pH scale. Buffer solutions. pH scale. Buffer solutions. ColligativeColligative properties of properties of

solutionssolutionsNatalyaNatalya VODOLAZKAYAVODOLAZKAYA

Department of Physical ChemistryDepartment of Physical Chemistry

V.N. V.N. KarazinKarazin KharkovKharkov National UniversityNational University

Medical Chemistry Medical Chemistry Module 1. Lecture 3Module 1. Lecture 3

December, 2013December, 2013

22

LLectureecture topicstopics

√√ Acidity of solutionsAcidity of solutions√√ CHEMISTRY in Action: Antacids and the pH Balance CHEMISTRY in Action: Antacids and the pH Balance

in Your Stomachin Your Stomach√√ AcidAcid--base indicatorsbase indicators√√ Hydrolysis of saltsHydrolysis of salts√√ Buffer solutionsBuffer solutions√√ ColligativeColligative properties of solutionsproperties of solutions

33

Acidity of solutionsAcidity of solutionsQuantitative representation of acidity of solutions, i.e. the coQuantitative representation of acidity of solutions, i.e. the content ntent

of of hydrogen ions in solutionhydrogen ions in solution, is the , is the рНрН valuevalue that equals to the that equals to the negative decimal logarithm of hydrogen ions activity:negative decimal logarithm of hydrogen ions activity:

In a dilute solution activities are close to concentrations (In a dilute solution activities are close to concentrations (γγ±± ≈≈ 1), 1), so it is possible to set the so it is possible to set the рНрН value of solution equals to analytical value of solution equals to analytical concentration of hydrogen ion:concentration of hydrogen ion:

In liquid water solution In liquid water solution autoionizationautoionization process takes place:process takes place:

It can be characterized by equilibrium constant:It can be characterized by equilibrium constant:

+ +H HpH log log( )a c ±= − = − ⋅ γ

+HpH log c≈ −

+2H O H + OH−

2

H OH

H O

a aK

a+ −⋅

=

44

The degree of water dissociation is very small, so the The degree of water dissociation is very small, so the aa((HH22O) O) value is constant and equation can be represented as follows:value is constant and equation can be represented as follows:

Constant Constant KKww is known as is known as ionic product of waterionic product of water. At 25. At 25 °°C the C the KKwwvalue is equal to 1.008value is equal to 1.008⋅⋅1010––1414. Usually this constant is represented as . Usually this constant is represented as the negative decimal logarithm: the negative decimal logarithm:

at 25at 25 °°C.C.At 25At 25°°C if the contents of hydrogen and hydroxyl ions in a solution C if the contents of hydrogen and hydroxyl ions in a solution

are equal, , then are equal, , then рНрН == pOHpOH == 7, such media is called 7, such media is called neutralneutral. . In In acidic solutionsacidic solutions , in , in alkaline mediaalkaline media ..

Acidity of solutionsAcidity of solutions

2H OH OH wa a K a K−⋅ = ⋅ =+

p logw wK K= − p 14wK =

H OHa a −=+

H OHa a −>+ H OHa a −<+

55

pOHpOH = = ––log[OHlog[OH––] ] and and

pOHpOH + pH = + pH = ppKKww = 14= 14

The pH and The pH and pOHpOH values of diluted values of diluted solutions are in range 0solutions are in range 0––14. But 14. But concentrated solutions of a strong acids concentrated solutions of a strong acids may have zero or even negative pH may have zero or even negative pH values, and concentrated solutions of a values, and concentrated solutions of a strong bases may have pH values more strong bases may have pH values more than 14.than 14.

Acidity of solutionsAcidity of solutions

66

CHEMISTRY in ActionCHEMISTRY in ActionAntacids and the pH Balance in Your Antacids and the pH Balance in Your

StomachStomachAn average adult produces between 2 and 3 L of gastric juice

daily. Gastric juice is a thin, acidic digestive fluid secreted by glands in the mucous membrane that lines the stomach. It contains, among other substances, hydrochloric acid (HCl). The pH of gastric juice is about 1.5, which corresponds to a hydrochloric acid concentration of 0.03 M – a concentration strong enough to dissolve zinc metal!

