01 solutions _electrolytes__protolytic_equilibria

Solutions of substancesColligative properties, osmosis

Medical Chemistry

Lecture 1 2007 (J.S.)

Dissociation of electrolytesThe equilibria in electrolyte solutions

Protolytic reactionsAcids and bases, the quantity pH

2

Liquid dispersions

consist of a solvent (dispersion medium, dissolving agent) – usually makes up the greater proportion of the solutionand some of the following components (dispersed fraction):

dissolved solids (solutes) – molecular compounds

– ionic compounds dissociated to ions,colloid particles – macromolecules or micellesparticulate materials – aggregates of molecules

– precipitated solids, bacteria, cells

Analytical dispersions – homogenous, "true“ solutions

Colloid dispersions – either colloid sols or colloid solutions

Crude dispersions – heterogeneous suspensions and emulsions

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Dispersion CRUDE COLLOID ANALYTICAL

Particle size

Particle visibility

Filtering capacity

Sedimentation

Particle movement

DiffusionColligativeproperties

Optical properties

> 500 nm

microscope

paper filter

spontaneous

slow Brownian

no

no

turbid ornon-transparent

1 - 500 nmelectronmicroscope

ultrafilters

in ultracentrifuge

rapid Brownian

very slow

low max. valuesopalescentTyndall effect

< 1nm

no

no

no

rapid thermal

rapid

intensive

transparent

Liquid dispersions – three types:

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− Originate in spontaneous dissolving of solutes (either molecular or ionic in size) in solvents,

− the term solubility describes the amount of one substance that will dissolve in the solvent,

− solubility depends on the polarity of the solute and solvent, on temperature, solubility of gases in liquids also on the pressure of that gas above the solution,

− "like dissolves like“ – the most usual solvent of polar compounds is water (weak attraction forces have an important role), nonpolar substances tend to be miscible with nonpolar solvents (e.g., hexane, benzene, diethyl ether, tetrachloromethane).

Analytical dispersions (true solutions)

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Concentration of solutionsThe term dilute or concentrated solutions shows, in a quite relative way, the amount of solute dissolved in a unit volume of solution.The most common types of expressing the concentration of solutions:

Amount concentration (molarity), symbol cx,is defined as the amount of the solute (in moles) in one litre of solution, nx / V. Dimension mol l–1, mmol l–1, etc. (or M, mM).

Mass concentration, symbol ρx (rho)- the mass of the solute (in grams, milligrams, etc.) in one litre ofsolution, mx / V ; is used when molarity cannot be applied.

Dimension – g l–1, mg l–1, μg l–1, etc.

Mass fraction, symbol wx (equal to the percentage by mass)

- the ratio of the solute mass to the mass of the solution,mx / (mx+ msolvent). Comparative relation in mass, without units. Example: Mass fraction wx = 0.05 = 5 % . Such solution contains 5 g of the solute in each 100 g of the solution.

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On special occasions, molality is used instead of molarity.

Molality of a solution, mc,is the concentration expressed as the amount of solute (in moles) dissolved in 1 kg of solvent, nx / msolvent .

Usual dimension – mmol kgH2O–1 .

For unionized solutes, the colligative properties of a solution are directly proportional to its molality. The value of molality is independent on temperature.It declares the constant ratio between the number of solute andsolvent molecules.

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What may happen, if a low-molecular weight compound dissolves in water?

– Molecules of the compound are dispersed inj water – the solute is a nonelectrolyte.

– The compound splits into ions during dissolution -

– the formation of ions from a molecular solute (ionization) is only partial, both molecules and ions of the solute are dispersed – the solute is a weak electrolyte.

– the compound is ionized or dissociated into ions completely– the solute is a strong electrolyte.

8

The colligative properties of solutions

Colligative properties of solutions:

– osmotic pressure,

– boiling temperature elevation,

– freezing temperature depression, and

– solvent vapour pressure lowering

are the properties that depend only on the solution molality

(on the relative numbers of solute and solvent particles)

and not on the identity of particles (their relative masses,

shapes, and electric charges).

