Chapter 16. Acid-Base Equilibria Acids and Bases: A Brief Review Brønsted-Lowry Acids and Bases. Conjugate Acid-Base Pairs

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1 16.1 Acids and Bases: A Brief Review Arrhenius concept of acids and bases: an acid increases [H + ] and a base increases [OH ] Brønsted-Lowry Acids and Bases In the Brønsted-Lowry system, a Brønsted-Lowry acid is a species that donates H + and a Brønsted-Lowry base is a species that accepts H +. Therefore a Brønsted-Lowry base does not need to contain OH. NH 3 is a Brønsted-Lowry base but not an Arrhenius base. Consider NH 3 (aq) + H 2 O(l) NH 4 + (aq) + OH (aq): H 2 O donates a proton to ammonia. water is acting as an acid. NH 3 accepts a proton from water. ammonia is acting as a base. Amphoteric substances can behave as acids and bases. Thus water is an example of an amphoteric species. Conjugate Acid-Base Pairs Whatever is left of the acid after the proton is donated is called its conjugate base. Similarly, a conjugate acid is formed by adding a proton to the base

2 Sample Exercise 16.1 (p. 671) a) What is the conjugate base of each of the following acids: HClO 4 H 2 S PH 4 + HCO - 3? b) What is the conjugate acid of each of the following bases? CN - SO 4 2- H 2 O - HCO 3 Practice Exercise 16.1 Write the formula for the conjugate acid of each of the following: HSO 3 - F - PO 4 3- CO Sample Exercise 16.2 (p. 671) The hydrogen sulfite ion (HSO 3 - ) is amphoteric. a) Write an equation for the reaction of HSO 3 - with water, in which the ion acts as an acid. b) Write an equation for the reaction of HSO 3 - with water, in which the ion acts as a base. In both cases identify the conjugate acid-base pairs. Practice Exercise 16.2 When lithium oxide (Li 2 O) is dissolved in water, the solution turns basic from the reaction of the oxide ion (O 2- ) with water. Write the reaction that occurs, and identify the conjugate acid-base pairs

3 Relative Strengths of Acids and Bases The stronger an acid is, the weaker its conjugate base will be. 1. Strong acids completely transfer their protons to water. 2. Weak acids only partially dissociate in aqueous solution. 3. Substances with negligible acidity do not transfer a proton to water. In every acid-base reaction, the position of the equilibrium favors the transfer of a proton from the stronger acid to the stronger base. H + is the strongest acid that can exist in equilibrium in aqueous solution. OH is the strongest base that can exist in equilibrium in aqueous solution. Sample Exercise 16.3 (p. 673) For the following proton-transfer reaction, use the above figure to predict whether the equilibrium lies predominantly to the left or to the right HSO 4 - (aq) + CO 3 2- (aq) SO 4 2- (aq) + HCO 3 - (aq) Practice Exercise 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) HPO 4 2- (aq) + H 2 O (l) H 2 PO 4 - (aq) + OH - (aq) b) NH 4 + (aq) + OH - (aq) NH 3(aq) + H 2 O (l) - 3 -

4 16.3 The Autoionization of Water autoionization of water: 2H 2 O(l) H 3 O + (aq) + OH (aq) The Ion Product of Water equilibrium constant expression for the autoionization of water: Sample Exercise 16.4 (p. 674) 1.0 [ ] = K w = H O OH 3 Calculate the values of [H + ] and [OH - ] in a neutral solution at 25 o C. Practice Exercise 16.4 Indicate whether solutions with each of the following ion concentrations is neutral, acidic, or basic: a) [H + ] = 4 x 10-9 M b) [OH - ] = 1 x 10-7 M c) [OH - ] = 7 x M Sample Exercise 16.5 (p. 675) Calculate the concentration of H + (aq) in a) a solution in which [OH - ] is M (1.0 x M) b) a solution in which [OH - ] is 1.8 x 10-9 M (5.0 x 10-6 M) Assume T = 25 o C

