SKKU Physical Pharmacy...
Transcript of SKKU Physical Pharmacy...
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Solution : a liquid in which a solid substance has been
dissolved.
• Solute : a solid substance that is dissolved in a liquid.
• Solvent : a liquid that can dissolve other substances.
Solubility :
• the concentration of solute in a saturated solution at
equilibrium at a given temperature
• given as per weight or volume of solvent
g (solute) / 100g (solvent)
1g (solute) / volume (ml) of solvent
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Solubility (continue)
• Unbuffered solubility
• Water solubility
• Buffered solubility
• Intrinsic solubility (cf. dissolution - extrinsic property)
• solubility of an ionizable compound in its neutral form
(the molar solubility of the undissociated acid S0)
• Thermodynamic solubility
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Saturated Solutionthe solute is in equilibrium with the solid phase
Unsaturated or Subsaturated Solutionone containing the dissolved solute in a concentration
that necessary for complete saturation at a definite
temperature
Supersaturated Solution one that contains more of the dissolved solute than it
would normally contain at a definite temperature
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Miscible
when a solute is a liquid and will form a solution with a
solvent over any concentration range
The Phase RuleF = C – P + 2
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Description Forms
(Solubility Definition)
Parts of Solvent
Required
for One Part of Solute
Solubility Range
(mg/mL)
Solubility Assigned
(mg/mL)
Very soluble(VS) <1 >1,000 1,000
Freely soluble(FS) From 1 to 10 100 - 1000 100
Soluble From 10 to 30 33 - 100 33
Sparingly soluble(SPS) From 30 to 100 10 - 33 10
Slightly soluble(SS) From 100 to 1,000 1 - 10 1
Very slightly soluble(VSS) From 1,000 to 10,000 0.1 - 1 0.1
Practically insoluble(PI) >10,000 <0.1 0.01
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
USP Chart of Descriptive terms
TermParts solvent to 1 part
solute
Very soluble Less than 1
Freely soluble 1-10 (3-10%)
Soluble 10-30
Sparingly soluble 30-100
Slightly soluble 100-1000
Very slightly soluble 1000-10,000
Practically insoluble, insoluble
More than 10,000
용어
썩 잘 녹는다
잘 녹는다
녹는다
조금 녹는다
녹이 어렵다
매우 녹기 어렵다
거의 녹지 않는다
대한약전 제 11개정
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Temperature
Pressure
pH
Common Ion Effects
Chemical Structures- Dipole moment
- Dielectric properties
- Hydrogen bonding
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
“Like Dissolves Like”
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Polar Solvents
Nonpolar Solvents
Semipolar Solvents
Hydrogen bondingcapability
Yes No No
Dielectric constant High Low
InteractionDipole interaction
Induced dipole interaction(London type)
Induce polarity in non-polar solvent
Example Water HydrocarbonsKetones, alcohols
Amphiprotic Cosolvents
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Influential Factors• Dipole moment
• Hydrogen bonds
• Acidic and basic character of constituents
• Structural features
Mechanism • High dielectric constant
• Amphiprotic
• Dipole interaction force
Water
(dissolve ionic solutes and other polar substances)
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Influential Factors• Induced dipole interactions
• Weak van der Waals-London type forces
• Low dielectric constant, No hydrogen bond
Hydrocarbons
(dissolve nonpolar solutes)
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Influential Factors• Induce a certain degree of polarity in non-polar solvent molecules
• No hydrogen bond
• Cosolvent
Ketones and alcohols
(Intermediate solvents)
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Solubility of Gases in Liquids
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Henry’s Law
C2 = σp
C2 = concentration of the dissolve gas (g/l)
p = partial pressure (mm of the undissolved gas)
σ = inverse of the Henry’s law constant, K
in a dilute solution at constant temperature, the
concentration of dissolved gas is proportional to the
partial pressure of the gas above the solution at
equilibrium
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
As the temperature increases, the solubility of most gases
decreases, owing to the greater tendency of the gas to expand
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Gases are often liberated from solutions in which they are
dissolved by the introduction of an electrolytes and
sometimes by a nonelectrolyte
NaCl or
sucrosegases
carbonated solution
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Gases (HCl, NH3, CO2) + Solvent
→ Chemical reaction
→ Increase solubility
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Inverse Henry’s law constant,
C2 = P
Bunsen absorption coefficient,
: 일정온도, gas의 partial pressure 1 기압하에 solvent 1L에녹는 gas의 volume (L)
Saturated condition : 0℃, 760mmHg
Vgas. STP
Vsoln.