What is the purpose of this highly acidic medium? Where do the H+ ions come from? What happens when there is an excess of H+

ions present in the stomach? A simplified diagram of the stomach is shown on the Figure.

77

Antacids and the pH Balance in Your Antacids and the pH Balance in Your StomachStomach

Figure. A simplified diagram of the human stomach.

88

The inside lining is made up of parietal cells, which are fused The inside lining is made up of parietal cells, which are fused together to form tight junctions. The interiors of the cells aretogether to form tight junctions. The interiors of the cells areprotected from the surroundings by cell membranes. These protected from the surroundings by cell membranes. These membranes allow water and neutral molecules to pass in and out membranes allow water and neutral molecules to pass in and out of the stomach, but they usually block the movement of ions suchof the stomach, but they usually block the movement of ions suchas Has H++, Na, Na++, K, K++, and , and ClCl––. The H. The H++ ions come from carbonic acid ions come from carbonic acid (H(H22COCO33) formed as a result of the hydration of CO) formed as a result of the hydration of CO22, an end , an end product of metabolism:product of metabolism:

Antacids and the pH Balance in Antacids and the pH Balance in Your StomachYour Stomach

99

These reactions take place in the blood plasma bathing the cellsThese reactions take place in the blood plasma bathing the cells in the in the mucosa. By a process known as active transport, Hmucosa. By a process known as active transport, H++ ions move across the ions move across the membrane into the stomach interior. (Active transport processes membrane into the stomach interior. (Active transport processes are aided by are aided by enzymes.) To maintain electrical balance, an equal number of enzymes.) To maintain electrical balance, an equal number of ClCl–– ions also ions also move from the blood plasma into the stomach. Once in the stomachmove from the blood plasma into the stomach. Once in the stomach, most of , most of these ions are prevented from diffusing back into the blood plasthese ions are prevented from diffusing back into the blood plasma by cell ma by cell membranes. membranes. The purpose of the highly acidic medium within the stomach is The purpose of the highly acidic medium within the stomach is to digest food and to activate certain digestive enzymes. Eatingto digest food and to activate certain digestive enzymes. Eating stimulates Hstimulates H++

ion secretion.ion secretion. A small fraction of these ions normally are reabsorbed by the A small fraction of these ions normally are reabsorbed by the mucosa, causing many tiny hemorrhages. About half a million cellmucosa, causing many tiny hemorrhages. About half a million cells are shed s are shed by the lining every minute, and a healthy stomach is completely by the lining every minute, and a healthy stomach is completely relined every relined every three days or so. However, if the acid content is excessively hithree days or so. However, if the acid content is excessively high, the gh, the constant influx of Hconstant influx of H++ ions through the membrane back to the blood plasma ions through the membrane back to the blood plasma can cause muscle contraction, pain, swelling, inflammation, and can cause muscle contraction, pain, swelling, inflammation, and bleeding. bleeding. One way to temporarily reduce the HOne way to temporarily reduce the H++ ion concentration in the stomach is to ion concentration in the stomach is to take an take an antacidantacid. .

Antacids and the pH Balance in Antacids and the pH Balance in Your StomachYour Stomach

1010

The major function of antacids is to neutralize excess The major function of antacids is to neutralize excess HClHCl in gastric juice.in gastric juice.The reactions by which antacids neutralize stomach acid are as The reactions by which antacids neutralize stomach acid are as follows:follows:

The COThe CO22 released by most of these reactions increases gas pressure in released by most of these reactions increases gas pressure in the stomach, causing the person to belch. The fizzing that takesthe stomach, causing the person to belch. The fizzing that takes place when place when an Alkaan Alka--Seltzer tablet dissolves in water is caused by carbon dioxide, wSeltzer tablet dissolves in water is caused by carbon dioxide, which hich is released by the reaction between citric acid and sodium bicaris released by the reaction between citric acid and sodium bicarbonate:bonate:

Antacids and the pH Balance in Antacids and the pH Balance in Your StomachYour Stomach