5 Practice Exercise 16.5 Calculate the concentration of OH - (aq) in a solution in which a) [H + ] = 2 x 10-6 M b) [H + ] = [OH - ] c) [H + ] = 100 x [OH - ] 16.4 The ph Scale In most solutions [H + ] is quite small. We express the [H + ] in terms of ph: ph = log[h + ] = log[h 3 O + ] Sample Exercise 16.6 (p. 677) Calculate the ph values for the two solutions described in Sample Exercise (a) (12.00) b) (5.25) Practice Exercise 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 window-cleaning solution has a [OH - ] of 1.9 x 10-6 M. What is the ph? (8.28) - 5 -

6 Sample Exercise 16.7 (p. 677) A sample of freshly pressed apple juice has a ph of Calculate [H + ]. (1.7 x 10-4 M) Practice Exercise 16.7 A solution formed by dissolving an antacid tablet has a ph of Calculate [H + ]. (6.6 x M) Other p Scales poh = log[oh ] log[h + ]+ ( log[oh ]) = ph + poh = logk w = Measuring ph ph meter. acid-base indicators

7 16.5 Strong Acids and Bases Strong Acids The most common strong acids are HCl, HBr, HI, HNO 3, HClO 3, HClO 4, and H 2 SO 4. MEMORIZE THESE! Strong acids are strong electrolytes and ionize completely in solution: HNO 3 (aq) + H 2 O(l) H 3 O + (aq) + NO 3 (aq) or HNO 3 (aq) H + (aq) + NO 3 (aq) In solution the strong acid is usually the only source of H +. Therefore, the ph of a solution of a monoprotic acid may usually be calculated directly from the initial molarity of the acid. Sample Exercise 16.8 (p. 680) What is the ph of a M solution of HClO 4? (1.40) Practice Exercise 16.8 An aqueous solution of HNO 3 has a ph of What is the concentration of the acid? ( M) Strong Bases The most common strong bases are ionic hydroxides of the alkali metals or the heavier alkaline earth metals (e.g., NaOH, KOH, and Ca(OH) 2 are all strong bases). MEMORIZE THESE Strong bases are strong electrolytes and dissociate completely in solution. For example: NaOH(aq) Na + (aq) + OH (aq) The poh (and thus the ph) of a strong base may be calculated using the initial molarity of the base. Not all bases contain the OH ion. Ionic metal oxides, hydrides, and nitrides are basic. The oxide, hydride and nitride ions are stronger bases than hydroxide. They are thus able to abstract a proton from water and generate OH

8 Sample Exercise 16.9 (p. 680) What is the ph of a) a M solution of NaOH? (12.45) b) a M solution of Ca(OH) 2? (11.34) Practice Exercise 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) 16.6 Weak Acids Weak acids are only partially ionized in aqueous solution: mixture of ions and un-ionized acid in solution. Therefore, weak acids are in equilibrium: HA(aq) + H 2 O(l) H 3 O + (aq) + A (aq) Or HA(aq) H + (aq) + A (aq) We can write an equilibrium constant expression for this dissociation: [ ][ ] + H 3O A Ka = or K [ HA] K a is called the acid-dissociation constant. + [ H ][ A ] [ HA] The larger the K a, the stronger the acid. K a is larger since there are more ions present at equilibrium relative to un-ionized molecules. If K a >> 1, then the acid is completely ionized and the acid is a strong acid. a = - 8 -

9 Calculating Ka from ph In order to find the value of K a, we need to know all of the equilibrium concentrations. The ph gives the equilibrium concentration of H +. Sample Exercise (p. 682) A student prepared a 0.10 M solution of formic acid (HCHO 2 ) and measured its ph. The ph at 25 o C was found to be Calculate the K a for formic acid at this temperature. (1.8 x 10-4 ) - 9 -

