Chemistry, The Central Science, 11th edition Theodore L. Brown, H. Eugene LeMay, Jr., and Bruce E. Bursten Chapter 16 Acids and Bases Review of 16.1-16.5 Acids and Bases © 2009, Prentice-Hall, Inc. Some Definitions • Brønsted-Lowry – An acid is a proton donor. – A base is a proton acceptor. Acids and Bases © 2009, Prentice-Hall, Inc. A Brønsted-Lowry acid… …must have a removable (acidic) proton. A Brønsted-Lowry base… …must have a pair of nonbonding electrons. Acids and Bases © 2009, Prentice-Hall, Inc. If it can be either… …it is amphiprotic. HCO3 HSO4 H2O Acids and Bases © 2009, Prentice-Hall, Inc. What Happens When an Acid Dissolves in Water? • Water acts as a Brønsted-Lowry base and abstracts a proton (H+) from the acid. • As a result, the conjugate base of the acid and a hydronium ion are formed. Acids and Bases © 2009, Prentice-Hall, Inc. Conjugate Acids and Bases • The term conjugate comes from the Latin word “conjugare,” meaning “to join together.” • Reactions between acids and bases always yield their conjugate bases and acids. Acids and Bases © 2009, Prentice-Hall, Inc. Practice - Brønsted-Lowry acids and bases Identify the conjugate acid-base pairs: HClO + H2O D ClO- + H3O+ HS- + H2O D H2S + OH- HPO42- + H2O D H2PO4- + OHHPO42- + H2O D PO43- + H3O+ An amphoteric compound is able to act as either an acid or a base. Which compounds in the above equations are amphoteric? Acids and Bases © 2009, Prentice-Hall, Inc. Identify the conjugate acid-base pairs: HClO + H2O D ClO- + H3O+ HS- + H2O D H2S + OH- HPO42- + H2O D H2PO4- + OHHPO42- + H2O D PO43- + H3O+ An amphoteric compound is able to act as either an acid or a base. Which compounds in the above equations are amphoteric? Acids and Bases © 2009, Prentice-Hall, Inc. Practice - Brønsted-Lowry acids and bases Each of the following can act as both a Brønsted acid and a Brønsted base EXCEPT HCO3- H2O SO42HS- HSO3Acids and Bases © 2009, Prentice-Hall, Inc. Practice - Brønsted-Lowry acids and bases Each of the following can act as both a Brønsted acid and a Brønsted base EXCEPT HCO3- H2O SO42HS- HSO3Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.1 (p. 675) a) What is the conjugate base of each of the following acids: HClO4 ClO4H2S HSPH4+ PH3 HCO3- CO32- b) What is the conjugate acid of each of the following bases? CNHCN SO42HSO4H2O H3O+ HCO3- H2CO3 Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.1) Consider the following equilibrium reaction: HSO4-(aq) + OH-(aq) D SO42-(aq) + H2O(l) a) Which substances are acting as acids in the reaction? b) HSO4- and OHc) HSO4- and H2O d) OH- and SO42e) SO42- and H2O Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.1) Consider the following equilibrium reaction: HSO4-(aq) + OH-(aq) D SO42-(aq) + H2O(l) a) Which substances are acting as acids in the reaction? b) HSO4- and OHc) HSO4- and H2O d) OH- and SO42e) SO42- and H2O Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.1) Write the formula for the conjugate acid of each of the following: HSO3FPO43CO Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.1) Write the formula for the conjugate acid of each of the following: HSO3FPO43CO H2SO3 HF HPO42HCO+ Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.2 (p. 676) The hydrogen sulfite ion (HSO3-) is amphoteric. a) Write an equation for the reaction of HSO3- with water, in which the ion acts as an acid. b) Write an equation for the reaction of HSO3- with water, in which the ion acts as a base. In both cases identify the conjugate acid-base pairs. Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.2 (p. 676) a) Write an equation for the reaction of HSO3- with water, in which the ion acts as an acid. HSO3- + H2O D SO32- + H3O+ HSO3- (acid) and SO32- (conjugate base) H2O (base) and H3O+ (conjugate acid) b) Write an equation for the reaction of HSO3- with water, in which the ion acts as a base. HSO3- + H2O D H2SO3 + OHHSO3- (base) and H2SO3 (conjugate acid) Acids and H2O (acid) and OH- (conjugate base) Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.2) The dihydrogen phosphate ion, H2PO4-, is amphiprotic. In which of the following reactions is this ion serving as a base? H3O+(aq) + H2PO4- D H3PO4(aq) + H2O(l) H3O+(aq) + HPO42- D H2PO4- + H2O(l) H3PO4(aq) + HPO42- D 2 H2PO4- + H2O(l) a) (i) only b) (i) and (ii) c) (i) and (iii) d) (ii) and (iii) e) (i), (ii) and (iii) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.2) The dihydrogen phosphate ion, H2PO4-, is amphiprotic. In which of the following reactions is this ion serving as a base? H3O+(aq) + H2PO4- D H3PO4(aq) + H2O(l) H3O+(aq) + HPO42- D H2PO4- + H2O(l) H3PO4(aq) + HPO42- D 2 H2PO4- + H2O(l) a) (i) only b) (i) and (ii) c) (i) and (iii) d) (ii) and (iii) e) (i), (ii) and (iii) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.2) When lithium oxide (Li2O) is dissolved in water, the solution turns basic from the reaction of the oxide ion (O2-) with water. Write the reaction that occurs, and identify the