1111

This action helps to disperse the ingredients and even enhances This action helps to disperse the ingredients and even enhances the the taste of the solution. The mucosa of the stomach is also damagetaste of the solution. The mucosa of the stomach is also damaged by the d by the action of aspirin, the chemical name of which is acetylsalicylicaction of aspirin, the chemical name of which is acetylsalicylic acid. Aspirin acid. Aspirin is itself a moderately weak acid:is itself a moderately weak acid:

Antacids and the pH Balance in Antacids and the pH Balance in Your StomachYour Stomach

1212

In the presence of the high concentration of HIn the presence of the high concentration of H++ ions in the stomach, ions in the stomach, this acid remains largely this acid remains largely nonionizednonionized. A relatively . A relatively nonpolarnonpolar molecule, molecule, acetylsalicylic acid has the ability to penetrate membrane barriacetylsalicylic acid has the ability to penetrate membrane barriers that are ers that are also made up of also made up of nonpolarnonpolar molecules. However, inside the membrane are molecules. However, inside the membrane are many small water pockets, and when an acetylsalicylic acid molecmany small water pockets, and when an acetylsalicylic acid molecule ule enters such a pocket, it ionizes into Henters such a pocket, it ionizes into H++ and acetylsalicylate ions. These and acetylsalicylate ions. These ionic species become trapped in the interior regions of the membionic species become trapped in the interior regions of the membrane. rane. The continued buildup of ions in this fashion weakens the structThe continued buildup of ions in this fashion weakens the structure of the ure of the membrane and eventually causes bleeding. Approximately 2 membrane and eventually causes bleeding. Approximately 2 mLmL of blood of blood are usually lost for every aspirin tablet taken, an amount not gare usually lost for every aspirin tablet taken, an amount not generally enerally considered harmful. However, the action of aspirin can result inconsidered harmful. However, the action of aspirin can result in severe severe bleeding in some individuals. It is interesting to note that thebleeding in some individuals. It is interesting to note that the presence of presence of alcohol makes acetylsalicylic acid even more soluble in the membalcohol makes acetylsalicylic acid even more soluble in the membrane, rane, and so further promotes the bleeding.and so further promotes the bleeding.

Antacids and the pH Balance in Antacids and the pH Balance in Your StomachYour Stomach

1313

AcidAcid--base indicatorsbase indicatorsAn An acidacid--base indicatorbase indicator is a substance which varies color of the is a substance which varies color of the

solution according to the hydrogen ion concentration of its envisolution according to the hydrogen ion concentration of its environment. ronment. An acidAn acid--base indicator is a substance which may exist in at least two base indicator is a substance which may exist in at least two

(or more) (or more) tautomerictautomeric forms in equilibrium with one another. These forms forms in equilibrium with one another. These forms have have different structuresdifferent structures and and different colorsdifferent colors. Color of the solution of the . Color of the solution of the indicator is determined by the ratio of the concentrations of thindicator is determined by the ratio of the concentrations of the colored e colored forms. forms.

It is thus possible to determine the pH value of a solution by It is thus possible to determine the pH value of a solution by observing the color of a suitable indicator when it is placed inobserving the color of a suitable indicator when it is placed in that that solution. solution.

In the simplest case of existing of two forms of indicator it isIn the simplest case of existing of two forms of indicator it is possible possible to approximate the actual state of equilibrium between the formsto approximate the actual state of equilibrium between the forms using using dissociation constant: dissociation constant: HIn ↔ H+ + In–,

[H ][In ] ,[HIn]

K+ −

= [In ]pH p log[HIn]

K−

= +

1414

AcidAcid--base indicatorsbase indicatorsSince two forms of indicator have different colors, for example, A

and B for acidic and alkaline media, the actual color exhibited by the indicator will depend on the hydrogen ion concentration of the medium.

If the pK value of indicator is known, and the ratio of color B to color A of the indicator in the given solution is measured, the pH of the solution can be evaluated.

In theory, the ratio of the intensities of color B to color A may have any value, but in practice it is possible to detect the proportions of the two colors in a mixture within certain limits only.

In practice, it is necessary that there should be a minimum of about 10 per cent of a particular color for it can be easily detected in the presence of another color. This leads to that indicators might be utilized for determination of the pH of the solution in the range of the pH values in: pH p 1K= ±

This interval of the pH values is called the transition or useful range of the indicator.