10 Practice Exercise Niacin, one of the B vitamins, has the following molecular structure: A M solution of niacin has a ph of What is the acid-dissociation constant, K a, for niacin? (1.5 x 10-5 ) Percent ionization is another method to assess acid strength. For the reaction % ionization = HA(aq) H + (aq) + A (aq) + [ H ] [ HA] equilibrium initial 100 The higher the percent ionization, the stronger the acid. However, we need to keep in mind that percent ionization of a weak acid decreases as the molarity of the solution increases

11 Sample Exercise (p. 684) 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%) Practice Exercise A M solution of niacin has a ph of Calculate the percent ionization of the niacin. (2.7%)

12 Using K a to Calculate ph Using K a, we can calculate the concentration of H + (and hence the ph). 1. Write the balanced chemical equation clearly showing the equilibrium. CH 3 COOH (aq) H + (aq) + CH 3 COO - (aq) 2. Write the equilibrium expression. Look up the value for K a (in a table). K a = [H + ][ CH 3 COO - ] = 1.8 x 10-5 [CH 3 COOH] 3. Write down the initial and equilibrium concentrations for everything except pure water. We usually assume that the equilibrium concentration of H + is x. 4. Substitute into the equilibrium constant expression and solve. K a = 1.8 x 10-5 = [H + ][C 2 H 3 O - 2 ] = (x)(x) [HC 2 H 3 O 2 ] x Note that K a is very small (1.8 x 10-5 ) relative to [HC 2 H 3 O 2 ] (0.30 M). Keep this x x 2 = 1.8 x x Neglect x in the denominator since it is extremely small relative to (Use ballpark figure of 10 3 X difference for neglecting x in the denominator ) x 2 = (1.8 x 10-5 )(0.30) = 5.4 x 10-6 x 2 = (5.4 x 10-6 ) X = 2.3 x 10-3 M = [H + ] Check: Compare x with original [HC 2 H 3 O 2 ] of 0.30 M: 2.3 x 10-3 M x 100% = 0.77%, which is < 5% 0.30 M 5. Convert x ([H + ]) to ph. ph = - log (2.3 x 10-3 ) = 2.64 What do we do if we are faced with having to solve a quadratic equation in order to determine the value of x?

13 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. Sample Exercise (p. 685) Calculate the ph of a 0.20 M solution of HCN. Refer to Table 16.2 for K a. (5.00) Practice Exercise The K a for niacin is 1.6 x What is the ph of a M solution of niacin? (3.41)

14 Sample Exercise (p. 687) Calculate the percentage of HF molecules ionized in a) a 0.10 M HF solution (7.9%) b) a M HF solution (23%) Practice Exercise In Practice Exercise 16.11, we found that the percent ionization of niacin (K a = 1.5 x 10-5 ) in a M solution is 2.7%. Calculate the percentage of niacin molecules ionized in a solution that is a) M (3.9%) b) a 1.0 x 10-3 M (12%)

15 Polyprotic Acids Polyprotic acids have more than one ionizable proton. The protons are removed in successive steps. e.g. H 2 SO 3 (sulfurous acid): H 2 SO 3 (aq) H + (aq) + HSO 3 (aq) K a1 = 1.7 x 10 2 HSO 3 (aq) H + (aq) + SO 3 2 (aq) K a2 = 6.4 x 10 8 It is always easier to remove the first proton in a polyprotic acid than the second: K a1 > K a2 > K a3, etc. The majority of the H + (aq) at equilibrium usually comes from the first ionization (i.e., the K a1 equilibrium). If the successive K a values differ by a factor of 0 3, we can usually get a good approximation of the ph of a solution of a polyprotic acid by only considering the first ionization. Sample Exercise (p. 689) The solubility of CO 2 in pure water at 25 o C and 0.1 atm pressure is M. the common practice is to assume that all of the dissolved CO 2 is in the form of carbonic acid (H 2 CO 3 ), which is produced by reaction between the CO 2 and H 2 O: CO 2(aq) + H 2 O (l) H 2 CO 3(aq) What is the ph of a M solution of H 2 CO 3? (4.40)