conjugate acid-base pairs. O2- + H2O D OH- + OH- O2- (conjugate base) and OH- (conjugate acid) H2O (conjugate acid) and OH- (conjugate base) Acids and Bases © 2009, Prentice-Hall, Inc. Acid and Base Strength • Strong acids are completely dissociated in water. – Their conjugate bases cannot pull protons away “abstract protons”, are very weak. • Weak acids only dissociate partially in water. – Their conjugate bases have a slight ability to pull protons away, they are Acids and weak bases. Bases © 2009, Prentice-Hall, Inc. Acid and Base Strength • Substances with negligible acidity do not dissociate in water. – Their conjugate bases are exceedingly strong – abstract protons from acids/water readily. Acids and Bases © 2009, Prentice-Hall, Inc. Acid and Base Strength • In any acid-base reaction, the equilibrium will favor the reaction that moves the proton to the stronger base. HCl (aq) + H2O (l) H3O+ (aq) + Cl- (aq) • H2O is a much stronger base than Cl-, so the equilibrium lies so far to the right that K is not measured (K>>1). Acids and Bases © 2009, Prentice-Hall, Inc. Acid and Base Strength • In any acid-base reaction, the equilibrium will favor the reaction that moves the proton to the stronger base. CH3CO2H (aq) + H2O (l) H3O+ (aq) + CH3CO2- (aq) • Acetate is a stronger base than H2O, so the equilibrium favors the left side (K<1). Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.3 (p. 677) For the following proton-transfer reaction, use the above figure to predict whether the equilibrium lies predominantly to the left or to the right HSO4-(aq) + CO32-(aq)D SO42-(aq) + HCO3-(aq) Which base is more able to pull protons off the acid? CO32- or HCO3-? Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.3 (p. 677) For the following proton-transfer reaction, use the above figure to predict whether the equilibrium lies predominantly to the left or to the right HSO4-(aq) + CO32-(aq)D SO42-(aq) + HCO3-(aq) Which base is more able to pull protons off the acid? CO32- or HCO3-? equilibrium lies to the right Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.3) Based on the information in Figure 16.4, place the following equilibria in order from smallest to largest value of Kc: i. CH3COOH(aq) + HS-(aq) D CH3COO-(aq) + H2S(aq) ii. F-(aq) + NH4+(aq) D HF(aq) + NH3(aq) iii. H2CO3 (aq) + Cl-(aq) D HCO3-(aq) + HCl(aq) a) b) c) d) e) (i) < (ii) < (iii) (ii) < (i) < (iii) (iii) < (i) < (ii) (ii) < (iii) < (i) (iii) < (ii) < (i) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.3) Based on the information in Figure 16.4, place the following equilibria in order from smallest to largest value of Kc: i. CH3COOH(aq) + HS-(aq) D CH3COO-(aq) + H2S(aq) ii. F-(aq) + NH4+(aq) D HF(aq) + NH3(aq) iii. H2CO3 (aq) + Cl-(aq) D HCO3-(aq) + HCl(aq) a) b) c) d) e) (i) < (ii) < (iii) (ii) < (i) < (iii) (iii) < (i) < (ii) (ii) < (iii) < (i) (iii) < (ii) < (i) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.3) For each of the following reactions, use the above figure to predict whether the equilibrium lies predominantly to the left or to the right: a) HPO42-(aq)+ H2O(l) D H2PO4-(aq)+ OH(aq) b) NH4+(aq) + OH-(aq) D NH3(aq) + H2O(l) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.3) a) For each of the following reactions, use the above figure to predict whether the equilibrium lies predominantly to the left or to the right: HPO42-(aq)+ H2O(l) D H2PO4-(aq)+ OH-(aq) to the left, as OH- is a stronger base than HPO42and grabs one of the H’s from H2PO4- to form H2O b) NH4+(aq) + OH-(aq) D NH3(aq) + H2O(l) to the right, as OH- is a stronger base than NH3 and grabs one of the H’s from NH4+ to form H2O Acids and Bases © 2009, Prentice-Hall, Inc. Autoionization of Water • As we have seen, water is amphoteric. • In pure water, a few molecules act as bases and a few act as acids. H2O (l) + H2O (l) H3O+ (aq) + OH- (aq) • This is referred to as autoionization. Acids and Bases © 2009, Prentice-Hall, Inc. Ion-Product Constant • The equilibrium expression for this process is Kc = [H3O+] [OH-] • This special equilibrium constant is referred to as the ion-product constant for water, Kw. • At 25C, Kw = 1.0 10-14 Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.4 (p. 679) Calculate the values of [H+] and [OH-] in a neutral solution at 25oC. Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.4 (p. 679) Calculate the values of [H+] and [OH-] in a neutral solution at 25oC. 1.0 x 10-14 = [H+][OH-] = x2 x = 1.0 x 10-7 M = [H+][OH-] Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.4) In a certain acidic solution at 25oC, [H+] is 100 times greater than [OH-]. What is the value for [OH-] for the solution? a) b) c) d) e) 1.0 x 10-8 M 1.0 x 10-7 M 1.0 x 10-6 M 1.0 x 10-2 M 1.0 x 10-9 M Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.4) In a certain acidic solution at 25oC, [H+] is 100 times greater than [OH-]. What is the value for [OH-] for the solution? a) b) c) d) e) 1.0 x 10-8 M 1.0 x 10-7 M 1.0 x 10-6 M 1.0 x 10-2 M 1.0 x 10-9 M Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.4) Indicate whether solutions with each of the following ion concentrations is neutral, acidic, or basic: a) b) c) [H+] = 4 x 10-9 M [OH-] = 1 x 10-7 M [OH-] = 7 x 10-13 M Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.4) Indicate whether solutions with each of the following ion concentrations is neutral, acidic, or basic: a) b) c) [H+] = 4 x 10-9 M basic [OH-] = 1 x 10-7 M neutral [OH-] = 7 x 10-13 M acidic Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.5 (p. 680) Calculate the concentration of H+(aq) in a) a solution in which [OH-] is 0.010 M (1.0 x 10-12 M) b) a solution in which [OH-] is 1.8 x 10-9 M (5.0 x 10-6 M) Assume T = 25oC. Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.5) A solution has [OH-] = 4.0 x 10-8 M. What is the value of [H+] for the solution? a) b) c) d) e) 2.5 x 10-8 M 4.0 x 10-8 M 2.5 x 10-7 M 2.5 x 10-6 M 4.0 x 10-6 M Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.5) A solution has [OH-] = 4.0 x 10-8 M. What is the value of [H+] for the solution? a) b) c) d) e) 2.5 x 10-8 M 4.0 x 10-8 M 2.5 x 10-7 M 2.5 x 10-6 M 4.0 x 10-6 M Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.5) Calculate the concentration of OH-(aq) in a solution in which a) [H+] = 2 x 10-6 M 5 x 10-9 M b) [H+] = [OH-] 1 x 10-7 M c) [H+] = 100 x [OH-] 1 x 10-6 M Acids and Bases © 2009, Prentice-Hall, Inc. pH pH is defined as the negative base-10 logarithm of the concentration of hydronium ion. pH = -log [H3O+] Acids and Bases © 2009, Prentice-Hall, Inc. pH • In pure water, Kw = [H3O+] [OH-] = 1.0 10-14 • Since in pure water [H3O+] = [OH-], [H3O+] = 1.0 10-14 = 1.0 10-7 Acids and Bases © 2009, Prentice-Hall, Inc. pH • Therefore, in pure water, pH = -log (1.0 10-7) = 7.00 • An acid has a higher [H3O+] than pure water, so its pH is <7. • A base has a lower [H3O+] than pure water, so its pH is >7. Acids and Bases © 2009, Prentice-Hall, Inc. pH These are the pH values for several common substances. Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.6 (p. 681) Calculate the pH values for the two solutions described in Sample Exercise 16.5. (a) 12.00 b) 5.25) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.6) A solution at 25oC has [OH-] = 6.7 x 10-3 M. What is the pH of the solution? a) b) c) d) e) 0.83 2.2 2.17 11.83 12 Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.6) A solution at 25oC has [OH-] = 6.7 x 10-3 M. What is the pH of the solution? a) b) c) d) e) 0.83 2.2 2.17 11.83 12 Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.6) a) In a sample of lemon juice [H+] is 3.8 x 10-4 M. What is the pH? (3.42) b) A commonly available windowcleaning solution has a [OH-] of 1.9 x 10-6 M. What is the pH? (8.28) Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.7 (p. 683) A sample of freshly pressed apple juice has a pH of 3.76. Calculate [H+]. (1.7 x 10-4 M) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.7) A solution at 25oC has pOH = 10.53. Which of the following statements is or are true? i. The solution is acidic. ii. The pH of the solution is 14.00 – 10.53. iii. For this solution, [OH-] = 10-10.53 M. a) b) c) d) e) Only one of the statements is true. Statements (i) and (ii) are true. Statements (i) and (iii) are true. Statements (ii) and (iii) are true. All three statements are true. Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.7) A solution at 25oC has pOH = 10.53. Which of the following statements is or are true? i. The solution is acidic. ii. The pH of the solution is 14.00 – 10.53. iii. For this solution, [OH-] = 10-10.53 M. a) b) c) d) e) Only one of the statements is true. Statements (i) and (ii) are true. Statements (i) and (iii) are true. Statements (ii) and (iii) are true. All three statements are true. Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.7) A solution formed by dissolving an antacid tablet has a pH of 9.18. Calculate [H+]. (6.6 x 10-10 M) Acids and Bases © 2009, Prentice-Hall, Inc. Other “p” Scales • The “p” in pH tells us to take the negative base-10 logarithm of the quantity (in this case, hydronium ions). • Some similar examples are – pOH: -log [OH-] – pKw: -log Kw Acids and Bases © 2009, Prentice-Hall, Inc. Watch This! Because [H3O+] [OH-] = Kw = 1.0 10-14, we know that -log [H3O+] + -log [OH-] = -log Kw = 14.00 or, in other words, pH + pOH = pKw = 14.00 Acids and Bases © 2009, Prentice-Hall, Inc. How Do We Measure pH? • For less accurate measurements, one can use – Litmus paper • “Red” paper turns blue above ~pH = 8 • “Blue” paper turns red below ~pH = 5 – Or an indicator. Acids and Bases © 2009, Prentice-Hall, Inc. How Do We Measure pH? For more accurate measurements, one uses a pH meter, which measures the voltage in the solution. Acids and Bases © 2009, Prentice-Hall, Inc. Strong Acids • You will recall that the seven strong acids are HCl, HBr, HI, HNO3, H2SO4, HClO3, and HClO4. • These are, by definition, strong electrolytes and exist totally as ions in aqueous solution. • For the monoprotic strong acids, [H3O+] = [acid]. Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.8 (p. 685) What is the pH of a 0.040 M solution of HClO4? (1.40) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.8) Order the following three solutions from smallest to largest pH. i. 0.20 M HClO3 ii. 0.0030 M HNO3 iii. 1.50 M HCl a) b) c) d) e) (i) < (ii) < (iii) (ii) < (i) < (iii) (iii) < (i) < (ii) (ii) < (iii) < (i) (iii) < (ii) < (i) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.8) Order the following three solutions from smallest to largest pH. i. 0.20 M HClO3 ii. 0.0030 M HNO3 iii. 1.50 M HCl a) b) c) d) e) (i) < (ii) < (iii) (ii) < (i) < (iii) (iii) < (i) < (ii) (ii) < (iii) < (i) (iii) < (ii) < (i) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.8) An aqueous solution of HNO3 has a pH of 2.34. What is the concentration of the acid? (0.0046 M) Acids and Bases © 2009, Prentice-Hall, Inc. Strong Bases • Strong bases are the soluble hydroxides, which are the alkali metal and heavier alkaline earth metal hydroxides (Ca2+, Sr2+, and Ba2+). • Again, these substances dissociate completely in aqueous solution. Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.9 (p. 685) What is the pH of a) a 0.028 M solution of NaOH? (12.45) b) a 0.0011 M solution of Ca(OH)2? (11.34) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.9) Order the following three solutions from smallest to largest pH: i. 0.030 M Ba(OH)2 ii. 0.040 M KOH iii. Pure water a) b) c) d) e) (i) < (ii) < (iii) (ii) < (i) < (iii) (iii) < (i) < (ii) (ii) < (iii) < (i) (iii) < (ii) < (i) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.9) Order the following three solutions from smallest to largest pH: i. 0.030 M Ba(OH)2 ii. 0.040 M KOH iii. Pure water a) b) c) d) e) (i) < (ii) < (iii) (ii) < (i) < (iii) (iii) < (i) < (ii) (ii) < (iii) < (i) (iii) < (ii) < (i) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.9) What is the concentration of a solution of a) KOH for which the pH is 11.89? (7.8 x 10-3 M) b) Ca(OH)2 for which the pH is 11.68? (2.4 x 10-3 M) Acids and Bases © 2009, Prentice-Hall, Inc. Overview of Chapter 16 New material: On your own: • Arrhenius acids and bases • Brønsted-Lowry acids and bases • Conjugate acid-base pairs • Relative strengths of acids and bases • Autoionization of water and Kw • [H+] > pH • [OH-] > pOH • pH + pOH = 14.00 • Determine pH and/or pOH of strong acids and bases • • • • • • • • • • • Application of equilibrium to weak acids and bases: Ka, Kb Calculate Ka from pH and vice versa Calculate percent ionization of weak acids Polyprotic acids and their successive Ka’s Types of weak bases Calculate concentrations of all species of weak acids and weak bases at equilibrium, using Ka, Kb, pH or pOH Relationship between Ka and Kb, derived from Kw – S2 Application of Ka/Kb: acid-base properties of salt solutions – S2 Factors that affect acid strength – binary acids and oxyacids – S2 Carboxylic acids – S2 Acids Lewis acids and bases – S2 and Bases © 2009, Prentice-Hall, Inc. Application of Equilibrium to Weak Acids and Weak Bases Acids and Bases © 2009, Prentice-Hall, Inc. Dissociation Constants • For a generalized acid dissociation, HA (aq) + H2O (l) A- (aq) + H3O+ (aq) the equilibrium expression would be [H3O+] [A-] Kc = [HA] • This equilibrium constant is called the acid-dissociation constant, Ka. • Note that H2O is omitted from Ka because it is a pure liquid Acids and Bases © 2009, Prentice-Hall, Inc. Dissociation Constants The larger the Ka, the stronger the acid If Ka >> 1, then the acid is completely ionized strong acid Acids and Bases © 2009, Prentice-Hall, Inc. Dissociation Constants The greater the value of Ka, the stronger is the acid. Acids and Bases © 2009, Prentice-Hall, Inc. Ionization Constants and Equations WS Acids and Bases © 2009, Prentice-Hall, Inc. Calculating Ka from the pH • pH [H+] at equilibrium • Equilibrium [H+] RICE table • Use RICE table to find the [other species] Acids and Bases © 2009, Prentice-Hall, Inc. Calculating Ka from the pH Sample Exercise 16.10 (p. 688) The pH of a 0.10 M solution of formic acid, HCOOH, at 25C is 2.38. Calculate Ka for formic acid at this temperature. We know that [H3O+] [HCOO-] Ka = [HCOOH] Acids and Bases © 2009, Prentice-Hall, Inc. Calculating Ka from the pH The pH of a 0.10 M solution of formic acid, HCOOH, at 25C is 2.38. Calculate Ka for formic acid at this temperature. To calculate Ka, we need the equilibrium concentrations of all three things. We can find [H3O+], which is the same as [HCOO-], from the pH. Acids and Bases © 2009, Prentice-Hall, Inc. Calculating Ka from the pH pH = -log [H3O+] 2.38 = -log [H3O+] -2.38 = log [H3O+] 10-2.38 = 10log [H3O+] = [H3O+] 4.2 10-3 M = [H3O+] = [HCOO-] Acids and Bases © 2009, Prentice-Hall, Inc. Calculating Ka from pH Now we can set up a table… [HCOOH], M [H3O+], M [HCOO-], M Initially 0.10 0 0 Change - 4.2 10-3 + 4.2 10-3 + 4.2 10-3 0.10 - 4.2 10-3 = 0.0958 = 0.10 4.2 10-3 4.2 10-3 At Equilibrium Acids and Bases © 2009, Prentice-Hall, Inc. Calculating Ka from pH Note that the [HCOOH] remains at 0.10 M at equilibrium – sig figs. This will become very important later in this chapter. Acids and Bases © 2009, Prentice-Hall, Inc. Calculating Ka from pH [4.2 10-3] [4.2 10-3] Ka = [0.10] = 1.8 10-4 Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.10) A 0.50 M solution of an acid HA has pH = 2.24. What is the value of Ka for the acid? a) b) c) d) e) 1.7 x 10-12 3.3 x 10-5 6.6 x 10-5 5.8 x 10-3 1.2 x 10-2 Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.10) A 0.50 M solution of an acid HA has pH = 2.24. What is the value of Ka for the acid? a) b) c) d) e) 1.7 x 10-12 3.3 x 10-5 6.6 x 10-5 5.8 x 10-3 1.2 x 10-2 Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.10) Niacin, one of the B vitamins, has the following molecular structure: A 0.020 M solution of niacin has a pH of 3.26. What is the acid-dissociation constant, Ka, for niacin? (1.6 x 10-5) Acids and Bases © 2009, Prentice-Hall, Inc. Calculating Percent Ionization Sample Exercise 16.11 (p. 689) A 0.10 M solution of formic acid (HCOOH) contains 4.2 x 10-3 M H+(aq). Calculate the percentage of the acid that is ionized. (4.2%) Acids and Bases © 2009, Prentice-Hall, Inc. Calculating Percent Ionization Sample Exercise 16.11 (p. 689) [H3O+]eq • Percent Ionization = [HA] 100 initial • In this example [H3O+]eq = 4.2 10-3 M [HCOOH]initial = 0.10 M 4.2 10-3 Percent Ionization = 100 0.10 = 4.2% Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.11) A 0.077 M solution of an acid HA has pH = 2.16. What is the percentage of the acid that is ionized? a) b) c) d) e) 0.090% 0.69% 0.90% 3.6% 9.0% Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.11) A 0.077 M solution of an acid HA has pH = 2.16. What is the percentage of the acid that is ionized? a) b) c) d) e) 0.090% 0.69% 0.90% 3.6% 9.0% Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.11) A 0.020 M solution of niacin has a pH of 3.26. Calculate the percent ionization of the niacin. (2.7%) Acids and Bases © 2009, Prentice-Hall, Inc. Using Ka to Calculate pH • Using Ka, we can calculate the concentration of H+ (and hence the pH). Example: Calculate the pH of a 0.30 M solution of acetic acid, HC2H3O2, at 25C. Ka for acetic acid at 25C is 1.8 10-5. Acids and Bases © 2009, Prentice-Hall, Inc. Using Ka to Calculate pH 1. Write the balanced chemical equation clearly showing the equilibrium. CH3COOH(aq) D H+(aq) + CH3COO-(aq) Acids and Bases © 2009, Prentice-Hall, Inc. Using Ka to Calculate pH 2. Write the equilibrium expression. Look up the value for Ka (in a table). Ka = [H+][ CH3COO-] = 1.8 x 10-5 [CH3COOH] Acids and Bases © 2009, Prentice-Hall, Inc. Using Ka to Calculate pH 3. Write down the initial and equilibrium concentrations for everything except pure water. We usually assume that the equilibrium concentration of H+ is x. Acids and Bases © 2009, Prentice-Hall, Inc. Using Ka to Calculate pH 3. Write down the initial and equilibrium concentrations for everything except pure water. Acids and Bases © 2009, Prentice-Hall, Inc. Using Ka to Calculate pH 4. Substitute into the equilibrium constant expression and solve. Ka = 1.8 x 10-5 = [H+][C2H3O2-] = (x)(x) [HC2H3O2] 0.30 – x Note that Ka is very small (1.8 x 10-5) relative to [HC2H3O2] (0.30 M). Acids and Bases © 2009, Prentice-Hall, Inc. Using Ka to Calculate pH 4. Substitute into the equilibrium constant expression and solve. Keep this x x2 = 1.8 x 10-5 0.30 – x Neglect x in the denominator since it is extremely small relative to 0.30. (Use ballpark figure of 103 X difference for neglecting x in the denominator ) Acids and Bases © 2009, Prentice-Hall, Inc. Using Ka to Calculate pH 4. Substitute into the equilibrium constant expression and solve. x2 = (1.8 x 10-5 )(0.30) = 5.4 x 10-6 x2 = (5.4 x 10-6) x = 2.3 x 10-3 M = [H+] Acids and Bases © 2009, Prentice-Hall, Inc. Using Ka to Calculate pH 4. Substitute into the equilibrium constant expression and solve. Check: Compare x with original [HC2H3O2] of 0.30 M: 2.3 x 10-3 M x 100% = 0.77%, which is < 5% 0.30 M Acids and Bases © 2009, Prentice-Hall, Inc. Using Ka to Calculate pH 5. Convert x ([H+]) to pH. pH = - log (2.3 x 10-3) = 2.64 Acids and Bases © 2009, Prentice-Hall, Inc. What do we do if we are faced with having to solve a quadratic equation in order to determine the value of x? Often this cannot be avoided. • However, if the Ka value is quite small, we find that we can make a simplifying assumption. • Assume that x is negligible compared to the initial concentration of the acid. • This will simplify the calculation. • • It is always necessary to check the validity of any assumption. Once we have the value of x, check to see how large it is compared to the initial concentration. • If x is <5% of the initial concentration, the assumption is probably a good one. If