9

Osmotic pressure of a solution

Pressure Π (pi) is the external pressure exactly sufficient to oppose osmosis and stop it.

A semipermeable membranethat allows the free passage of water(solvent) but not the molecules of solutes

osmosis Π

Π

Water diffuses through the semipermeable membrane from a region of higher water concentration (dilute solution) to one of lower water concentration (more concentrated solution).

10

Measurement of osmotic pressure of solutionsby means of osmometers:

Calculation of osmotic pressureif the concentration of a solution is known:

– membrane osmometers for direct measurements,– osmometers based on cryoscopy - the freezing temperature depression ΔTf is measured and from that value of the solution

molality obtained, which is proportional to Π: Tf = Kf mc . Thermometers have to distinguish changes by 0.001 °C.

= i c RT (in kilopascals)

c – concentration of the solute (in moles) in approximate calculations, for accurate results molality and activity of the solute should be used;

i – factor respecting the number of ions formed by dissociation of the solute;

R – ideal gas constant equal to 8.314 J /(K mol); T – temperature (in kelvins).

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The value of i

for non-electrolytes equals 1, i = 1

for strong electrolytes is a whole number greater than 2,

i > 2

αc – degree of dissociation at the concentration c

N – number of ions resulting from dissociation of the formal unit

Examples: NaCl Na+ + Cl– i = 2Na2SO4 2 Na+ + SO4

2– i = 3

MgCl2 Mg2+ + 2 Cl– i = 3

Na3PO4 3 Na+ + PO43– i = 4

Factor i in the equation = i c RT :

For weak electrolytes i = 1 + αcc (N – 1)

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All various solutions that have the same osmotic pressure,because of the same osmolality, are isotonic to each other.

Hypertonic solutions are solutions at higher osmolality than those towhich they are compared;similarly, hypotonic solutions are those with lower osmotic pressure.

Solutions isotonic with blood plasmahave osmotic pressure about 765 kPa (osmolality about 290 mmol/kgH2O).

Sodium chloride solution isotonic with blood plasma(called inaccurately "physiological saline solution“) contains 154 mmol NaCl per litre (154 mmol/l Na+ and 154 mmol/l Cl–), that is 9 g NaCl / l (0.9% sodium chloride).

Glucose solution isotonic with blood plasma contains 308 mmol glucose per litre, that is 55 g / l (5% glucose solution).

In order to prevent possible injury to blood cells by osmosis, fluids forintravenous use are usually prepared at approx. isotonic concentration.

13

A cell in an isotonic fluid

H2O

H2OH2O

Osmosis in a hypertonicfluid – a cell shrinks

H2OH2O

H2O

A cell swells ina hypotonic fluid

Cytolysis

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Blood plasma osmolality 280 – 295 mmol kgH2O–1

Hypoosmolality (up to 230 mmol/kg) – deficit in Na+ or hyperhydrationHyperosmolality (up to 400 mmol/kg) – retention of Na+, dehydration,

hyperglycaemia, uremic syndrome, unusual compounds(e.g. ethanol, ethylene glycol, acetone).

It is under the strict hormonal control (aldosterone, vasopressin,atrial natriuretic peptides).

Blood plasma osmolality is measured by means of osmometers.

Plasma osmolality (mmol kgH2O-1) ≈ 2 [Na+] + [glucose] + [urea] (mmol/l)

or ≈ 1.86 [Na+] + [glucose] + [urea] + 9 (mmol/l)The marked difference between the measured and the roughly estimated value is the sign of the "osmolar gap“ that is usually caused by high concentration of other unionized compounds (ethanol, acetone, etc.).