16 Practice Exercise (p. 690) a) Calculate the ph of a M solution of oxalic acid (H 2 C 2 O 4 ). (see Table 16.3 for K a1 and K a2 ). b) Calculate the concentration of oxalate ion [C 2 O 2-4 ]. (ph = 1.80; [C 2 O 2-4 ] = 6.4 x 10-5 M)

17 16.7 Weak Bases Weak bases remove protons from substances. There is an equilibrium between the base and the resulting ions: Weak base + H 2 O(l) conjugate acid + OH (aq) Example: NH 3 (aq) + H 2 O(l) NH 4 + (aq) + OH (aq). The base-dissociation constant, K b, is defined as The larger K b, the stronger the base. K b = + [ NH ][ OH ] 4 [ NH 3 ] Sample Problem (p. 691) Calculate the concentration of OH - in a 0.15M solution of NH 3. (1.6 x 10-3 M)

18 Practice Problem Which of the following compounds should produce the highest ph as a 0.05 M solution: pyridine, methylamine, or nitrous acid? (methylamine) 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., CH 3 NH 2 is methylamine). Like NH 3, amines can abstract a proton from a water molecule by forming an additional N-H bond, as shown in this figure for methylamine. 2. Anions of weak acids are also weak bases. e.g.: ClO is the conjugate base of HClO (weak acid): ClO (aq) + H 2 O(l) HClO(aq) + OH (aq) K b = 3.3 x 10 7 Sample Exercise (p. 692) A solution made by adding solid sodium hypochlorite (NaClO) to enough water to make 2.00 L of solution has a ph of How many moles of NaClO were added to the water? (See info immediately above.) (0.60 mol)

19 Practice Exercise A solution of NH 3 in water has a ph of What is the molarity of the solution? (0.12 M)

20 16.8 Relationship Between K a and K b Consider the following equilibria: NH 4 + (aq) NH 3 (aq) + H + (aq) NH 3 (aq) + H 2 O(l) NH 4 + (aq) + OH (aq) We can write equilibrium expressions for these reactions: K a [NH3 ][H ] = + [NH ] 4 If we add these equations together: NH 4 + (aq) NH 3 (aq) + H + (aq) NH 3 (aq) + H 2 O(l) NH 4 + (aq) + OH (aq) The net reaction is the autoionization of water. H 2 O(l) H + (aq) + OH (aq) + [NH 4 ][OH ] = [NH ] Recall that: K w = [H + ][OH ] K a x K b = K w Or pk a + pk b = pk w = (at 25 o C) Thus, the larger K a (and the smaller pk a), the smaller K b (and the larger pk b ). The stronger the acid, the weaker its conjugate base and vice versa. K b Sample Exercise (p. 695) Calculate a) the base-dissociation constant, K b, for the fluoride ion (F - ); (1.5 x ) b) the acid-dissociation constant, K a, for the ammonium ion (NH 4 + ). (5.6 x )

21 Practice Exercise a) Which of the following anions has the largest base-dissociation constant: NO 2 -, PO 4 3-, or N 3 -? (PO 4 3-, K b = 2.4 x 10-2 ) b) The base quinoline has the following structure: Its conjugate acid is listed in handbooks as having a pk a of What is the base-dissociation constant for quinoline? (7.9 x )