x>5% of the initial concentration, then it may be best to solve the quadratic equation or use successive approximations. • Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.12 (p. 691) Calculate the pH of a 0.20 M solution of HCN. Refer to Table 16.2 for Ka. (5.00) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.12) What is the pH of a 0.40 M solution of benzoic acid, C6H5COOH? (The Ka value for benzoic acid is given in Table 16.2.) a) b) c) d) e) 2.30 2.10 1.90 4.20 4.60 Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.12) What is the pH of a 0.40 M solution of benzoic acid, C6H5COOH? (The Ka value for benzoic acid is given in Table 16.2.) a) b) c) d) e) 2.30 2.10 1.90 4.20 4.60 Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.12) The Ka for niacin is 1.6 x 10-5. What is the pH of a 0.010 M solution of niacin? (3.41) Acids and Bases © 2009, Prentice-Hall, Inc. Polyprotic Acids… …have more than one acidic proton If the difference between the Ka for the first dissociation and subsequent Ka values is 103 or more, the pH generally depends only on the first dissociation. Acids and Bases © 2009, Prentice-Hall, Inc. Weak Bases Weak bases remove protons from substances. They react with water to produce hydroxide ion. Acids and Bases © 2009, Prentice-Hall, Inc. Weak Bases The equilibrium constant expression for this reaction is [HB] [OH-] Kb = [B-] where Kb is the base-dissociation constant. The larger Kb, the stronger the base. Acids and Bases © 2009, Prentice-Hall, Inc. Weak Bases The equilibrium constant expression for this reaction is [NH4+] [OH-] Kb = [NH3] where Kb is the base-dissociation constant. Acids and Bases © 2009, Prentice-Hall, Inc. Weak Bases Kb can be used to find [OH-] and, through it, pH. Acids and Bases © 2009, Prentice-Hall, Inc. pH of Basic Solutions Sample Exercise 16.15 (p. 697) Calculate the concentration of OH- in a 0.15M solution of NH3. (1.6 x 10-3 M) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Problem 1 (16.15) What is the pH of a 0.65 M solution of pyridine, C5H5N? Kb = 1.7 x 10-9 a) b) c) d) e) 4.48 8.96 9.52 9.62 9.71 Acids and Bases © 2009, Prentice-Hall, Inc. Practice Problem 1 (16.15) What is the pH of a 0.65 M solution of pyridine, C5H5N? Kb = 1.7 x 10-9 a) b) c) d) e) 4.48 8.96 9.52 9.62 9.71 Acids and Bases © 2009, Prentice-Hall, Inc. Practice Problem 2 (16.15) (more of a conceptual question) Which of the following compounds should produce the highest pH as a 0.05 M solution: pyridine, methylamine, or nitrous acid? (methylamine) Acids and Bases © 2009, Prentice-Hall, Inc. Types of Weak Bases Weak bases generally fall into one of two categories. 1. Neutral substances with a lone pair of electrons that can accept protons. Most neutral weak bases contain nitrogen. Amines are related to ammonia and have one or more N–H bonds replaced with N–C bonds (e.g., CH3NH2 is methylamine). Acids and Bases © 2009, Prentice-Hall, Inc. Types of Weak Bases Like NH3, amines can abstract a proton from a water molecule by forming an additional N-H bond, as shown in this figure for methylamine. Acids and Bases © 2009, Prentice-Hall, Inc. Types of Weak Bases 2. Anions of weak acids are also weak bases. e.g.: ClO– is the conjugate base of HClO (weak acid): ClO–(aq) + H2O(l) D HClO(aq) + OH–(aq) Kb = 3.3 x 10–7 Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.16 (p. 698) A solution made by adding solid sodium hypochlorite (NaClO) to enough water to make 2.00 L of solution has a pH of 10.50. How many moles of NaClO were added to the water? Kb = 3.3 x 10-7 (See info immediately above.) (0.60 mol) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.16) The benzoate ion, C6H5COO-, is a weak base with Kb = 1.6 x 10-10. How many moles of sodium benzoate are present in 0.50 L of a solution of NaC6H5COO if the pH is 9.04? a) b) c) d) e) 0.38 0.66 0.76 1.5 2.9 Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.16) The benzoate ion, C6H5COO-, is a weak base with Kb = 1.6 x 10-10. How many moles of sodium benzoate are present in 0.50 L of a solution of NaC6H5COO if the pH is 9.04? a) b) c) d) e) 0.38 0.66 0.76 1.5 2.9 Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.16) A solution of NH3 in water has a pH of 11.17. What is the molarity of the solution? Kb = 1.8 x 10-5 (0.12 M) Acids and Bases © 2009, Prentice-Hall, Inc. Ka and Kb Note: Conjugate acid has one more H+ than its conjugate base. Ka and Kb are related in this way: Ka Kb = Kw Therefore, if you know one of them, you can calculate the other. Alternatively, pKa + pKb = pKw = 14.00 (at 25oC) Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.17 (p. 701) Calculate a) the base-dissociation constant, Kb, for the fluoride ion (F-); (1.5 x 10-11) b) the acid-dissociation constant, Ka, for the ammonium ion (NH4+). (5.6 x 10-10) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.17) (Use Appendix D for Ka) By using information from Appendix D, put the following three substances in order