Biochemistry for Students VK Malhotra
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BiophysicsCHAPTER 1

 
HYDROGEN ION CONCENTRATION pH
Acids are substances which furnish hydrogen ions (H+) in the solution, whereas bases are substances that furnish hydroxide ions (OH) in the solution. Substances that dissociate in water into a cation (positively charged ion) and an anion (negatively charged ion) are classified as electrolytes. Whereas sugar or alcohols which dissolve in water but do not carry a charge or dissociate into species with a positive and negative charge are classified as non-electrolytes.
Strong electrolytes are completely ionized in aqueous solutions whereas weak electrolytes are partially ionized in aqueous solutions.
pH of a solution is defined as the negative logarithm of its hydrogen ion concentration.
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Pure water has equal concentration of H+ and OH ions, the concentrations of each is very small and each being equal to 10−7 moles/liter at room temperature.
Water dissociates into:
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From the Law of Mass action, the dissociation of water can be represented as
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2
The bracket indicates the concentration of each component in moles per litre.
The concentration of undissociated water is so large as compared to the concentration of H+ and OH ions, so that for all the practical purposes it is fairly constant. This simplifies the above equation to:
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Where Kw is ionic product of water or the dissociation constant of water. Electrical conductivity measurements have shown that dissociation constant of water is constant at a given temperature and changes with the change in temperature.
Ionic product of water is usually taken as 10−14 at the room temperature (25°C).
Then:
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Taking logarithm of both sides
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By rearrangement,
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According to the definition of pH, the above equation simplifies to
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At neutrality, both hydrogen and hydroxide ions have equal concentration, i.e.
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There exists an inverse relationship between [H+] and [OH+] ions in solution. As hydrogen ion concentration increases, the hydroxide ion concentration decreases and vice versa.
The acidity or alkalinity of a solution is determined by the amount of [H+] and [OH] ions present.3
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A solution having hydrogen ions concentration of one nor-mality (1N) will have a pH 0, and other having hydroxide concentration of one normality (1N) will have pH 14.
It should also be kept in mind that a change of one pH unit brings a ten-fold change in acidity or alkalinity, i.e. a solution of pH 5 has ten times more the hydrogen ion concentration than that of a solution of pH 6 and a hundred times more than that of a solution of pH 7. If hydrogen ion concentration is doubled, the pH falls by 0.3 units.
The average pH values of some body fluids are:
Gastric juice
1.4
Saliva
6.8
Urine
6.0
Milk
7.1
Tears
7.2
Blood
7.4
Pancreatic juice
8.0
Q. Calculate the pH of a solution of which hydrogen ion concentration is 4.6 × 10−9 M.
A. pH
= –log10 [CH+]
= –log10 [4.6 × 10−9]
= –log10 4.6 + 9 log10 10
= −0.66 + 9
= 8.34.
Q. Calculate the hydrogen ion concentration of a solution, the pH of which is 4.50.
A. pH = –log10 [CH+]4
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Buffers
Buffers are the solutions, which resist changes in pH, when small amount of acid or alkali is added to them. The best buffer is the one which gives the smallest change. Buffers act like shock absorber against the sudden changes of pH. Acetic acid: sodium acetate (CH3COOH; CH3COONa) and carbonic acid: sodium carbonate (H2CO3;NaHCO3) are examples of buffer systems.
A buffer is a pair of weak acid and its salt with a strong base or a pair of weak base and its salt with a strong acid. If either free H+ or free OH are added to a solution of such a pair they will be partially converted to the unionized form.
Thus:
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Where HB denotes a weak acid and B its conjugate base.
The combination of a weak acid and the base that is formed on dissociation is referred to as a conjugate pair. Ammonium ion NH4+ is an acid because it dissociates to yield a H+ and NH3 which is conjugate base. Phosphoric acid (H3PO4) is an acid and PO4−3 is a base.
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The ability to buffer hydrogen ions is more important to the body than the buffering of hydroxyl ions.