22 16.9 Acid-Base Properties of Salt Solutions Acid-base properties of salts are a consequence of the reactions of their ions in solution. An Anion s Ability to React with Water Anions from weak acids are basic: They will cause an increase in ph. Anions from strong acids are neutral. They do not cause a change in ph. Anions with ionizable protons (e.g., HSO 4 ) are amphiprotic. They are capable of acting as an acid or a base. If K a > K b, the anion tends to decrease the ph. If K b > K a, the anion tends to increase the ph. A Cation s Ability to React with Water Polyatomic cations that have 1 or more ionizable protons are conjugate acids of weak bases decrease ph. Metal cations of Group 1A and heavy alkaline earth metals are cations of strong bases and do not alter ph. Other metal ions can cause a decrease in ph. Combined Effect of Cation and Anion in Solution The ph of a solution may be qualitatively predicted using the following guidelines: Salts derived from a strong acid and a strong base are neutral. Examples are NaCl and Ca(NO 3 ) 2. Salts derived from a strong base and a weak acid are basic. Examples are NaClO and Ba(C 2 H 3 O 2 ) 2. Salts derived from a weak base and a strong acid are acidic. An example is NH 4 Cl. Salts derived from a weak acid and a weak base can be either acidic or basic. Equilibrium rules apply! We need to compare K a and K b for hydrolysis of the anion and the cation. For example, consider NH 4 CN. Both ions undergo significant hydrolysis. Is the salt solution acidic or basic? The K a of NH 4 + is smaller than the K b of CN, so the solution should be basic

23 Sample Exercise (p. 698) Determine whether aqueous solutions of each of the following salts will be acidic, basic, or neutral: a) Ba(CH 3 COO) 2, b) NH 4 Cl c) CH 3 NH 3 Br d) KNO 3 e) Al(ClO 4 ) 3 Practice Exercise In each of the following, indicate which salt in each of the following pairs will form the more acidic (or less basic) M solution: a) NaNO 3 or Fe(NO 3 ) 3 b) KBr, or KBrO c) CH 3 NH 3 Cl or BaCl 2 d) NH 4 NO 2 or NH 4 NO

24 Sample Exercise (p. 698) Predict whether the salt Na 2 HPO 4 will form an acidic or a basic solution on dissolving in water. (basic) Practice Exercise Predict whether the dipotassium salt of citric acid (K 2 HC 6 H 5 O 7 ) will form an acidic or basic solution in water. (see Table 16.3 for data) (acidic)

25 16.10 Acid-Base Behavior and Chemical Structure Factors That Affect Acid Strength The H X bond must be polar with H δ+ and X δ-. In ionic hydrides, the bond polarity is reversed. The H X bond is polar with H δ- and X δ+ : the substance is a base. Other factors important in determining acid strength include: The strength of the bond: the H X bond must be weak enough to be broken. The stability of the conjugate base, X : the greater the stability of the conjugate base, the more acidic the molecule. Binary Acids Group trends: The H X bond strength tends to decrease as the element X increases in size. Acid strength increases down a group; base strength decreases down a group. Period trends: Acid strength increases and base strength decreases from left to right across a period as the electronegativity of X increases. Oxyacids Acids that contain OH groups (and often additional oxygen atoms) bound to the central atom All oxyacids have the general structure Y O H, e.g. H 2 SO 4 The strength of the acid depends on Y and the atoms attached to Y. As the electronegativity of Y increases, so does the acidity of the substance. The bond polarity increases and the stability of the conjugate base (usually an anion) increases. Summary: For oxyacids with the same number of OH groups and the same number of oxygen atoms: Acid strength increases with increasing electronegativity of the central atom, Y. Example: HClO > HBrO > HIO For oxyacids with the same central atom, Y: Acid strength increases as the number of oxygen atoms attached to Y increases. Example: HClO 4 > HClO 3 > HClO 2 > HClO

26 Strength of oxyacids Sample Exercise (p.702) Arrange the compounds in each of the following series in order of increasing acid strength: a) AsH 3, HI, NaH, H 2 O; b) H 2 SO 4, H 2 SeO 3, H 2 SeO 4. Practice Exercise In each of the following pairs choose the compound that leads to the more acidic (or less basic) solution: a) HBr, HF; b) PH 3, H 2 S; c) HNO 2, HNO 3 ; d) H 2 SO 3, H 2 SeO 3. Carboxylic Acids There is a large class of acids that contain a COOH group (a carboxyl group). Acids that contain this group are called carboxylic acids: e.g. acetic acid, benzoic acid, formic acid