In spite of the known value of osmolality gained by measurement, it is useful to calculate the rough estimate of plasma osmolality from the values of major plasma solutes:

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Osmotic pressure of molecular colloid solutions(oncotic pressure)

is very small when compared to that of true solutions;because of large size of molecules, colloid solution of high-molecular compounds cannot reach high osmolality values .

Oncotic pressure of blood plasma proteins representsless than 0.5 % of the oncotic pressure of blood plasma.In spite of this low value, oncotic pressure is extremelyimportant for shifts of water between blood plasma andinterstitial fluid in blood capillaries.

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When certain low-molecular weight substancedissolves in water and

– molecules of the compound are dispersed, the solute is a nonelectrolyte (the solution is a nonconductor);

– ions of the compound exist the solution that is a conductor of electricity, the solute is an electrolyte.

– if the formation of ions from a molecular solute (ionization) is only partial, the solute is a weak electrolyte, both molecules and ions of the solute are present,

– if the compound splits into ions completely due to dissociation or ionization, the solute is a strong electrolyte.

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Electrolytesare solutions of compounds that are split into ions due to interactionwith a polar solvent.

Ionic compounds dissociate completely, polar molecular compoundsare ionized completely. Ions are surrounded by a certain number ofwater molecules (hydrated). Concentration of particles is higher (in strong electrolytes at leasttwo times, if only two ions are formed)

– remember the colligative properties and factor i !

Weak electrolytes:

AB(s) A+(aq) + B–(aq) + AB(aq)H2O

Weak electrolytes are ionized to only a slight extent, the concentrationof ions are relatively low; most solute molecules do not split into ions.

AB(s) A+(aq) + B–(aq)H2O

Strong electrolytes:

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strong acids

strong hydroxides

most soluble salts

Strong electrolytes Weak electrolytes

weak acids

weak bases

(a few salts)

Strong acids: H2SO4, HNO3, HCl, HBr, HI HClO3, HClO4,alkyl sulfates, alkanesulfonic acids

Strong hydroxides: NaOH, KOH, Ca(OH)2, Sr(OH)2, Ba(OH)2,tetraalkylammonium hydroxides

Water and exceptions among salts,e.g. calcium citrate, ZnCl2, HgCl2

Weak acid:all not named among the strong(nearly all organic acids included)

Weak bases: ammonia all other nitrogenous bases

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Strong electrolytes

Concentrations of ions in solutions of strong electrolytesis always higher than the concentration of the compound.

For example: c(Na2SO4) = 0.1 mol / l In this solution c(Na+) = 0.2 mol / l and c(SO4

2–) = 0.1 mol / l,

i.e. c(Na++Cl–) = 0.3 mol / l Due to the mutual electrostatic interactions at higherconcentrations (exceeding 10–4 mol / l), there are certaindifferences in the behaviour (in colligative properties) ofstrong electrolyte solutions. The solutions seem to bemore diluted than the real concentration proved bychemical analysis.

Real colligative properties correspond more with the quantity called activity of ions than with the "analytical“concentration of ions.

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ai activity of the ion i

i activity coefficient of ion i at ci

ci concentration of ion i

( 1 )

ai = ic ci

Only for ci < 10–4 mol/l yic 1 and ai = ci

Activity of ions is a quantity representing theconcentration of ions corrected for interionic interactions.

Activity coefficients take values up to 1 (= no difference betweenactivity and concentration).

In most cases that will be dealt with in this course, the differencebetween ci and ai will be neglected (what is fully true for concentrationslower than 10–4 mol/l).