1515

Table. Colors and useful ranges for some pH indicatorsTable. Colors and useful ranges for some pH indicators

AcidAcid--base indicatorsbase indicators

Determination of the pH using indicators

Due to the ability of indicators to change a color with pH of solution they are employed for determination of the acidity of solutions.

Universal indicator is a mixture of several indicators displaying a variety of colors over a wide pH range. Usually it is used as a test paperthat changes color in accordance with the solution pH value.

1616

Test papers of universal indicator are used only for an Test papers of universal indicator are used only for an approximate pH of the solution. For precise determination of approximate pH of the solution. For precise determination of the pH value, the pH value, colorimetriccolorimetric or or potentiometricpotentiometric methodsmethods are are used.used.

AcidAcid--base indicatorsbase indicators

1717

Hydrolysis of saltsHydrolysis of saltsThe term The term salt hydrolysissalt hydrolysis describes describes the reaction of an anion or a the reaction of an anion or a

cationcation of a salt, or both, with water.of a salt, or both, with water. Salt hydrolysis usually affects Salt hydrolysis usually affects the pH of a solution.the pH of a solution.

The salts composed of an alkali or alkaline earth metal ion and The salts composed of an alkali or alkaline earth metal ion and the residue of a strong acidthe residue of a strong acid do not undergodo not undergo hydrolysis and their hydrolysis and their solutions are assumed solutions are assumed to be neutralto be neutral. .

Another situation is observed when dissolved salt is formed by Another situation is observed when dissolved salt is formed by a a weak base or (and) a weak baseweak base or (and) a weak base. For example, the dissociation . For example, the dissociation of sodium acetate, that is strong electrolyte, in water proceedsof sodium acetate, that is strong electrolyte, in water proceedsaccording to equation: according to equation: CH3COONa → Na+(aq) + CH3COO– (aq).

The sodium ion does not react with water. The acetate ion CH3COO–

has an affinity for H+ ions. The hydrolysis reaction of this anion is given by equation: CH3COO– (aq) + H2O ↔ CH3COOH (aq) + OH– (aq).

1818

Hydrolysis of saltsHydrolysis of saltsDue to formation of OHDue to formation of OH–– ions in this reaction the solution of sodium acetate ions in this reaction the solution of sodium acetate

will be will be basicbasic. The equilibrium constant for the hydrolysis reaction of CH. The equilibrium constant for the hydrolysis reaction of CH33COONa COONa is determined by dissociation constant of acetic acid and ionic is determined by dissociation constant of acetic acid and ionic product of water:product of water:

3

3

[CH COOH] [HO ][CH COO ]

wh

acid

KKK

−

−⋅

= =

When a salt derived from a strong acid and a weak base dissolves in water, the solution becomes acidic. For example, in solution of NH4Cl the dissociation process gives NH4

+ and Cl– ions: NH4Cl → NH4+ (aq) + Cl– (aq).

The ammonium ion NH4+ is the conjugate acid of the weak base NH3 and

reacts with water molecule: NH4+ (aq) + H2O ↔ NH3 (aq) + H3O+ (aq).

Because this reaction produces H3O+ ions, the pH of the solution decreases. The equilibrium constant (hydrolysis constant) for this process is given by equation:

3 3

4

[NH ] [H O ][NH ]

wh

base

KKK

+

+⋅

= =

1919

Hydrolysis of saltsHydrolysis of saltsFor salts formed by a weak acid and a weak base, both the For salts formed by a weak acid and a weak base, both the cationcation and and

the anion hydrolyze. The hydrolysis constant in this case is detthe anion hydrolyze. The hydrolysis constant in this case is determined ermined by both dissociation constants of the acid and the base:by both dissociation constants of the acid and the base:

wh

acid base

KKK K

=⋅

If Kbase > Kacid then the solution must be basic because the anion will hydrolyze to a greater extent than the cation. At equilibrium, there will be more OH– ions than H+ ions.

If Kbase for the anion is smaller than Kacid for the cation, the solution will be acidic because cation hydrolysis will be more extensive than anion hydrolysis.

If Kbase is approximately equal to Kacid, the solution will be nearly neutral.