27 These molecules are acidic because: 1. The additional oxygen atom on the carboxyl group increases the polarity of the O H bond and stabilizes the conjugate base. 2. The conjugate base exhibits resonance. This gives it the ability to delocalize the negative charge over the carboxylate group, further increasing the stability of the conjugate base. The acid strength also increases as the number of electronegative groups in the acid increases. For example, acetic acid is much weaker than trichloroacetic acid. Comparison of Different Types of Acids and Bases 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. Brønsted-Lowry Acids and Bases (1923) Acid: H + (proton) donor Base: H + (proton) acceptor NH 3 + H 2 O + NH 4 + OHammonia water ammonium ion hydroxide ion (B-L base) (B-L acid) (B-L acid) (B-L base) Note: Every Brønsted-Lowry acid/base is also a Lewis acid/base. Lewis Acids and Bases (1920 s) Acid: accepts pair of e- s Base: donates pair of e- s H+ + [:O:H]- H:O:H Lewis acid Lewis base

28 16.11 Lewis Acids and Bases A Brønsted-Lowry acid is a proton donor. Lewis: emphasize the shared electron pair. A Lewis acid is an electron pair acceptor. A Lewis base is an electron pair donor. Note: Lewis acids and bases do not need to contain protons. Therefore, the Lewis definition is the most general definition of acids and bases. What types of compounds can act as Lewis acids? Lewis acids generally have an incomplete octet (e.g., BF 3 ). For a substance to be a proton acceptor (a Brønsted- Lowry base), it must have an unshared pair of electrons for binding the proton. NH 3, for example, acts as a proton acceptor. Using Lewis structures, we can write the reaction between H + and NH 3 as shown in the firugre. Consider the reaction between NH 3 and BF 3. This reaction occurs because BF 3 has a vacant orbital in its valence shell. It therefore acts as an electron-pair acceptor (a Lewis acid) toward NH 3, which donates the electron pair. The curved arrow shows the donation of a pair of electrons from N to B to form a covalent bond. Transition-metal ions are generally Lewis acids. Lewis acids must have a vacant orbital (into which the electron pairs can be donated). Compounds with multiple bonds can act as Lewis acids. For example, consider the reaction: H 2 O(l) + CO 2 (g) H 2 CO 3 (aq) Water acts as the electron pair donor and carbon dioxide as the electron pair acceptor in this reaction. Overall, the water (Lewis base) has donated a pair of electrons to the CO 2 (Lewis acid)

29 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, e.g. Fe(H 2 O) 3+ 6 (aq) Fe(H 2 O) 5 (OH) 2+ (aq) + H + (aq) K a = 2 x In general: The higher the charge, the stronger the M OH 2 interaction: K a values generally increase with increasing charge The smaller the metal ion, the more acidic the ion. K a values generally decrease with decreasing ionic radius Thus the ph of an aqueous solution increases as the size of the ion increases (e.g., Ca 2+ vs. Zn 2+ ) and as the charge increases (e.g., Na + vs. Ca 2+ and Zn 2+ vs. Al 3+ ). The Amphoteric Behavior of Amino Acids Amino acids: building blocks of proteins. Each contains a carboxyl group AND an amine group. Thus amino acids have both acidic and basic groups. They undergo a proton transfer in which the proton of the carboxyl is transferred to the basic nitrogen atom of the amine group A zwitterion or dipolar ion results. Sample Integrative Exercise 16 (p. 706) Phosphorous acid (H 3 PO 3 ) has the following Lewis structure: a) Explain why phosphorous acid is diprotic and not triprotic. b) A 25.0 ml sample of a solution of H 3 PO 3 is titrated with M NaOH. It requires 23.3 ml of NaOH to neutralize both acidic protons. What is the molarity of the H 3 PO 3 solution? c) This solution has a ph of Calculate the percent ionization and K a1 for H 3 PO 3, assuming that K a1 >>K a2. d) How does the osmotic pressure of a M solution of HCl compare qualitatively with that of a M solution of H 3 PO 3? Explain

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