The most commonly used buffers in the laboratory are:
Acetate Buffer (Sodium acetate/Acetic acid).
Phosphate Buffer (Na2HPO4/KH2PO4).
Citrate Buffer (Sodium citrate/Citric acid).5
Barbitone Buffer (Sodium diethyl barbiturate/Diethyl barbituric acid).
The pH of a buffer solution is calculated by the Henderson-Hasselbalch equation.
Suppose the solution is composed of a weak acid [HA] and its salt with a strong base [BA].
The dissociation of weak acid [HA] and salt [BA] can be represented as follows:
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[HA] dissociates less because it is a weak acid, whereas [BA] dissociates completely because it is a salt of a strong base.
The dissociation constant of equation (1) is represented as
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By rearrangement:
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As the acid [HA] is weak acid, it will be very slightly ionized, and most of it will be present as [HA], whereas the salt [BA] will be highly ionized, the concentration of [A] can be taken as the total concentration of [BA].
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Taking logarithm of both sides
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6
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This equation is called Henderson-Hasselbalch equation.
If the value of K (the dissociation constant) is known, the pH of a buffer solution of a given composition can be readily calculated.
The above equation indicates that the pH of the buffer solution depends on the ratio of the concentrations of the salt and the acid.
The buffering power of a mixture of a weak acid and its salt is greatest when the two substances are present in equivalent proportions. Then the buffer has its maximum capacity to absorb either H+ or OH ions. So that pH is approximately equal to the pK of the acid, i.e., when the acid is half neutralized.
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Therefore
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The effective range of a buffer is 1 pH unit higher or lower than the pKa. The pKa value of most of the acids produced in the body is well below the physiological pH, hence they ionizes, immediately and add H+ to the medium.
The effect of dilution on the pH of a buffer mixture and on the apparent pK of the acid is slight. The pH depends upon the ratio of salt: acid and this ratio is not much affected by dilution.
The pH of the buffer solution is determined by the pK and the ratio of salt to acid concentration. Lower the pK value, lower is the pH of the solution; whereas the ratio of salt to acid concentration may vary with no change in pH as long as the ratio remains the same. When the ratio between the salt 7and the acid is 10;1, the pH will one unit higher than the pKa whereas when the ratio between salt and acid is 1;10, the pH will be one unit lower than the pKa.
Buffers are of main importance in regulating the pH of the body fluids and tissues within limits consistent with life and normal function. Many biochemical reactions, including those catalysed by enzymes, require pH control which is provided by buffers.
Dissociation constant and pK of compounds of importance in biochemistry.
Compound
Dissociation constant
pK
Acetic acid
1.74 × 10−5
4.76
Citric acid
8.12 × 10−4
3.09
Lactic acid
1.38 × 10−4
3.86
Pyruvic acid
3.16 × 10−3
2.50
Water
1 × 10−14
14
Succinic acid
6.46 × 10−5
4.19
Q. A mixture of equal volumes of 0.1M NaHCO3 and 0.1M H2CO3 shows a pH of 6.1. Calculate the pKa of H2CO3.
A. Concentration of H2CO3, i.e., acid = 0.1M.
Concentration of NaHCO3, i.e., salt = 0.1M.
Applying Henderson-Hasselbalch equation
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Q. Phosphate buffers are prepared by mixing together 0.1M Na2HPO4 and 0.1M KH2PO4 in different ratios. Calculate the expected pH of the buffer solution prepared by mixing the salt and the acid in the above system in the ratio 2:1 (Given log 2 = 0.30 and pK2 of phosphoric acid 6.7)8
A. Concentration of Na2HPO4 (i.e., salt) = 2 × 0.1M.
Concentration of KH2PO4 (i.e., acid) = 1 × 0.1M. Applying Henderson-Hasselbalch equation
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So the e×pected pH of the buffer solution is 7.