= P
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Solubility of Liquids in Liquids
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Complete Miscibility
Solvents are said to be completely miscible when they are
mix in all proportions
Partial Miscibility
When certain amounts of two liquids are mixed, two liquid
layers are formed, each containing some of the other liquid in
the dissolved state
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Mixture of polar and semipolar solvents ▪ Water-Alcohol
▪ Glycerin-Alcohol
Mixture of nonpolar solvents▪ Benzene-Carbon tetrachloride
“Completely miscible liquid mixtures in generalcreate no solubility problems”
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Phenol-Water System Triethylamine-Water System Nicotine-Water System
Consolute temperature※ mixture of water-ether mixture – no consolute temp.
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
The solubility of peppermint oil in various
portions of water and polyethylene glycol.
Triangular phase diagram for the three-
component system.
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
If the added material is soluble in only one of the two components /
if the solubilities in the two liquids are markedly different
When the third substance is soluble in both of the liquids roughly
the same extent
✓ The mutual solubility of the liquid pair is decreased
✓ The mutual solubility of the liquid pair is increased
Blending
“The increase in mutual solubility of two partially miscible solvents by another agent”
Micellar Solubilization
”Solubility in water of a non-polar liquid is increased by a micelle-forming surfactant”
BinaryAdded
materialTernary
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Solubility of Solids in Liquids
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Acidic
Basic
Amphoteric
Indomethacin
Chlorpromazine
Oxytetracycline
Figure 25. Alexander T. Florence and David Attwood. 『Physicochemical Principles of Pharmacy』, Pharmaceutical Press(2016) p.165
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Weak Acids
−+ +=+ AOHOHHA 32
][
]][[ 3
HA
AOHK a
−+
=
분자형 이온형 −+= AHAS
)][
1]([][
][][
33++
+=+=OH
KHA
OH
HAKHAS a
a
약전해질 포화용해도 𝑆0 ≈ [𝐻𝐴] )][
1(3
0 ++=
OH
KSS a
apKpHa
a OHKOH
K −+
+=→=−→= 10log]log[log
][3
3
S0, pKa를 알면 주어진 pH에서의 S 계산𝑆 = 𝑆0(1 + 10𝒑𝑯−𝒑𝑲𝒂)
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Weak Acids
0
0logS
SSpKpH ap
−+=
][ 3
00 ++=
OH
KSSS a
][ 3
00 +=−
OH
KSSS a
]log[loglog)log( 300+−+=− OHSKSS a
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Weak Bases−+ + OHBHB
][
][][
B
OHBHKb
−+ +=
0
0logSS
SpKpH ap
−+=
𝑆 = 𝑆0(1 + 10𝒑𝑲𝒂−𝒑𝑯)
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Strong Electrolytes :strong acids and bases and all salts are soluble in water
Weak Electrolytes :weak acids and bases with high molecular weight are not soluble in water
Nonelectrolytes :high-molecular-weight organic drugs that do not dissociate or associate in water are generally soluble in organic solvents and have little or no solubility in water
Cosolvency :a solute is more soluble in a mixture of solvents than in one solvent alone
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
The solubility of phenobarbital in a mixture
of water, alcohol, and glycerin at 25℃
Cosolvencya solute is more soluble in a mixture
of solvents than in one solvent alone
“cosolvents”
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
The influence of alcohol concentration on the
dissociation constant (ka) of phenobarbital. Example 9-3.