2020

Buffer solutionsBuffer solutionsBuffer solutionsBuffer solutions are solutions with ability to keep constant the are solutions with ability to keep constant the рНрН

value at dilution or addition of small amounts of a strong acid value at dilution or addition of small amounts of a strong acid or a strong or a strong base. base.

Usually buffer solution consists of a weak acid (weak base) and Usually buffer solution consists of a weak acid (weak base) and salt salt of this acid (base) which is strong electrolyte, e.g. CHof this acid (base) which is strong electrolyte, e.g. CH33COOH + COOH + CHCH33COONa COONa –– acetate buffer; NHacetate buffer; NH44OH + NHOH + NH44Cl Cl –– ammonia buffer, etc. ammonia buffer, etc.

In general form it is possible to say, that the buffer solution In general form it is possible to say, that the buffer solution consists consists from conjugated acid and base. from conjugated acid and base.

The pH value of a buffer solution may be calculated using quantiThe pH value of a buffer solution may be calculated using quantities ties of the components forming it, for example, for acid buffer:of the components forming it, for example, for acid buffer:

oHAoMeA

pH p log cKc

= −

pK – negative decimal logarithm of the acid dissociation constant; co –initial concentrations of the acid and its salt in the solution. This equation is known as Henderson-Hasselbach equation.

2121

Ability of buffer solutions to keep the Ability of buffer solutions to keep the рНрН value at addition of a value at addition of a strong acid or a base is called strong acid or a base is called buffer actionbuffer action. .

As a measure of buffer action As a measure of buffer action the buffer capacitythe buffer capacity is used. is used.

Buffer capacityBuffer capacity is an added amount of a strong acid or a is an added amount of a strong acid or a strong base, which addition to one liter of a buffer solution strong base, which addition to one liter of a buffer solution changes the changes the рНрН value to unity.value to unity.

Buffer solutionsBuffer solutions

Buffer solutions in the organismBuffer solutions in the organismThe pH of the blood plasma is maintained at about 7.40 by several

buffer systems but the most important is the bicarbonic buffer system. This pH value is dependent upon two coupled reactions. First, the equilibrium of gaseous carbon dioxide dissolved in the blood and water producing the carbonic acid: CO2(aq) + H2O ↔ H2CO3(aq).

2222

The amount of carbon dioxide in the blood is coupled to the The amount of carbon dioxide in the blood is coupled to the amount present in the lungs. Second, the equilibrium between amount present in the lungs. Second, the equilibrium between carbonic acid and bicarbonate ion:carbonic acid and bicarbonate ion:

HH22COCO3 3 (aq) (aq) ↔↔ HCOHCO33−− (aq) + H(aq) + H+ + ((aqaq), ), ppKK = 6.37.= 6.37.

These reactions lead to the presence in solution the These reactions lead to the presence in solution the conjugate pair HCOconjugate pair HCO33

−−/H/H22COCO33 that forms the buffer system. The that forms the buffer system. The fact that the pH of normal blood is 7.40 implies that fact that the pH of normal blood is 7.40 implies that [HCO[HCO33

−−]/[H]/[H22COCO33] = 20. The excess of an acid in the blood is fixed ] = 20. The excess of an acid in the blood is fixed by interaction with by interaction with hydrocarbonatehydrocarbonate ion, the excess of a base ion, the excess of a base –– by by interaction with carbonic acid.interaction with carbonic acid.

HydrophosphateHydrophosphate buffer system is formed by buffer system is formed by hydrophosphatehydrophosphateandand dihydrophosphatedihydrophosphate ions. There is an ions. There is an protolyticprotolytic equilibrium equilibrium between these two ions:between these two ions:

HH22POPO44−− ↔↔ HH++ + HPO+ HPO44

22−−, , ppKK == 7.21.7.21.

Buffer solutionsBuffer solutions

2323

If If рНрН value of the blood is 7.40, the ratio of the concentrations of value of the blood is 7.40, the ratio of the concentrations of the the ions [HPOions [HPO44

22−−]/[H]/[H22POPO44−−] is 1.55] is 1.55 :: 1.1.