of weakest to strongest base: i. (CH3)3N ii. HCOOiii. BrOa) b) c) d) e) (i) < (ii) < (iii) (ii) < (i) < (iii) (iii) < (i) < (ii) (ii) < (iii) < (i) (iii) < (ii) < (i) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.17) (Use Appendix D for Ka) By using information from Appendix D, put the following three substances in order of weakest to strongest base: i. (CH3)3N ii. HCOOiii. BrOa) b) c) d) e) (i) < (ii) < (iii) (ii) < (i) < (iii) (iii) < (i) < (ii) (ii) < (iii) < (i) (iii) < (ii) < (i) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.17) (Use Appendix D for Ka) a) Which of the following anions has the largest basedissociation constant: NO2-, PO43-, or N3-? (PO43-, Kb = 2.4 x 10-2) b) The base quinoline has the following structure: Its conjugate acid is listed in handbooks as having a pKa of 4.90. What is the base-dissociation constant for quinoline? Acids (7.9 x 10-10) and Bases © 2009, Prentice-Hall, Inc. Acid/Base Properties of Salt Solutions Acids and Bases © 2009, Prentice-Hall, Inc. Reactions of Anions with Water • Anions are bases. • As such, they can react with water in a hydrolysis reaction to form OH- and the conjugate acid: X- (aq) + H2O (l) HX (aq) + OH- (aq) Acids and Bases © 2009, Prentice-Hall, Inc. Reactions of Cations with Water • Cations with acidic protons (like NH4+) will lower the pH of a solution. • Most metal cations that are hydrated in solution also lower the pH of the solution. Acids and Bases © 2009, Prentice-Hall, Inc. Reactions of Cations with Water • Attraction between nonbonding electrons on oxygen and the metal causes a shift of the electron density in water. • This makes the O-H bond more polar and the water more acidic. • Greater charge and smaller size make a cation more acidic. Acids and Bases © 2009, Prentice-Hall, Inc. Predicting the pH of a solution (qualitatively) 1. Salts derived from a strong acid and strong base are neutral. e.g. NaCl, Ca(NO3)2 2. Salts derived from a strong base and weak acid are basic. e.g. NaClO, Ba(C2H3O2)2 3. Salts derived from a weak base and strong acid are acidic. e.g. NH4Cl Acids and Bases © 2009, Prentice-Hall, Inc. Predicting the pH of a solution (qualitatively) 4. Salts derived from a weak acid and weak base can be either acidic or basic. We need to compare Ka and Kb for hydrolysis of the anion and the cation. e.g. NH4CN Both ions undergo significant hydrolysis. Is the salt solution acidic or basic? Ka of NH4+ < Kb of CN solution should be basic. Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.18 (p. 704) Determine whether aqueous solutions of each of the following salts will be acidic, basic, or neutral: Hint: Analyze each compound – derived from strong or weak acids and bases? a) Ba(CH3COO)2, b) NH4Cl c) CH3NH3Br d) KNO3 e) Al(ClO4)3 Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.18 (p. 704) a) b) c) d) e) Determine whether aqueous solutions of each of the following salts will be acidic, basic, or neutral: Ba(CH3COO)2, anion of weak acid basic NH4Cl cation of weak base acidic CH3NH3Br cation of weak base acidic KNO3 neutral – derived from strong acid + strong base Al(ClO4)3 cation of weak base (Al(OH)3) acidic, Al3+ - increase the polarity of O-H in H2O Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.18) Order the following solutions from lowest to highest pH: i. 0.10 M NaClO ii. 0.10 M KBr iii. 0.10 M NH4ClO4 a) b) c) d) e) (i) < (ii) < (iii) (ii) < (i) < (iii) (iii) < (i) < (ii) (ii) < (iii) < (i) (iii) < (ii) < (i) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.18) Order the following solutions from lowest to highest pH: i. 0.10 M NaClO ii. 0.10 M KBr iii. 0.10 M NH4ClO4 a) b) c) d) e) (i) < (ii) < (iii) (ii) < (i) < (iii) (iii) < (i) < (ii) (ii) < (iii) < (i) (iii) < (ii) < (i) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.18) In each of the following, indicate which salt in each of the following pairs will form the more acidic (or less basic) 0.010 M solution: a) NaNO3 or Fe(NO3)3 b) KBr, or KBrO c) CH3NH3Cl or BaCl2 d) NH4NO2 or NH4NO3 Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.18) In each of the following, indicate which salt in each of the following pairs will form the more acidic (or less basic) 0.010 M solution: a) NaNO3 (neutral) or Fe(NO3)3 (acidic) b) KBr (neutral), or KBrO (basic) c) CH3NH3Cl (acidic) or BaCl2 (neutral) d) NH4NO2 or NH4NO3 Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.19 (p. 705) Predict whether the salt Na2HPO4 will form an acidic or a basic solution on dissolving in water. (basic) Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.19) How many of the following salts are expected to produce acidic solutions (See Table 16.3 for data): NaHSO4, NaHC2O4, NaH2PO4, NaHCO3 a) b) c) d) e) 0 1 2 3 4 Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 1 (16.19) How many of the following salts are expected to produce acidic solutions (See Table 16.3 for data): NaHSO4, NaHC2O4, NaH2PO4, NaHCO3 a) b) c) d) e) 0 1 2 3 