = 1.87, recorded at Inverpolley Forest, Scotland in Calculate the concentration of Ca 2+ cations in a solution formed when this rain becomes saturated with calcium carbonate. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

16.5 Complexation Equilibria Learning objective: Calculate the concentrations of species involved in complex-ion formation Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

16.5 Complexation Equilibria Stoichiometry of Complexes  A species that bonds to a metal cation to form a complex is known as a ligand.  The number of ligands (also called coordination number) provides a shorthand notation for the stoichiometry of the metal complex. Ag + (aq) + 2 NH 3 (aq) Ý [Ag(NH 3 ) 2 ] + (aq) Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. NH 3 is the ligand

Complexation Calculations Ag + (aq) + NH 3 (aq) Ý [Ag(NH 3 )] + (aq) [Ag(NH 3 )] + (aq) + NH 3 (aq) Ý [Ag(NH 3 ) 2 ] + (aq) Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example 16 – 22 Formation of a Gold Complex The small amounts of gold contained in low-grade ores can be extracted using a combination of oxidation and complexation. Gold is oxidized to Au +, which forms a very strong complex with cyanide anions. Au + (aq) + 2 CN - (aq) Ý [Au(CN) 2 ] - (aq) K f = 2 x Suppose that a sample of ore containing 2.5 x mol of gold is extracted with 1.0 L of 4.0 x M aqueous KCN solution. Calculate the concentrations of the three species involved in the complexation equilibrium. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

The Chelate Effect Ligands that have two or more donor atoms are chelating ligands. Ethylenediamine (H 2 NCH 2 CH 2 NH 2 ) is a common one and is abbreviated as “en” Each nitrogen has a lone pair of electrons which can be donor atoms, thus en is said to be bidentate Chelating ligands bond more tightly to the metal cations. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Ca(EDTA) 2- (with the H atoms removed)

The Chelate Effect The stabilization of a metal complex by a ligand with more than one donor atom is known as the chelate effect. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Complex Formation and Solubility Complexation can enhance solubility by removing metal cations from solution causing the equilibrium to shift to the right, and dissolve more solid. Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. AgCl (s) Ag(NH 3 ) 2+ (aq) NH 3 (aq)

Example 16 – 23 Capacity of Thiosulphate Fixer What mass of AgBr will dissolve in 1.5L of fixer solution that contains 0.50 M of thiosulphate ions? Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Chapter 16 Visual Summary

Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 16 Visual Summary

Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 16 Visual Summary

Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 16 Visual Summary

Chemistry, 2 nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 16 Visual Summary