In the erythrocytes the pH is 7.25, the principal buffer systemsIn the erythrocytes the pH is 7.25, the principal buffer systems are are bicarbonate HCObicarbonate HCO33

−−/H/H22COCO33 and hemoglobin systems. As a very rough and hemoglobin systems. As a very rough approximation, we can treat it as a weak approximation, we can treat it as a weak monoproticmonoprotic acid of the form acid of the form HHbHHb that dissociates in solution:that dissociates in solution:

HHb(aqHHb(aq) ) ↔↔ HH++(aq(aq) + ) + HbHb––((aqaq),),

HHbHHb represents the hemoglobin molecule and represents the hemoglobin molecule and HbHb–– the conjugate the conjugate base of base of HHbHHb. . OxyhemoglobinOxyhemoglobin (HHbO(HHbO22), formed by the combination of ), formed by the combination of oxygen with hemoglobin, is a stronger acid than oxygen with hemoglobin, is a stronger acid than HHbHHb::

HHbOHHbO22(aq) (aq) ↔↔ HH++(aq(aq) + HbO) + HbO22–– (aq).(aq).

Buffer solutionsBuffer solutions

2424

ColligativeColligative properties of solutions properties of solutions ColligativeColligative properties of solutionsproperties of solutions are several important are several important

properties that depend on the number of solute particles in properties that depend on the number of solute particles in solution and not on the nature of the solute particles.solution and not on the nature of the solute particles.

The particles may be atoms, ions or molecules. It is important The particles may be atoms, ions or molecules. It is important to keep in mind that we are talking about relatively dilute to keep in mind that we are talking about relatively dilute solutions, that is, solutions whose concentrations are less 0.1 solutions, that is, solutions whose concentrations are less 0.1 mol/Lmol/L.. The term The term ““colligativecolligative propertiesproperties”” denotes denotes ““properties that properties that depend on the collectiondepend on the collection””..

The The colligativecolligative properties are:properties are:vapor pressure lowering, vapor pressure lowering, boilingboiling--point elevation, point elevation, freezingfreezing--point depression, point depression, osmotic pressure. osmotic pressure.

2525

If a solute is If a solute is nonvolatilenonvolatile vapor pressure of the solution is always less vapor pressure of the solution is always less than that of the pure solvent and depends on the concentration othan that of the pure solvent and depends on the concentration of the f the solute. solute.

The relationship between solution vapor pressure and solvent vapThe relationship between solution vapor pressure and solvent vapor or pressure is known as pressure is known as RaoultRaoult’’ss lawlaw. This law states that . This law states that the vapor pressure the vapor pressure of a solvent over a solution of a solvent over a solution ((pp11)) equals the product of vapor pressure of the equals the product of vapor pressure of the pure solvent pure solvent ((pp11°°)) and the mole fraction of the solvent in the solution and the mole fraction of the solvent in the solution ((xx11):):

pp11 = = xx11pp11°°..In a solution containing only one solute, than In a solution containing only one solute, than xx11 = 1 = 1 –– xx22, where , where xx22 is the is the

mole fraction of the solute. Equation of the mole fraction of the solute. Equation of the RaoultRaoult’’ss law can therefore be law can therefore be rewritten asrewritten as

((pp11°° –– pp11)/)/pp11°° = = xx22..One can see that the One can see that the relative decrease in vapor pressure of the solvent relative decrease in vapor pressure of the solvent

is directly proportional to the mole fraction of the solute in sis directly proportional to the mole fraction of the solute in solutionolution. .

ColligativeColligative properties of solutions:properties of solutions:Vapor pressure loweringVapor pressure lowering

2626

ColligativeColligative properties of solutions:properties of solutions:The elevation of boiling pointThe elevation of boiling point

The boiling of a pure liquid or a solution occurs at that The boiling of a pure liquid or a solution occurs at that temperature at which its vapor pressure becomes equal the externtemperature at which its vapor pressure becomes equal the external al atmospheric pressure. atmospheric pressure.

Because at any temperature the vapor pressure of the solution isBecause at any temperature the vapor pressure of the solution islower than that of the pure solvent, the vapor pressure of solutlower than that of the pure solvent, the vapor pressure of solution ion reaches atmospheric pressure at a reaches atmospheric pressure at a higherhigher temperature than the temperature than the normal boiling point of the pure solvent. normal boiling point of the pure solvent.

