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Lecture Presentation
Chapter 16
Aqueous Ionic
Equilibrium
Sahil Gahlawat
Narayana IIT-PMT Academy

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• Most brands of antifreeze contain ethylene
glycol
...


Why Is Glycolic Acid Toxic?
• In high enough concentration in the bloodstream,
glycolic acid overwhelms the buffering ability of the
HCO3− in the blood, causing the blood pH to drop
...


– Acidosis

HbH+(aq) + O2(g)  HbO2(aq) + H+(aq)

• One treatment is to give the patient ethyl alcohol,
which has a higher affinity for the enzyme that
catalyzes the metabolism of ethylene glycol
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Buffer Solutions
• Resist changes in pH when an acid or base is
added
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• Contain either
– Significant amounts of a weak acid and its conjugate base
– Significant amounts of a weak base and its conjugate acid
– Blood has a mixture of H2CO3 and HCO3−

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NaOH(aq) + HC2H3O2(aq)  H2O(l) + NaC2H3O2(aq)

• If the amount of NaOH added is less than the
amount of acetic acid present, the pH change is
small
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An Acidic Buffer Solution
• If a strong acid is added, it is neutralized by the
conjugate base (NaC2H3O2) in the buffer
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• Buffer solutions contain significant amounts of the weak
acid molecules, HA
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HA(aq) + OH−(aq) → A−(aq) + H2O(l)
– You can also think of the H3O+ combining with the OH−
to make H2O; the H3O+ is then replaced by the shifting
equilibrium
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How Buffers Work

H2O

new
A−

HA
HA



Added
HO−
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• These ions combine with added acid to make
more HA
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−
A−

+

H3O+

Common Ion Effect
HA(aq) + H2O(l)  A−(aq) + H3O+(aq)
• Adding a salt containing the anion NaA, which is
the conjugate base of the acid (the common ion),
shifts the position of equilibrium to the left
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Henderson–Hasselbalch Equation
• An equation derived from the Ka expression that
allows us to calculate the pH of a buffer solution
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Deriving the Henderson–Hasselbalch
Equation

Taking the logarithm of both sides and expanding since
log (AB) = log A + log B

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Deriving the Henderson–Hasselbalch
Equation
HA(aq) + H2O(l)  H3O+(aq) + A-(aq)
Since pH = –log[H3O+] and pKa = logKa
pH = pKa + log([A–]/[HA) (see page 758)
We can then generalize as follows:

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•

Generally, the “x is small” approximation will work when
both of the following are true:
a) The initial concentrations of acid and salt are not
very dilute
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•

For most problems, this means that the initial acid and
salt concentrations should be over 100 to 1000 times
larger than the value of Ka
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How Much Does the pH of a Buffer Change
When an Acid or Base Is Added?
•

Calculating the new pH after adding acid or base requires
breaking the problem into two parts:
1
...

 Added acid reacts with the A− to make more HA
 Added base reacts with the HA to make more A−
2
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Action of a Buffer

Figure 16
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Basic Buffers
B:(aq) + H2O(l)  H:B+(aq) + OH−(aq)
• Buffers can also be made by mixing a weak
base, (B:), with a soluble salt of its conjugate
acid, H:B+Cl−
H2O(l) + NH3 (aq)  NH4+(aq) + OH−(aq)

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The chemical equation of a basic buffer is written with a
weak base as a reactant and its conjugate acid as a
product
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H:B+ + H2O  B: + H3O+


This does not affect the concentrations, just the way we are looking
at the reaction
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Relationship between pKa and pKb

• Just as there is a relationship between the Ka of a
weak acid and Kb of its conjugate base, there is
also a relationship between the pKa of a weak acid
and the pKb of its conjugate base
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0 x 10−14
−log(Ka  Kb) = −log(Kw) = 14
−log(Ka) + −log(Kb) = 14
pKa + pKb = 14

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The chemical equation of a basic buffer is written
with a weak base as a reactant and its conjugate
acid as a product
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• However, there is a limit to how much can be
added before the pH changes significantly
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• The buffering range is the pH range the buffer
can be effective
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– Equal concentrations of acid and base

• A buffer will be effective when
0
...

• A buffer will be most effective when the [acid]
and the [base] are large
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Buffering Range
• We have said that a buffer will be effective when
0
...

• Substituting into the Henderson–Hasselbalch
equation we can calculate the maximum and
minimum pH at which the buffer will be effective
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When choosing an acid to make a buffer, choose
one whose pKa is closest to the pH of the buffer
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Buffering Capacity

• Buffering capacity is the amount of acid or base
that can be added to a buffer without causing a
large change in pH
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• Buffers that need to work mainly with added acid
generally have [base] > [acid]
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– When the reaction is complete we have reached the
endpoint of the titration
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– An indicator is a chemical that changes color when the
pH changes
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Titration Curve
• It is a plot of pH versus the amount of added titrant
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• Prior to the equivalence point, the known solution in
the flask is in excess, so the pH is closest to its pH
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– Equivalence point of neutral salt, pH = 7
– Equivalence point of acidic salt, pH < 7
– Equivalence point of basic salt, pH > 7

• Beyond the equivalence point, the unknown solution in
the burette is in excess, so the pH approaches its pH
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Titration Curve: Strong Base
Added to Strong Acid

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• The initial pH is determined using the Ka of the
weak acid
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• The pH at the equivalence point is determined
using the Kb of the conjugate base of the weak acid
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– The basicity from the conjugate base anion is negligible
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Titrating Weak Acid with a Strong Base
• The initial pH is that of the weak acid solution
...
5 and 15
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– Calculate mol HAinit and mol A−init using reaction
stoichiometry
– Calculate pH with Henderson–Hasselbalch using mol HAinit
and mol A−init

• Half-neutralization pH = pKa

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– Mol A− = original mole HA

• Calculate the volume of added base as you did in
Example 4
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– [A−]init = mol A−/total liters
– Calculate like a weak base equilibrium problem

• For example, 15
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– [OH−] = mol MOH xs/total liters
– [H3O+][OH−] = 1 × 10−14

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Titration of a Polyprotic Acid
• If Ka1 >> Ka2, there will be two equivalence points
in the titration
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Titration of 25
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100 M
H2SO3 with 0
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Monitoring pH During a Titration
• The general method for monitoring the pH during
the course of a titration is to measure the
conductivity of the solution due to the [H3O+]
...