Q. You are provided with ample supply of carbonic acid and sodium bicarbonate. How would you prepare a buffer solution of pH 6.1. Give the theoretical basis of the procedure to be followed. (pKa of carbonic acid = 6.1)
A. Applying Henderson-Hasselbalch equation:
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pKa of carbonic acid = 6.1
The buffer solution to be prepared should have a pH of 6.1.
This can be achieved if the concentration of sodium carbonate and carbonic acid is the same.
So buffer solution of pH 6.1 can be made by mixing equal volume of sodium carbonate and carbonic acid of same concentration.
Q. What would be the pH of 100 cm3 of a 0.2M acetic acid solution to which has been added 10 cm3 of 1.5M sodium hydroxide. (Given the pK for acetic acid 4.74.)
A. Before the addition of NaOH,
The number of moles of acetic acid present is:
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9
Also the number of moles of sodium hydroxide present in 10 cm3 of 1.5M NaOH solution are
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Before the start of reaction, the concentration of acetic acid is 0.02M and that of sodium hydroxide is 0.015M.
When the reaction takes place, i.e., 0.015M NaOH neutralizes 0.015M of CH3COOH to form 0.015M of sodium acetate. After the reaction is over, the concentration of CH3COOH left behind 0.02M − 0.015M = 0.005M.
Reaction CH3COOH + NaOH CH3COONa + H2O
Now, applying Henderson-Hasselbalch equation:
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Blood Buffers
The buffer systems of blood are:
  1. Bicarbonate-carbonic acid (BHCO3 : H2CO3)
  2. Hemoglobinate-hemoglobin (B.Hb : H.Hb)
  3. Oxyhemoglobinate-oxyhemoglobin (B.HbO2 : H.HbO2)
  4. Phosphate buffer (B2HPO4 : BH2PO4)
  5. Protein buffer (B. Protein : H. Protein)
The most important buffer of plasma is bicarbonate-carbonic acid system. It is present in high concentration. It is of great importance in the acid-base balance of the extracellular fluid and in the maintenance of the blood pH within normal limits. The bicarbonate system is of prime physiological importance, and acts cooperatively with other buffers.10
The hemoglobinate-hemoglobin and oxyhemoglobinate-oxyhemoglobin buffer, i.e., hemoglobin buffers are of prime importance in the erythrocytes. Hemoglobin actually absorbs 60 percent of the hydrogen ions produced by H2CO3.
Hemoglobin is a better buffer than most proteins at pH 7.4 because of relatively high concentration of imidazole group (pKa approximately 7) of the constituent histidine molecules.
Deoxyhemoglobin is a better buffer than oxyhemoglobin. The converse is also true, i.e., the hydrogen ions decrease the affinity of hemoglobin for oxygen.
Protein and phosphate buffers are of little importance in the blood, i.e., they are the minor buffering systems in the blood. Proteins are present in much higher concentrations in cells than in plasma. They are probably important in buffering H+ ions before their release from cells. But phosphate buffer is of importance in raising the plasma pH through excretion of H2PO4 by kidney. It is an important urinary buffer and works cooperatively with the bicarbonate system.
Approximate contribution of individual buffers to total buffering in whole blood is given below.
Individual buffers
Percent buffering in whole blood
Hemoglobin and oxyhemoglobin
35
Organic phosphates
3
Inorganic phosphates
2
Plasma proteins
7
Plasma bicarbonate
35
Erythrocyte bicarbonate
18
 
Indicators
Indicators are substances which change in color with change in the pH of the solution in which they are present. Indicators are dyes which are weak acids or weak bases and have the property of dissociating in solution. Their ionized form have one color and their unionized form have another color. The color of an indicator solution depends on the relative amounts of its acid and base form present in the solution.
An indicator which is a weak acid, is undissociated in acid solution and gives the acid color. In the presence of alkali, it forms a salt which dissociates and displays alkali color.11
Indicators are used in:
  1. Determining the end point in acid-base titrations.
  2. Determining pH of solutions.
 
Universal Indicator
It is a mixture of a number of indicators which gives a variety of color changes over a wide-range of pH.
