Aqueous Equilibria:

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Chapter 15

• Aqueous Equilibria
• Acids and Bases

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Everyday Acids and Bases.

• Acids vinegar, lemon juice, sulfuric acid
• Bases antacids, ammonia

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A. Acid-Base Concepts The Bronsted-Lowry Theory

• So far, weve discussed the Arrhenius theory of
  acids and bases
• Acids dissociate to produce H (examples HCl,
  H2SO4)
• Bases dissociate to produce OH- (examples NaOH,
  Ba(OH)2 )
• But -- as some bases dont contain OH, this is
  limiting.

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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.

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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!

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examples

• Write balanced equations for the dissociation of
  the following Bronsted-Lowry acids in water
• a. H2SO4
• b. H3O

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Examples -- answer

• H2SO4 H2O HSO4- H3O
• H3O H2O H2O H3O
• BOOKKEEPING -- be able to label acid, base,
  conjugate acid, conjugate base! (by convention,
  CA/CB are on the product side)

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Examples

• What is the conjugate acid of
• HCO3-
• CO32-

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Examples -- answers

• H2CO3
• HCO3-

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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 H2O H3O A-
• Which is the stronger base H2O or A-? Which
  wants the proton more? This will determine
  whether the equilibrium lies more to the right
  or to the left.

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Acid/Base Strength cont.

• If H2O is a stronger proton acceptor than A-, H2O
  will get the protons, and the solution will
  mostly contain H3O and A-.
• Conversely, if A- is the stronger proton
  acceptor,, the solution will mostly contain HA
  and H2O.
• The proton is always transferred to the
  stronger base.

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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 H2O A- H3O
• if this is the stronger the equilibrium will
  lie to the right
• acid
• Because a strong acid will dissociate more
  thoroughly/completely.

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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 H3O 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.

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What does it mean to be a weak acid?

• Only partially dissociated in water.
• Solution contains mostly undissociated HA.
• Not much H3O 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.

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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 H3O gt hydronium ion.

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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 H2O A- H3O
• If base is present, water is an acid
• B H2O HB OH-

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Dissociation of Water cont.

• Or, water can act as both an acid and a base!
• H2O H2O H3O OH-
• acid base
  acid base
• This process is referred to as the dissociation
  of water, and has a dissociation constant, Kw.

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Dissociation of Water cont.

• For the dissociation of water,
• Kw H3OOH-
• Remember that pure liquids, such as H2O, are
  not included in equilibrium expressions.
• equilibrium constant for the dissociation of
  water (also referred to as the ion product
  constant for water)

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Dissociation of Water cont.

• Very little of water is ionized the equilibrium
  lies far to the left.
• At 25oC, H3O OH- 1.0 10-7 M
• so
• Kw H3OOH- 1.0 10-14 M
• This is true for any aqueous solution at 25oC.

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H3O vs. OH-

• Defining acidic/basic/neutral solutions
• In an acidic solution, H3O gt OH-
• In a basic solution, H3O lt OH-
• In a neutral solution, H3O OH-

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example

• The concentration of OH- in a sample of 25oC
  seawater is 5.0 10-6 M. Calculate the
  concentration of H3O ions, and classify the
  solution as acidic, neutral, or basic.

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Example -- answer

• Kw H3OOH-
• At 25oC, Kw 1.0 10-14 M
• Given OH- 5.0 10-6 M
• Solve for H3O
• H3O Kw/OH-
• (1.0 10-14)/(5.0 10-6)
• 2 10-9 M
• Since OH- gt H3O -- basic

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E. The pH Scale

• pH is a more convenient way to express the
  concentration of hydronium ion in a solution.
• pH -logH3O
• pH lt 7 -- acidic
• pH gt 7 -- basic
• pH 7 -- neutral

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example

• Calculate the pH of a solution that has an H3O
  of 6.0 10-5 M.

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Example -- answer

• If pH -log (6.0 10-5)
• then pH 4.22
• This solution is acidic.

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F. Measuring pH

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

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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)

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Equilibrium Constant for a Weak Acid Dissociation

• For the reaction
• HA(aq) H2O(l) H3O(aq) A-(aq)
• Ka H3OA-/HA
• In dilute aqueous solution, H2O is essentially
  constant.
• pKa -log Ka

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example

• The pH of 0.10 M HOCl is 4.23. Calculate Ka for
  hypochlorous acid. How close did you come to the
  true value?

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Example -- answer

• Ka H3O-OCl/HOCl
• H3O 10-pH 10-4.23 5.89 10-5 M
• -OCl
• HOCl 0.10 - 5.89 10-5 0.0999 M
• Ka (5.89 10-5)2/0.0999 3.47 10-8

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H. Calculating Equilibrium Concentrations in
Solutions of Weak Acids

• How are Ka 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.

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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.
• HCN H2O
• acid acid or base

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Concentration of in 0.10 M HCN cont.

• Step 2 What proton transfer reactions can occur,
  given the aforementioned molecules?
• HCN H2O H3O CN-
• Ka 4.9 10-10
• H2O H2O H3O OH-
• Kw 1.0 10-14
• Ka values in Table 15.2

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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

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Concentration of in 0.10 M HCN cont.