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Examples of the activity coefficient values

Cations and anions of the strong electrolyte type MX2

c = 0.01 mol/l c = 0.1 mol/l c = 1 mol/l

n(MX2)/n(H2O) 1 : 5550 1 : 555 1 : 56

The mean ion activity a± = y± ci

The values of activity coefficients y± :

HCl 0.97 0.92 0.78NaCl 0.95 0.83 0.61H2SO4 0.81 0.61 < 0.50

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Ionic strength of solutions I is the function of ion concentration and electric chargeand id defined by the relation

ci concentration of ion i , zi electric charge of ion i

I = ‒12 c1 z1

2 + c2 z22 + … cn zn

2 = 12‒ ci zi

2

i

The value of an activity coefficient depends on the concentration andelectric charge of all ionic species in the solution,

e.g. for concentrations up to 10–2 mol/l – log yic = A zi2 , where

is a new quantity I named. This quantity cannot be measured, it can be

only calculated:

I

Not all ions exhibit the same effect in a solution, polyvalent ionsplay a greater role than monovalent ions.

23

In various types of salts and other strong electrolytes,the relations between concentration of the compound,concentration of ions, and ionic strength are different.

Examples:

Type of salt csalt cparticles Ionic strength I

Na+Cl– csalt 2 csalt csalt

Ca2+Cl2– csalt 3 csalt 3 csalt

Zn2+SO42– csalt 2 csalt 4 csalt

Fe3+Cl3– csalt 4 csalt 6 csalt

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Various types of equilibria in electrolyte solutions

Four types of equilibria may occur in aqueous electrolyte solutions:

1 Protolytic equilibria (acid-base equilibria)deal with the exchange of protons (hydronium ions)between acids and bases

2 Complex-forming equilibriaexist between donors and acceptors of valence shellelectron pairs

3 Dissolution equilibriaexpress relations of solids to ions and polar solvents insaturated solutions

4 Oxidation-reduction equilibriadeal with the exchange of electrons in redox reactions

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Acids and bases pH values of acids and bases solutions

Protolytic reactions

26

Acids and basesaccording to the Brønsted concept:

Acids are proton donors. Any molecule or ion that can lose a proton, if a base is present to accept it, is an acid.

Bases are proton acceptors. Any molecule or ion that have an unshared electron pair able to bind a proton released by an acid by coordinate bond is a base.

HA + H2O A– + H3O+ acid water as a base

Bl + H2O BH+ + OH– base water as an acid

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Conjugate pairs

Each acid after releasing a proton becomes a base that is called a conjugate base of the primary acid.

Similarly, each base gives its conjugate acid by accepting a proton.

Therefore, in any reaction of an acid with a base, two conjugate pairs must take part:

HA + B A– + BH+

conjugate pair

conjugate pair

The first conjugate pair: HA → H+ + A–

The second pair: B + H+ → BH+

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Notice that can help you in understanding the followingmatter and might be appreciated in the study of biochemistry,physiology, and clinical applications of protolytic reactions:

Strong hydroxides dissociate to the strong base OH– (conjugate base of water) and cations Na+, K+, Ca2+, etc. Those cations are not acids, cannot release H+, and do take part in protolytic reactions.They are called "strong" or spectator cations.

Quite generally, acids dissociate to give H+ and conjugate bases. Weak acids give H+ and strong conjugate bases that exhibit a

great affinity to H+; therefore, only a small part of molecules dissociates in aqueous solution. Conjugate bases of strong acids, anions Cl–, SO4

2–, NO3– , etc.,

are, on the contrary, exceedingly weak conjugate bases in the body (at physiological values of pH). They do not notice H+ (they do not take part in protolytic reactions) and are named"strong" or spectator anions.

Weak bases accept protons only to a small extent and give so strong conjugate acids.

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Ionization of water

Water molecules are polar and ionize to a very slight extent.Pure water is a very weak electrolyte.

2 H2O H3O+ + OH–

One molecule of water gains a proton forming thusa hydronium ion while another molecule formsa hydroxide anion.

Water molecules can act as either an acid or a bases; such species of particles are named amphoteric (or amphiprotic).

The symbol H+ is commonly used in describing protolytic reactions though there are no free protons in water or aqueous solutions; H+ must be always taken as a simplified notation of hydronium ions H3O+

(as well as of more hydrated H+.nH2O ions).

