Chapter 15 Aqueous Equilibria: Acids and Bases

Everyday Acids and Bases. Acids: vinegar, lemon juice, sulfuric acid Bases: antacids, ammonia

A. Acid-Base Concepts: The Bronsted-Lowry Theory So far, we’ve discussed the Arrhenius theory of acids and bases: –Acids dissociate to produce H + (examples: HCl, H 2 SO 4 ) –Bases dissociate to produce OH - (examples: NaOH, Ba(OH) 2 ) But -- as some bases don’t contain OH, this is limiting.

Bronsted-Lowry Theory of Acids and Bases An acid is a substance that can transfer H + A base is a substance that can accept H + HA + B BH + + A - Note conjugate acid base acid base acid/base pairs.

Conjugate Pairs… In the previous reaction, A - is the conjugate base of the acid HA B is the conjugate base of the acid HB + HA + B BH + + A - In an acid/base reaction, keep your eye on the proton!

examples Write balanced equations for the dissociation of the following Bronsted-Lowry acids in water: a. H 2 SO 4 b. H 3 O +

Examples -- answer a. H 2 SO 4 + H 2 OHSO H 3 O + b. H 3 O + + H 2 OH 2 O + H 3 O + BOOKKEEPING -- be able to label acid, base, conjugate acid, conjugate base! (by convention, CA/CB are on the product side)

Examples What is the conjugate acid of… a. HCO 3 - b. CO 3 2-

Examples -- answers a. H 2 CO 3 b. HCO 3 -

B. Acid Strength and Base Strength Think of the acid-base reaction as a “tug of war” between the two bases for a proton: HA + H 2 OH 3 O + + A - Which is the stronger base: H 2 O or A - ? Which wants the proton more? This will determine whether the equilibrium lies more to the right or to the left.

Acid/Base Strength cont. If H 2 O is a stronger proton acceptor than A -, H 2 O will get the protons, and the solution will mostly contain H 3 O + and A -. Conversely, if A - is the stronger proton acceptor,, the solution will mostly contain HA and H 2 O. **The proton is always transferred to the stronger base.

Acid/Base Strength: Equilibrium The strength of the acids and bases in an acid-base reaction will dictate the position of the equilibrium in an acid-base reaction. HA + H 2 O A - + H 3 O + if this is the strongerthe equilibrium will lie to the right acid Because a strong acid will dissociate more thoroughly/completely.

What does it mean to be a strong acid? Almost completely dissociated in water Equilibrium almost entirely to the right Solution consists almost entirely of H 3 O + and A - ions - - almost no HA molecules Strong acids have very weak conjugate bases. If HA has a strong tendency to lose its proton, A - will not be a good proton acceptor.

What does it mean to be a weak acid? Only partially dissociated in water. Solution contains mostly undissociated HA. Not much H 3 O + and A - ion present in solution. Equilibrium lies toward left. Weak acids have strong conjugate bases. If HA does not have a strong tendency to lose its proton, A - will be a good proton acceptor.

C. Hydrated Protons and Hydronium Ions H + does not exist by itself in aqueous solution, despite the fact that you frequently will see H + (aq) in acid- base equilibria. In aqueous solution, H + binds to a water molecule to form H 3 O + ==> hydronium ion.

D. Dissociation of Water Water can act either as an acid or base, depending on the situation. If acid is present, water is a base: HA + H 2 OA - + H 3 O + If base is present, water is an acid: B + H 2 OHB + OH -

Dissociation of Water cont. Or, water can act as both an acid and a base! H 2 O + H 2 OH 3 O + + OH - acid base This process is referred to as the dissociation of water, and has a dissociation constant, K w.

Dissociation of Water cont. For the dissociation of water, K w = [H 3 O + ][OH - ] Remember that pure liquids, such as H 2 O, are not included in equilibrium expressions. = equilibrium constant for the dissociation of water (also referred to as the ion product constant for water)

Dissociation of Water cont. Very little of water is ionized; the equilibrium lies far to the left. At 25 o C, [H 3 O + ] = [OH - ] = 1.0 * M so K w = [H 3 O + ][OH - ] = 1.0 * M **This is true for any aqueous solution at 25 o C.

[H 3 O + ] vs. [OH - ] Defining acidic/basic/neutral solutions: In an acidic solution, [H 3 O + ] > [OH - ] In a basic solution, [H 3 O + ] < [OH - ] In a neutral solution, [H 3 O + ] = [OH - ]

example The concentration of OH - in a sample of 25 o C seawater is 5.0 * M. Calculate the concentration of H 3 O + ions, and classify the solution as acidic, neutral, or basic.