Weak electrolyte buffered aqueous solution + Alcohol
→ 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒𝑠 the solubility ofthe un − ionized species ∶ 𝑆0 ↑
→ 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒𝑠 the dissociation ofa weak electrolyte ∶ 𝐾𝑎 ↓ (≡ 𝑝𝐾𝑎 ↑)
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Solubility product, :the real solution solubility of poorly soluble strong electrolytes in
water is calculated by using the solubility product constant
obtained from thermodynamics
Common ion :
adding a common ion is to reduce the solubility of a slightly
soluble electrolyte
spK
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Solubility determination:
1. Drug is added in a specific amount of solvent.
2. After equilibrium is achieved, excess drug is removed
(usually by filtering).
3. The concentration of the dissolved drug is measured
using standard analysis techniques such as HPLC.
“Saturation Shake Flask” Method
Limitations (p.196)
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
𝐹 = 𝐶 − 𝑃 + 2temperature, pressure and concentration, etc.
F = 1 (concentration)F = 0 (temp., pressure, conc. are constant)
solid state drug, P=2
“valid only for pure drug substance”saturate concentration
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
System having one impurity
solution saturated with the first component
solution saturated with two components
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
“measure a precipitation rate rather than solubility”
Using highthroughput kinetic measurement of antisolvent precipitation commonly referred to“kinetic solubility”
Use of Dimethyl sulfoxide(DMSO) stock solutions
Advantages but limitations
“small amount of stock solution is added to the aqueous buffer incrementally until the limit of solubility is achieved.”
“Speed up the process, limit compound consumption, reduce the occurrence of manual errors, and increase data consistency.”
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Solubility product, :the real solution solubility of poorly soluble strong electrolytes in
water is calculated by using the solubility product constant
obtained from thermodynamics
Common ion :
adding a common ion is to reduce the solubility of a slightly
soluble electrolyte
spK
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Partition Phenomena
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
The partition law :a solute will distribute itself between two immiscible
solvents so that the ratio of its conc. in each solvent is
equal to the ratio of its solubility in each one
Co = molar conc. in organic layer
Cw = molar conc. in aqueous layer
Kd = partition coefficient or distribution constant
w
dC
CK 0=
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Strong Electrolyte
Strong electrolytes are completely
dissociated in aqueous solution
→ cations & anions in aqueous layer
→ water soluble
Without ion pairing, do not partition
into the organic layer
Nonelectrolyte
OKd →w
dC
CK 0=
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
The partition law : depends on pH
pH different from pKa
(pH < pKa for weak acid ; pH > pKa for weak base)
For a weak organic acid,
For a weak organic base, w
dC
CK 0=
w
dHA
HAK
][
][ 0=
w
dC
CK 0=
w
dB
BK
][
][ 0=
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Effect of Ionic Dissociation and Molecular Association on Partitioning