This leads This leads to to elevation of boiling point elevation of boiling point of solutionof solution in comparison in comparison with pure solvent. The with pure solvent. The boilingboiling--point elevationpoint elevation is defined as:is defined as:

where where TTbb is the boiling point of the solution, is the boiling point of the solution, TTb,ob,o –– the boiling point the boiling point of the pure solvent. It has been found experimentally thatof the pure solvent. It has been found experimentally that

, 0b b b оT T TΔ = − >

2727

ColligativeColligative properties of solutions:properties of solutions:The elevation of boiling pointThe elevation of boiling point

ΔΔTTbb = = KKbbmm,,where where mm –– molalitymolality of the solute, of the solute, KKbb is the is the molalmolal boilingboiling--point point

elevation constant.elevation constant.

It has been proved theoretically that It has been proved theoretically that KKbb is determined only by is determined only by properties of the solvent:properties of the solvent:

RR –– universal gas constant, universal gas constant, MM11 –– molar mass of the solvent, molar mass of the solvent, ΔΔHH°°vapvap ––enthalpy change of vaporization of the pure solvent.enthalpy change of vaporization of the pure solvent.

The value of boilingThe value of boiling--point elevation constant for water is 0.52 point elevation constant for water is 0.52 KK··kgkg/mol. One can see that if the /mol. One can see that if the molalitymolality of an aqueous solution of an aqueous solution is 1.00 mol/kg, the boiling point will be 100.52is 1.00 mol/kg, the boiling point will be 100.52 °°C.C.

2, 1

1000b o

b ovap

RT MK

H⋅

=⋅Δ

2828

ColligativeColligative properties of solutions:properties of solutions:The depression of the freezing pointThe depression of the freezing point

The pure solvent freezes if itThe pure solvent freezes if it’’s vapor pressures in liquid and solid s vapor pressures in liquid and solid states are equal. The vapor pressure of a solid solvent depends states are equal. The vapor pressure of a solid solvent depends on on temperature only and decreases with decrease in temperature. temperature only and decreases with decrease in temperature.

These leads the temperature of the freezing of solution is These leads the temperature of the freezing of solution is lowerlower than than the freezing point of the solvent. the freezing point of the solvent. The The depression of freezing pointdepression of freezing point is is defined as:defined as:

TTo,fo,f –– freezing point of the pure solvent, and freezing point of the pure solvent, and TTff –– freezing point of the freezing point of the solution. The solution. The ΔΔTTff value is proportional to the value is proportional to the molalmolal concentration of the concentration of the solute:solute:

ΔΔTTff = = KKffmm,,where where mm –– molalitymolality of the solute, and of the solute, and KKff is the is the molalmolal freezingfreezing--point point

depression constantdepression constant. Like . Like KKbb, the , the KKff has the units has the units KK··kgkg··molmol––11..

, 0f o f fT T TΔ = − >

2929

ColligativeColligative properties of solutions:properties of solutions:The depression of the freezing pointThe depression of the freezing point

The The KKff value depends only on properties of the solvent:value depends only on properties of the solvent:

ΔΔHHfusfus is enthalpy change of fusion of the pure solvent.is enthalpy change of fusion of the pure solvent.

2, 1

1000f o

f ofus

RT MK

H

⋅=

⋅Δ

ColligativeColligative properties of solutions: Osmosisproperties of solutions: OsmosisOsmosis is the spontaneous movement of a pure solvent into a

solution separated from it by a semipermeable membrane. The membrane is permeable by the solvent molecules but not by

the solute and allows the solvent, but not the solute, to pass through. The osmotic pressure is the pressure that must be applied to the

solution to prevent the solvent transfer.

3030

For dilute solutions the osmotic pressure is given by the For dilute solutions the osmotic pressure is given by the van'tvan'tHoff equation:Hoff equation:

ππ = = cRTcRT,,TT –– absolute temperature,absolute temperature, cc –– molar concentration of the molar concentration of the

solute, solute, RR −− universal gas constant.universal gas constant.