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Ionic product of water Kw

From the quantitative point of view, the ionization of wateris described by the equilibrium ionization constant Kc:

Kc [H+] [OH–]

[H2O]Because the high value of unionized molecules of water[H2O] (55.5 mol/l) changes only slightly in real solutions,instead of Kc the constant ionic product of water Kw is used:

Kc [H2O] = Kw = [H+] [OH–] = 1.00 10–14 (25°C)

In any aqueous solutions, concentrations [H+] and [OH–]can achieve only those values that are in agreement with

the Kw value 1.00 10–14.

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In pure water, the concentrations [H+] and [OH–] are thesame and the concentration of each of this ions is equal to

1.00 10–7 mol/l (at 25 °C).

All aqueous solution in which [H+] equals [OH–] are neutral.In acidic solutions [H+] is greater than [OH–],in alkaline solutions (basic solutions) [OH–] > [H+].

Based upon Le Chatelier´s principle, adding H+ to a neutral aqueous solution will decrease [OH–] and similarly, adding OH– will decrease [H+].

A more convenient way for expressing [H+] and [OH–] in mol/l (small numbers, scientific notation) are

the expressions pH and pOH definedas the negative logarithms of [H+] and [OH–]:

pH = – log [H+] and pOH = – log [OH–]

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The values of pH and pOH for dilute aqueous solutionsfall between 0 and 14.

The same logarithmic notation can be also used for Kw:

Kw = [H+] [OH–] = 1.00 10–14

pKw = pH + pOH = 14

so that pH = 14 – pOH

The pH and pOH scales are logarithmic, not linear, scales !A change of pH by 1 represents the 10 times higher or lower concentration of [H+]; any two-fold increase in [H+] results in the decrease of pH by 0.3, because the logarithm of 2 equals 0.30.

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Dissociation of a strong acid: HA + H2O H3O+ + A–

In solutions of monoprotic strong acids, the concentration [H+] is equal to the total strong acid concentration cHA :

[H+] = cHA and pH = – log [H+] = – log cHA

Dissociation of a strong hydroxide: MeOH(aq) Me+ + OH–

In solutions of monobasic strong hydroxides,

[OH–] = cMeOH , pOH = – log [OH–] = – log cMeOH,

and pH = 14 – pOH

pH of strong acids and strong hydroxides solutionsStrong acid and strong hydroxides are strong electrolytesthat are fully dissociated in aqueous solutions.(In diluted solutions, the difference between the concentration and the activity of ions can be neglected.)

Let us remind the list of a few strong acids and hydroxides!

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The titration curve of a monoprotic strong acid ( cHA = 0.1 mol/l)

Linear decrease in [H+] in the course of titration results in a logarithmiccurve representing the increase of pH values.To reach the pH value greater by 1 than the initial, 90 % of the amountof an strong acid have to be neutralized.

12

10

8

6

4

2

0

pH

pH 7.00

(excess NaOH)

n(OH–)/n(acid)0 0.2 0.4 0.6 0.8 1.0

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Dissociation of weak electrolytes, (of weak acids and weak bases)

A weak monoprotic acid A weak base

Equilibrium constants of ionization

Acid and base ionization constants

Weak electrolytes are ionized to only a slight extent, the concentrationof ions are relatively low; most solute molecules do not split into ions.

HA + H2O H3O+ + A– B + H2O BH+ + OH–

Kc [H3O+] [A–]

[H2O] [HA]Kc [BH+] [OH–]

[H2O] [B]

The extent to which the weak electrolytes dissociates isexpressed by either ionization constants or degree of ionization.

KA [H+] [A–]

[HA]Kc [H2O] = KB

[BH+] [OH–][B]

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Displacement of a weak acidThe consequence of the Le Chatelier´s principle is that acidifying of the solution of a weak acid by adding a stronger acidwill suppress the dissociation of the weak acid.

If a weak acid is volatile (e.g. HCN, H2CO3), it can leak completelyfrom the solution.