Example -- answer K w = [H 3 O + ][OH - ] At 25 o C, K w = 1.0 * M Given [OH - ] = 5.0 * M Solve for [H 3 O + ] [H 3 O + ] = K w /[OH - ] = (1.0 * )/(5.0 * ) = 2 * M Since [OH - ] > [H 3 O + ] -- basic

E. The pH Scale pH is a more convenient way to express the concentration of hydronium ion in a solution. pH = -log[H 3 O + ] pH < 7 -- acidic pH > 7 -- basic pH = 7 -- neutral

example Calculate the pH of a solution that has an [H 3 O+] of 6.0 * M.

Example -- answer If pH = -log (6.0 * ) then pH = 4.22 This solution is acidic.

F. Measuring pH Color indicators are often used for approximation Examples: phenolphthalein (changes from colorless --> pink when going from acidic --> basic), bromothymol blue However, pH meters give you a more precise number, measuring the electrical potential of the solution (chapter 18)

G. Equilibria in Solutions of Weak Acids Beware: a weak acid is not the same thing as a dilute solution of a strong acid! Even when dilute, the equilibrium for the strong acid will lie to the right (not for the weak acid)

Equilibrium Constant for a Weak Acid Dissociation For the reaction HA(aq) + H 2 O(l) H 3 O + (aq) + A - (aq) K a = [H 3 O + ][A - ]/[HA] In dilute aqueous solution, [H 2 O] is essentially constant. pK a = -log K a

example The pH of 0.10 M HOCl is Calculate K a for hypochlorous acid. How close did you come to the true value?

Example -- answer K a = [H 3 O + ][ - OCl]/[HOCl] [H 3 O + ] = 10 -pH = = 5.89 * M = [-OCl] [HOCl] = * = M K a = (5.89 * ) 2 / = 3.47 * 10 -8

H. Calculating Equilibrium Concentrations in Solutions of Weak Acids How are K a values useful? Allows us to calculate the pH of an acidic solution, as well as equilibrium concentrations of all species present Example: Calculate concentrations of all species present, and the pH of, a 0.10 M HCN solution.

Concentration of all species in 0.10 M HCN soln. Step 1 List species present before any dissociation happens, and identify them as either acid or base. HCNH 2 O acidacid or base

Concentration of… in 0.10 M HCN cont. Step 2 What proton transfer reactions can occur, given the aforementioned molecules? HCN + H 2 OH 3 O + + CN - K a = 4.9 * H 2 O + H 2 OH 3 O + + OH - K w = 1.0 * **K a values in Table 15.2

Concentration of… in 0.10 M HCN cont. Step 3 Label the reaction that proceeds farther to the right (larger equilibrium constant) as the principal reaction; the other reaction(s) is the subsidiary reaction. HCN reaction: principal dissociation of water: subsidiary

Concentration of… in 0.10 M HCN cont. Step 4 Create an ICE table, expressing changes in concentration in terms of x. Principal rxnHCN + H 2 OH 3 O + + CN Initial (M)0.10 ~0 0 Change (M)-x +x +x Equil. (M) x x x H 2 O is not part of the equilibrium expression, and is present in excess.

Concentration of… in 0.10 M HCN cont. Step 5 Place the equilibrium values into the K a expression. K a = 4.9 * = [H 3 O + ][CN - ]/[HCN] = (x)(x)/( x)

Concentration of… in 0.10 M HCN cont. Step 5 continued In this particular case -- K a is small. This means the reaction does not proceed very far to the right. If this is the case, x is small, and to simplify our math, we can say that ( x) ~ 0.10 and 4.9 * ~ x 2 /0.10 Thus x 2 = 4.9 * and x = 7.0 * 10 -6

Concentration of… in 0.10 M HCN cont. Step 6 Now, you can use x to find all equilibrium concentrations. [H 3 O + ] = [CN - ] = x = 7.0 * M [HCN] = x = 0.10 M **x was small/negligible here. This is not always the case!

Concentration of… in 0.10 M HCN cont. Step 7 The only concentration left to calculate is [OH - ] from the subsidiary reaction. [OH - ] = K w /[H 3 O + ] = 1.0* /7.0*10 -6 = 1.4 * M Since [H 3 O + ] from the dissociation of water is also 1.4*10 -9 M, our assumption in the ICE table that [H 3 O + ] = 0 was valid.

Concentration of… in 0.10 M HCN cont. Step 8 Finally… calculate pH! pH = -log [H 3 O + ] = -log (7.0*10 -6 ) =5.15

J. Percent Dissociation in Solutions of Weak Acids Another way to measure/express acid strength: percent dissociation. The stronger the acid, the more dissociated it will be in aqueous solution. percent dissociation = ([HA] dissoc./[HA] initial) * 100%

K. Polyprotic Acids Are acids that contain more than one dissociable proton Examples: H 2 SO 4 H 3 PO 4 Dissociate in a stepwise manner, and each dissociation step has its own K a Note that each successive K a value decreases. After the first proton is removed, the remaining conjugate base will have a negative charge, making the next proton harder to remove.