• If you just need to know the amount of titrant
added to reach the endpoint, we often monitor the
titration with an indicator
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Monitoring pH During a Titration

Figure 16
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Indicators
• Many dyes change color depending on the pH of the
solution
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HInd(aq) + H2O(l)  Ind(aq) + H3O+(aq)

• The color of the solution depends on the relative
concentrations of Ind:Hind
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– When Ind:HInd > 10, the color will be a mix of the
colors of Ind
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1, the color will be a mix of the
colors of Hind
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Phenolphthalein

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Monitoring a Titration with an
Indicator
• For most titrations, the titration curve shows a
very large change in pH for very small additions
of titrant near the equivalence point
...

– pKa of HInd ≈ pH at equivalence point

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1 pg 783

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– However, many compounds have such low solubility in
water that we classify them as insoluble
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• For an ionic solid MnXm, the dissociation reaction is
MnXm(s)  nMm+(aq) + mXn−(aq)
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• For example, the dissociation reaction for PbCl2 is
PbCl2(s)  Pb2+(aq) + 2 Cl−(aq)
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Molar Solubility
• Solubility is the amount of solute that will dissolve in
a given amount of solution at a particular
temperature
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– The molarity of the dissolved solute in a saturated solution

For the general reaction MnXm(s)  nMm+(aq) + mXn−(aq)

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• But you cannot always compare solubilities of
compounds by comparing their Ksps
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• For example, addition of NaCl to the solubility
equilibrium of solid PbCl2 decreases the
solubility of PbCl2
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– And the lower the pH, the higher the solubility
– Higher pH = increased [OH−]

M(OH)n(s)  Mn+(aq) + nOH−(aq)
• For insoluble ionic compounds that contain anions
of weak acids, the lower the pH, the higher the
solubility
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Precipitation
• Precipitation will occur when the concentrations of
the ions exceed the solubility of the ionic
compound
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– Q = Ksp, the solution is saturated, no precipitation
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– Q > Ksp, the solution would be above saturation, the salt
above saturation will precipitate
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Selective Precipitation
• A solution containing several different cations
can often be separated by addition of a reagent
that will form an insoluble salt with one of the
ions, but not the others
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– Wet chemistry

• A sample containing several ions is subjected to
the addition of several precipitating agents
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A General Qualitative Analysis Scheme
Figure 16
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Group 1
• Group one cations are Ag+, Pb2+, and Hg22+
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– As long as the concentration is large enough
– PbCl2 may be borderline

• Molar solubility of PbCl2 = 1
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Group 2
• Group two cations are Cd2+, Cu2+, Bi3+, Sn4+, As3+,
Pb2+, Sb3+, and Hg2+
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• Precipitated by the addition of H2S in HCl
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Group 3

• Group three cations are Fe2+, Co2+, Zn2+, Mn2+,
Ni2+ precipitated as sulfides, as well as Cr3+, Fe3+,
and Al3+ precipitated as hydroxides
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• Precipitated by the addition of H2S in NaOH
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Group 4

• Group four cations are Mg2+, Ca2+, Ba2+
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• Precipitated by the addition of (NH4)2HPO4
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Group 5
• Group five cations are Na+, K+, NH4+
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• They are identified by the color of their flame
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Complex Ion Formation
• Transition metals tend to be good Lewis acids
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– H2O is the Lewis base, donating electron pairs to form
coordinate covalent bonds
...

– For example, Ag(H2O)2+

• The attached ions or molecules are called ligands
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Complex Ion Equilibria

• If a ligand is added to a solution that forms a
stronger bond than the current ligand, it will replace
the current ligand
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Ag+(aq) + 2 NH3(aq)  Ag(NH3)2+(aq)

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Ag+(aq) + 2 NH3(aq)  Ag(NH3)2+(aq)
• The equilibrium constant for the formation reaction
is called the formation constant, Kf
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Formation Constants

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AgCl(s)  Ag+(aq) + Cl−(aq)
Ksp = 1
...
7 × 107
• Adding NH3 to a solution in equilibrium with AgCl(s)
increases the solubility of Ag+
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Figure 16
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Solubility of Amphoteric Metal Hydroxides
• Many metal hydroxides are insoluble
...

– Shifting the equilibrium to the right by removing OH−

• Some metal hydroxides also become more soluble
in basic solution
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• Some cations that form amphoteric hydroxides
include Al3+, Cr3+, Zn2+, Pb2+, and Sb2+
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Al3+

• Al3+ is hydrated in water to form an acidic solution
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Al(H2O)5(OH)2+(aq) + OH−(aq)  Al(H2O)4(OH)2+(aq) + H2O (l)
Al(H2O)4(OH)2+(aq) + OH−(aq)  Al(H2O)3(OH)3(s) + H2O (l)

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