If two solutions are of equal concentration and, hence, of the If two solutions are of equal concentration and, hence, of the same osmotic pressure, they are said to be same osmotic pressure, they are said to be isotonicisotonic. .

If two solutions are of unequal osmotic pressures, the more If two solutions are of unequal osmotic pressures, the more concentrated solution is said to be concentrated solution is said to be hypertonichypertonic and the more and the more dilute solution is described as dilute solution is described as hypotonichypotonic..

ColligativeColligative properties of solutions: Osmosisproperties of solutions: Osmosis

3131

ColligativeColligative properties of solutions: Osmosisproperties of solutions: Osmosis

Figure. A cell in (a) an isotonic solution, (b) a hypotonic solution, and (c) a hypertonic solution.

The cell remains unchanged in (a), swells in (b), and shrinks in (c).

3232

ColligativeColligative properties of electrolyte properties of electrolyte solutionssolutions

The The colligativecolligative properties of electrolytes is characterized by properties of electrolytes is characterized by slightly different approach than the one used for the slightly different approach than the one used for the colligativecolligativeproperties of properties of nonelectrolytesnonelectrolytes. .

The The colligativecolligative properties of binary electrolyte solution should properties of binary electrolyte solution should be twice as great as those of an electrolyte solution containingbe twice as great as those of an electrolyte solution containing a a nonelectrolytenonelectrolyte in the same concentration. Similarly, we would in the same concentration. Similarly, we would expect a ternary electrolyte solution to depress the freezing poexpect a ternary electrolyte solution to depress the freezing point int by three times as much as a by three times as much as a nonelectrolytenonelectrolyte solution with the solution with the concentration. concentration. To account for this effect we must modify the To account for this effect we must modify the equations for equations for colligativecolligative properties as followsproperties as follows::

ΔΔTTbb = = iKiKbb··mm,,((pp11°° –– pp11)/)/pp11°° = = ixix22,,

ΔΔTTff = = iKiKff··mm,,ππ = = icRTicRT..

3333

The variable The variable i i is the is the vanvan’’tt HoffHoff’’s isotonic factors isotonic factor, which is , which is defined as the ratio of actual number of particles in solution adefined as the ratio of actual number of particles in solution after fter dissociation and number of molecules (structural units) of initidissociation and number of molecules (structural units) of initially ally dissolved substance.dissolved substance.

Thus, Thus, ii should be 1 for should be 1 for nonelectrolytesnonelectrolytes. For strong binary . For strong binary electrolytes such as electrolytes such as NaClNaCl and KNOand KNO33, should be 2, and for strong , should be 2, and for strong ternary electrolytes such as Naternary electrolytes such as Na22SOSO44 and MgCland MgCl22, , ii should be 3.should be 3.

ColligativeColligative properties of electrolyte properties of electrolyte solutionssolutions

3434

ReferencesReferences1. Chang1. Chang R. Chemistry. 10R. Chemistry. 10--th edition. NY: McGrawth edition. NY: McGraw--Hill, Hill,

2010. 11702010. 1170 p.p.2. 2. ChangChang R. R. GeneralGeneral ChemistryChemistry: : TheThe EssentialEssential ConceptsConcepts. .

66--thth eeditiondition. NY: McGraw. NY: McGraw--Hill, 2011. 853Hill, 2011. 853 p.p.3. Allen J.P. Biophysical Chemistry. Blackwell Publishing, 3. Allen J.P. Biophysical Chemistry. Blackwell Publishing,

2008. 4922008. 492 p.p.4. Atkins P., de Paola J. Physical Chemistry for the Life 4. Atkins P., de Paola J. Physical Chemistry for the Life

Sciences. Sciences. W.H.FreemanW.H.Freeman Publishers, 2006. 624 p.Publishers, 2006. 624 p.5. 5. EltsovEltsov S.V., S.V., VodolazkayaVodolazkaya N.A. Physical and colloid N.A. Physical and colloid

chemistry in the course chemistry in the course ““Medical ChemistryMedical Chemistry””. Theory . Theory and laboratory exercises: manual. and laboratory exercises: manual. KharkivKharkiv: : V.N.KarazinV.N.Karazin KharkivKharkiv National University, 2012. 132National University, 2012. 132 p.p.