L. Equilibria in Solutions of Weak Bases Consider the reaction NH 3 (aq) + H 2 O(l) NH 4 + (aq) + OH - (aq) There is a base-dissociation constant similar to that for an acid: K b = [BH + ][OH - ]/[B] = [NH 4 + ][OH - ]/[NH 3 ]

Weak Bases… cont. Weak bases are frequently amines Amines are derivatives of ammonia where one or more of the H has been replaced by a hydrocarbon group

example Calculate the pH and the concentrations of all species present in 0.40 M NH 3 (K b = 1.8 * ). Step 1 What species are present prior to dissociation? NH 3 H 2 O baseacid or base

Example -- cont Step 2/3 Seeing that K b for NH 3 is 1.8 * 10 -5, this is considered the principal reaction (as opposed to K w ) Step 4 NH 3 + H 2 O NH 4 + OH Initial(M) ~0 Change(M) -x +x +x Equil.(M) 0.40-x x x

Example -- cont. Step 5 K b = [NH 4 + ][OH - ]/[NH 3 ] = x 2 /0.40-x ~x 2 /0.40 =1.8 * x = 2.7 * M = [NH 4 + ] = [OH - ] [NH 3 ] = x = 0.40 M

Example -- cont [H 3 O + ] = K w /[OH - ] = 1.0 * /2.7 * = 3.7 * M Use this information to determine pH pH = -log[H 3 O + ] = -log(3.7 * ) = makes sense… NH 3 is basic!

M. Relationship Between K a and K b When dealing with a conjugate pair, you can calculate one from the other. Consider the following… NH 4 + (aq) + H 2 O(l) H 3 O + (aq) + NH 3 (aq) NH 3 (aq) + H 2 O(l) NH 4 + (aq) + OH - (aq) H 2 O(l) H 3 O + (aq) + OH - (aq)

K a and K b cont. Also consider equilibrium constants K a = [H 3 O + ][NH 3 ]/[NH 4 + ] = 5.6 * K b = [NH 4 + ][OH - ]/[NH 3 ] = 1.8 * and K w = [H 3 O + ][OH - ] = 1.0 * Net equilibrium constant of two reactions when added: K a * K b

K a and K b cont. In general, when you add two chemical reaction together, the net equilibrium constant is the product of the two individual equilibrium constants. K a * K b = (5.6 * )(1.8 * ) = 1.0 * = [H 3 O + ][NH 3 ]/[NH 4 + ] * [NH 4 + ][OH - ]/[NH 3 ] In aqueous solution, K a * K b = K w

N. Factors That Affect Acid Strength What makes one acid stronger than another? Often determined by strength and polarity of the H-A bond. How easily is the H-A bond broken? The more easily the bond is broken, the stronger the acid.

Acid Strength cont. How easily is the H-A bond broken? –The weaker the H-A bond, the more easily it is broken. –The more polar the H-A bond, the more easily the bond is broken. In a more polar bond, A is more electronegative. After the H-A bond is broken, A bears the negative charge. The more electronegative A is, the more stable A is in bearing the negative charge. The more easily the H-A bond is broken, the stronger the acid.

Acid Strength cont. Bond strength is the prevalent factor in groups(columns). As you go down a group on the periodic table, acid strength increases (HI is a stronger acid than HF, etc). This is due to atomic radius increasing and bond strength decreasing farther down the periodic table.

Acid Strength cont. Polarity is the prevalent factor comparing within a row. Within the same row of the periodic table, atomic radius does not appreciably change, but electronegativity increases going right. When H is bonded to a more EN atom, the acid is stronger. An -OH containing molecule is more acidic than an -NH containing molecule.

Strength of Oxoacids Oxoacid: contains an -OH bond, which also contains the acidic H Anything that might weaken the O-H bond increases the strength of the acid. Case 1 Increase EN of Y, increase acid strength. Shifts electron density toward Y. | --Y--O--HO will “feel” less negative charge | when Y is more EN = greater stability.

Strength of Oxoacids cont. Case 1 cont. Examples… HOCl > HOBr >HOI Case 2 If the identity of Y stays the same but more bonds are added to O, acid strength will also increase. perchloric acid > hypochlorous acid

Strength of Oxoacids cont. To continue the example… H-O-Cl is weaker than H-O-Cl-O which is weaker than O |The additional EN O’s draw H-O-Cl-Oelectron density away from the site of deprotonation.

Acid Strength Any time you’re considering the strength of an acid, think about the stability of the corresponding anion. If the corresponding anion (conjugate base) is particularly stable, the acid is more likely to dissociate. If there are more EN atoms nearby, there are more places to distribute the negative charge resulting from deprotonation. This results in a more stable anion.

O. Lewis Acids and Bases Another, more generalized, acid/base definition. Lewis acid: electron pair acceptor Lewis base: electron pair donor Lewis acids are frequently metal cations.

Lewis Acids and Bases Example: Cu :NH 3 --> Cu(NH 3 ) 4 2+ LewisLewiscomplex ion acidbase(deep blue)