4 Acids and Bases © 2009, Prentice-Hall, Inc. Practice Exercise 2 (16.19) Predict whether the dipotassium salt of citric acid (K2HC6H5O7) will form an acidic or basic solution in water. (see Table 16.3 for data) (acidic) Acids and Bases © 2009, Prentice-Hall, Inc. Factors Affecting Acid Strength (Sec. 16.10-16.11) • The more polar the H-X bond and/or the weaker the H-X bond, the more acidic the compound. • So acidity increases from left to right across a row and from top to bottom down a group. Acids and Bases © 2009, Prentice-Hall, Inc. Factors Affecting Acid Strength In oxyacids, in which an -OH is bonded to another atom, Y, the more electronegative Y is, the more acidic the acid. Acids and Bases © 2009, Prentice-Hall, Inc. Factors Affecting Acid Strength For a series of oxyacids, acidity increases with the number of oxygens. Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.20 (p. 708) Arrange the compounds in each of the following series in order of increasing acid strength: a) AsH3, HI, NaH, H2O; b) H2SO4, H2SeO3, H2SeO4. Acids and Bases © 2009, Prentice-Hall, Inc. Sample Exercise 16.20 (p. 708) Arrange the compounds in each of the following series in order of increasing acid strength: a) AsH3, HI, NaH, H2O NaH < AsH3 < H2O < HI b) H2SO4, H2SeO3, H2SeO4 H2SeO3 < H2SeO4 < H2SO4 Acids and Bases © 2009, Prentice-Hall, Inc. Practice 1 (16.20) Arrange the following substances in order from weakest to strongest acid: HClO3, HOI, HBrO2, HClO2, HIO2 a) b) c) d) e) HIO2 < HOI < HClO3 < HBrO2 < HClO2 HOI < HIO2 < HBrO2 < HClO2 < HClO3 HBrO2 < HIO2 < HClO2 < HOI < HClO3 HClO3 < HClO2 < HBrO2 < HIO2 < HOI HOI < HClO2 < HBrO2 < HIO2 < HClO3 Acids and Bases © 2009, Prentice-Hall, Inc. Practice 1 (16.20) Arrange the following substances in order from weakest to strongest acid: HClO3, HOI, HBrO2, HClO2, HIO2 a) b) c) d) e) HIO2 < HOI < HClO3 < HBrO2 < HClO2 HOI < HIO2 < HBrO2 < HClO2 < HClO3 HBrO2 < HIO2 < HClO2 < HOI < HClO3 HClO3 < HClO2 < HBrO2 < HIO2 < HOI HOI < HClO2 < HBrO2 < HIO2 < HClO3 Acids and Bases © 2009, Prentice-Hall, Inc. Practice 2 (16.20) In each of the following pairs choose the compound that leads to the more acidic (or less basic) solution: a) HBr, HF; b) PH3, H2S; c) HNO2, HNO3; d) H2SO3, H2SeO3. Acids and Bases © 2009, Prentice-Hall, Inc. Practice 2 (16.20) In each of the following pairs choose the compound that leads to the more acidic (or less basic) solution: a) HBr, HF; b) PH3, H2S; c) HNO2, HNO3; d) H2SO3, H2SeO3. Acids and Bases © 2009, Prentice-Hall, Inc. Factors Affecting Acid Strength Resonance in the conjugate bases of carboxylic acids stabilizes the base and makes the conjugate acid more acidic. Acids and Bases © 2009, Prentice-Hall, Inc. Comparison of Different Types of Acids and Bases Acids and Bases © 2009, Prentice-Hall, Inc. Arrhenius (traditional) acids and bases (C19th) • Acid: compound containing H that ionizes to yield H+ in solution • Base: compound containing OH that ionizes to yield OH- in solution (Note: does not describe acid/base behavior in solvents other than water) Note: Every Arrhenius acid/base is also a Brønsted-Lowry acid/base. Acids and Bases © 2009, Prentice-Hall, Inc. Bronsted-Lowry Acids and Bases (1923) • Acid: H+ (proton) donor • Base: H+ (proton) acceptor NH3 ammonia (B-L base) + H 2O D water (B-L acid) NH4+ ammonium ion (B-L acid) + OHhydroxide ion (B-L base) Note: Every Brønsted-Lowry acid/base is also a Lewis acid/base. Acids and Bases © 2009, Prentice-Hall, Inc. Lewis Acids and Bases (1920’s) (not required for AP Chem exam) • Acid: accepts pair of e-‘s • Base: donates pair of e-‘s .. H+ Lewis acid + .. - H:O:H [:O:H] .. .. Lewis base Acids and Bases © 2009, Prentice-Hall, Inc. Lewis Acids • Lewis acids are defined as electron-pair acceptors. • Atoms with an empty valence orbital can be Lewis acids. Acids and Bases © 2009, Prentice-Hall, Inc. Lewis Bases • Lewis bases are defined as electron-pair donors. • Anything that could be a Brønsted-Lowry base is a Lewis base. • Lewis bases can interact with things other than Acids protons, however. and Bases © 2009, Prentice-Hall, Inc. Hydrolysis of Metal Ions • The Lewis concept may be used to explain the acid properties of many metal ions. • Metal ions are positively charged and attract water molecules (via the lone pairs on the oxygen atom of water). • Hydrated metal ions act as acids. • For example: Fe(H2O)63+(aq) D Fe(H2O)5(OH)2+(aq) + H+(aq) Ka = 2 x 10–3 Acids and Bases © 2009, Prentice-Hall, Inc. Hydrolysis of Metal Ions In general: • The higher the charge, the stronger the M–OH2 interaction. • Ka values generally increase with increasing charge • The smaller the metal ion, the more acidic the ion. • Ka values generally decrease with decreasing ionic radius • Thus the pH of an aqueous solution increases as the size of the ion increases (e.g., Ca2+ vs. Zn2+) and as the charge increases (e.g., Na+ vs. Ca2+ and Zn2+ vs. Al3+). Acids and Bases © 2009, Prentice-Hall, Inc.