• Step 4 Create an ICE table, expressing changes
  in concentration in terms of x.
• Principal rxn HCN H2O H3O CN-
• --------------------------------------------------
  --------------------------------------------------
  ------------------
• Initial (M) 0.10 0
  0
• Change (M) -x x
  x
• Equil. (M) 0.10 - x
  x x
• H2O is not part of the equilibrium expression,
  and is present in excess.

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Concentration of in 0.10 M HCN cont.

• Step 5 Place the equilibrium values into the Ka
  expression.
• Ka 4.9 10-10 H3OCN-/HCN
• (x)(x)/(0.10 - x)

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Concentration of in 0.10 M HCN cont.

• Step 5 continued In this particular case -- Ka
  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 (0.10 - x) 0.10
• and 4.9 10-10 x2/0.10
• Thus x2 4.9 10-11 and x 7.0 10-6

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Concentration of in 0.10 M HCN cont.

• Step 6 Now, you can use x to find all
  equilibrium concentrations.
• H3O CN- x 7.0 10-6 M
• HCN 0.10 - x 0.10 M
• x was small/negligible here. This is not
  always the case!

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Concentration of in 0.10 M HCN cont.

• Step 7 The only concentration left to calculate
  is OH- from the subsidiary reaction.
• OH- Kw/H3O 1.010-14/7.010-6
• 1.4 10-9 M
• Since H3O from the dissociation of water is
  also 1.410-9 M, our assumption in the ICE table
  that H3O 0 was valid.

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Concentration of in 0.10 M HCN cont.

• Step 8 Finally calculate pH!
• pH -log H3O
• -log (7.010-6)
• 5.15

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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

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K. Polyprotic Acids

• Are acids that contain more than one dissociable
  proton
• Examples H2SO4 H3PO4
• Dissociate in a stepwise manner, and each
  dissociation step has its own Ka
• Note that each successive Ka value decreases.
  After the first proton is removed, the remaining
  conjugate base will have a negative charge,
  making the next proton harder to remove.

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L. Equilibria in Solutions of Weak Bases

• Consider the reaction
• NH3(aq) H2O(l) NH4(aq) OH-(aq)
• There is a base-dissociation constant similar
  to that for an acid
• Kb BHOH-/B NH4OH-/NH3

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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

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example

• Calculate the pH and the concentrations of all
  species present in 0.40 M NH3 (Kb 1.8 10-5).
• Step 1 What species are present prior to
  dissociation?
• NH3 H2O
• base acid or base

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Example -- cont

• Step 2/3 Seeing that Kb for NH3 is 1.8 10-5,
  this is considered the principal reaction (as
  opposed to Kw)
• Step 4
• NH3 H2O NH4
  OH-
• --------------------------------------------------
  --------------------------------------------------
  ------
• Initial(M) 0.40 0 0
• Change(M) -x x x
• Equil.(M) 0.40-x
  x x

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Example -- cont.

• Step 5
• Kb NH4OH-/NH3 x2/0.40-x x2/0.40
• 1.8 10-5
• x 2.7 10-3 M NH4 OH-
• NH3 0.40 - x 0.40 M

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Example -- cont

• H3O Kw/OH-
• 1.0 10-14/2.7 10-3
• 3.7 10-12 M
• Use this information to determine pH
• pH -logH3O -log(3.7 10-12) 11.43
• makes sense NH3 is basic!

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M. Relationship Between Ka and Kb

• When dealing with a conjugate pair, you can
  calculate one from the other. Consider the
  following
• NH4(aq) H2O(l) H3O(aq)
  NH3(aq)
• NH3(aq) H2O(l) NH4(aq)
  OH-(aq)
• --------------------------------------------------
  ------------------
• 2 H2O(l) H3O(aq) OH-(aq)

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Ka and Kb cont.

• Also consider equilibrium constants
• Ka H3ONH3/NH4 5.6 10-10
• Kb NH4OH-/NH3 1.8 10-5
• and Kw H3OOH- 1.0 10-14
• Net equilibrium constant of two reactions when
  added Ka Kb

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Ka and Kb cont.

• In general, when you add two chemical reaction
  together, the net equilibrium constant is the
  product of the two individual equilibrium
  constants.
• Ka Kb (5.6 10-10)(1.8 10-5) 1.0
  10-14
• H3ONH3/NH4 NH4OH-/NH3
• In aqueous solution, Ka Kb Kw

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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.

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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.

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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.

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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.

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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--H O will feel less
  negative charge
• when Y is more EN greater
• stability.

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Strength of Oxoacids cont.

• Case 1 cont.
• Examples HOCl gt HOBr gtHOI
• Case 2
• If the identity of Y stays the same but more
  bonds are added to O, acid strength will also
  increase.
• perchloric acid gt hypochlorous acid

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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 Os draw
• H-O-Cl-O electron density away from the
  site of deprotonation.

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Acid Strength

• Any time youre 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.

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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.

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Lewis Acids and Bases

• Example
• Cu2 4 NH3 --gt Cu(NH3)42
• Lewis Lewis complex ion
• acid base (deep blue)