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Schematic representation of the distribution of benzoic acid between water and an oil phase.
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실51
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Peanut Butter Oil & Water Solution
Benzoic acid
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
In Peanut Butter Oil In Water
𝐾 ∶ 𝑡𝑟𝑢𝑒 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡
𝐾′ ∶ 𝑎𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡
[𝐻𝐴]0: 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑏𝑒𝑛𝑧𝑜𝑖𝑐 𝑎𝑐𝑖𝑑 𝑖𝑛 𝑜𝑖𝑙
[𝐻𝐴]𝑤: 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑏𝑒𝑛𝑧𝑜𝑖𝑐 𝑎𝑐𝑖𝑑 𝑖𝑛 𝑤𝑎𝑡𝑒𝑟
𝐶𝑤: 𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑏𝑒𝑛𝑧𝑜𝑖𝑐 𝑎𝑐𝑖𝑑 𝑖𝑛 𝑤𝑎𝑡𝑒𝑟
𝐶𝑜: 𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑏𝑒𝑛𝑧𝑜𝑖𝑐 𝑎𝑐𝑖𝑑 𝑖𝑛 𝑜𝑖𝑙
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
In Peanut Butter Oil In Water
𝐾 ∶ 𝑡𝑟𝑢𝑒 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡
𝐶𝑤: 𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑏𝑒𝑛𝑧𝑜𝑖𝑐 𝑎𝑐𝑖𝑑 𝑖𝑛 𝑤𝑎𝑡𝑒𝑟
𝐶𝑜: 𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑏𝑒𝑛𝑧𝑜𝑖𝑐 𝑎𝑐𝑖𝑑 𝑖𝑛 𝑜𝑖𝑙
𝐶: 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑏𝑒𝑛𝑧𝑜𝑖𝑐 𝑎𝑐𝑖𝑑 𝑖𝑛 𝑤𝑎𝑡𝑒𝑟 𝑏𝑒𝑓𝑜𝑟𝑒 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Benzene & Acidic Water Solution
Benzoic acid
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
In Water In Oil (Benzene)
𝐾 ∶ 𝑡𝑟𝑢𝑒 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡
𝐾𝑑: 𝑑𝑖𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
[𝐻𝐴]𝑜: 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑏𝑒𝑛𝑧𝑜𝑖𝑐 𝑎𝑐𝑖𝑑 𝑖𝑛 𝑜𝑖𝑙
[𝐻𝐴]𝑤: 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑏𝑒𝑛𝑧𝑜𝑖𝑐 𝑎𝑐𝑖𝑑 𝑖𝑛 𝑤𝑎𝑡𝑒𝑟
𝐶𝑤: 𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑏𝑒𝑛𝑧𝑜𝑖𝑐 𝑎𝑐𝑖𝑑 𝑖𝑛 𝑤𝑎𝑡𝑒𝑟
𝐶𝑜: 𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑏𝑒𝑛𝑧𝑜𝑖𝑐 𝑎𝑐𝑖𝑑 𝑖𝑛 𝑜𝑖𝑙
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
Distribution of Solutes between Immiscible Solvents
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
𝐾 =𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑒 𝑖𝑛 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑠𝑜𝑙𝑣𝑒𝑛𝑡
𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑒 𝑖𝑛 𝑒𝑥𝑡𝑟𝑎𝑐𝑡𝑖𝑛𝑔 𝑠𝑜𝑙𝑣𝑒𝑛𝑡=
𝑤1/𝑣1(𝑤 − 𝑤1)/𝑣2
𝑤1 ∶ 𝑤𝑡. 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑜𝑙𝑢𝑡𝑒 𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 𝑖𝑛 𝑡ℎ𝑒 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑠𝑜𝑙𝑣𝑒𝑛𝑡𝑎𝑓𝑡𝑒𝑟 𝑒𝑥𝑡𝑟𝑎𝑐𝑡𝑖𝑛𝑔 𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑝𝑜𝑟𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑜𝑡ℎ𝑒𝑟 𝑠𝑜𝑙𝑣𝑒𝑛𝑡
Example 9-7
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
K: distribution coefficient
The most efficient extraction results when a larger number (𝑛) of extractions are carried out with small portions (𝑣) of extracting liquid
𝒗𝟐 𝒏 𝒘𝟏Amount extracted
10 1 0.005660 0.094339623
5 2 0.001148 0.098852041
2 5 6.54E-05 0.099934553
1 10 5.50E-06 0.099994501
0.5 20 5.43E-07 0.099999457
Total vol. of extracting liq. is fixed.
SKKU Physical Pharmacy Laboratory 성균관대학교 물리약학연구실
𝑻𝒐𝒕𝒂𝒍 𝑷𝒓𝒆𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒗𝒆 𝒂𝒅𝒅𝒆𝒅 = 𝑪 = 𝑪𝒐 + 𝑪𝒘
ww AHAHAC ][][][ 0
−++=
w
dHA
HAK
][
][ 0= wd HAKHA ][][ 0 =
][
][][
][
]][[
3
3
+
−−+
=→=OH
HAKA
HA
AOHK wa
w
w
wa
][
][][][
3
+++=
OH
HAKHAHAKC w
awwd
)][
1(][3
+++=
OH
KKHA a
dw
][1
][
3
+++
=
OH
KK
CHA
ad
w
Conc. of undissociated acid in the aqueous phase