Displacement of weak basesLike acids, the dissociation of which is kept down by addition ofstrong acids, alkalization of solutions suppresses ionizationof weak bases.

Weak acids and weak bases can be also displaced from the solutionsof their salts.

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pK = – log K

KA and KB are acid and base ionization constants.

Instead of them, the values of pKA and pKB are used:

The lower the value of pKA, the stronger is the weak acid.

"Moderately strong" weak acids and bases have pK value from 1 to 3, weak acids and bases from 4 to 8,

very weak acids and bases higher than 8.

pKB + pKA = 14 = pKw

KB KA = 1. 10-14 = Kw

The relation between KB and KA of weak bases

For any particular weak base in aqueous solution it holdsthat

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pKA of weak acids

Weak acid pKA 1 pKA 2 pKA 3

Oxalic (COOH)2 1.25. 4.29 -

H3PO4 2.16 7.20 12.29

HNO2 3.39 - -

Ascorbic 4.17 11.57 -

Acetic CH3COOH 4.76 - -

H2CO3 6.35 10.3 -

H2S 7.07 12.2 -

H3BO3 9.24 12.7 -

Weak bases pKB pKA conjugate acid

Guanidine 1.50 12.50

Methylamine 3.36 10.64

Ammonia 4.75 9.25

Imidazole 6.90 7.10

Pyridine 8.82 5.18

Aniline 9.38 4.64.

Coffeine 13.40 0.60

pKB and pKA of weak bases

The weaker is the acid,the stronger conjugate base is its anion.

The weaker is the base,the stronger conjugate acidis its cation.

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The second parameter that expresses the dissociation (ionization)of weak acids and weak bases isthe degree of ionization αc (the percentage of ionization).

It is found from the concentration of H+ (in acid solutions, ofOH– in solutions of bases) and the total concentration of the acid or base ctotal that is equal to the sum of both ionized and non-ionized molecules [H+]+[HA] or [OH–]+[BH].

For a monoprotic weak acid αc =

[H+]ctotal

The index specifies the total concentration, the value of α varies withthe ctotal. The more dilute the solution, the larger is the degree αc.

Because [H+] = αc ctotal , then KA = ctotal α2

1 – α

If the degree of ionization is low (αc < 0.10, i.e. 10 %), the relation issimpler: K ctotal αc

2 and αc ( K / ctotal )½ .

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Calculation of pH values in solutions of weak acids and bases

HA + H2O H3O+ + A– KA [H+] [A–]

[HA]

Solutions of weak monoprotic acids

The total acid concentration ctotal = [H+] + [HA] .

Because [H+] = [A–] (molecules of acid gives the same number of both), [H+] [A–] = [H+]2.

Now an approximation is induced: [HA], the concentration of undissociatedmolecules (ctotal – [H+]), is close to ctotal, when the dissociation degree αc isless than 0.10 (the minute difference of the denominator can be neglected).

Then , from which KA

[H+]2 ctotal

totalA cK [H+] =

and in logarithmic form log [H+] = ½ log KA + ½ log ctotal

The pH value of a weak acid solution

pH = ½ pKA – ½ log ctotal

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B + H2O BH+ + OH–

pOH = ½ pKB – ½ log cB

Solutions of weak bases

KB [BH+] [OH–]

[B]The total base concentration ctotal = [BH+] + [B] .Because [BH+] = [OH–] (molecules of base gives the same number of both),

[BH+] [OH–] = [OH–]2. The approximation as for acids: [B], the concentration of undissociatedbase (ctotal – [OH–]), is close to ctotal, when the dissociation degree αc isless than 0.10 (the minute difference of the denominator can be neglected).Then , from which

KB [OH–]2

ctotal[OH–] =

totalB cK

and in logarithmic form log [OH–] = ½ log KB + ½ log ctotal

The pH value of a weak base solution

pH = 14 – ½ pKB + ½ log cB