Some common indicators useful for biological pH range are:
Indicators
Color
pK
pH range solution
In acid solution
In alkaline
1. Thymol blue (acid range)
1.65
1.2–2.8
Red
Yellow
2. Methyl yellow (Topfer's reagent)
2.9–4.0
Red
Yellow
3. Methyl orange
3.46
3.1–4.4
Red
Orange
Yellow
4. Methyl red
5.00
4.3–6.1
Red
Yellow
5. Phenol red
7.81
6.7–8.3
Yellow
Red
6. Thymol blue (alkaline range)
8.90
8.0–9.6
Yellow
Blue
7. Phenolphthalein
9.70
8.2–10
Colorless
Pink
 
OSMOSIS AND OSMOTIC PRESSURE
Osmotic flow occurs whenever a semipermeable membrane separates a solution and its pure solvent or between two solutions differing in concentrations. Water molecules pass through the membrane until the concentration on both sides becomes same. Such a movement of solvent molecules from a pure solvent or dilute solution through a semipermeable membrane is called osmosis.
 
Osmotic Pressure
Osmotic pressure is the pressure that must be applied on a solution to keep it in equilibrium with the pure solvent when 12the two are separated by semipermeable membrane or Osmotic pressure is the force required to oppose the osmotic flow.
Hypertonic solutions If the osmotic pressure of the surrounding solution is high, water passes from the cell to the stronger solution outside, this causes the cell to shrink away.
Isotonic solutions If e×ternal solution has the same osmotic pressure, no flow of water takes place and hence no effect upon the cell protoplasm is observed.
Hypotonic solutions If the osmotic pressure of the surrounding solution is low, water passes into the cell from the surrounding, the cells become turgid and rupture.
Van't Hoff's law of osmotic pressure:
  1. The osmotic pressure of a solution is directly proportional to the concentration of the solute in the solution.
  2. The osmotic pressure of a solution is directly proportional to the absolute temperature.
Thus indirectly they follow Boyle's and Charle's Law.
Osmotic pressure is given by the formula.
π
= CRT
where
π
= Osmotic pressure
C
= Concentration in moles per liter
R
= Gas constant
T
= Absolute temperature
Osmotic pressure is dependent upon the number of dissolved particles (i.e., on concentration) and is independent of the size or weight of the particle.
According to the law of osmotic pressure, 1 molar solution exerts an osmotic pressure of 22.4 liters at 0°C.
The osmotic pressure of substances which ionizes is given by the formula.
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where i the isotonic coefficient is given by:
i
= 1 + α (n−1)
where
α
= degree of ionization
n
= number of ions obtained on ionization
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The value of i, depends upon the degree of dissociation of the electrolyte, which varies from one electrolyte to another. It increases as the dilution increases and depends upon the number of ions formed.
Since osmotic pressure is proportional to the total number of solute particles in solution, the substances which ionize, will have the higher osmotic pressure as compared to those substances which do not ionize.
The osmotic pressure exerted by colloidal solutions is always less as compared to that of crystalloids of similar concentrations in gram per liter because the magnitude of osmotic pressure depends upon number of particles present in unit volume of the solution. Solutions that exert the same osmotic pressure are called isomotic.
The osmotic pressure of 1M NaCl will be double, as compared to the osmotic pressure of 1M sucrose or glucose solution because each molecule of NaCl on ionization gives two ions, i.e., Na+ and Cl ions and each ion will exert the respective osmotic pressure.
The unit of osmotic pressure is osmol or milliosmol. An osmolar solution is defined as one e×erting the osmotic pressure of a molar solution of a nondissociated solute in one liter of solution. Thus the number of osmoles of a undissociated substance in a liter of solution would be the weight in grams divided by its molecular weight. The milliosmolar concentration of glucose in a sample of plasma containing 90 mg per 100 ml therefore would be:
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For nonelectrolytes such as glucose or sucrose, 1 millimol is equal to 1 milliosmol. For electrolytes such as NaCl, one millimol of NaCl is equivalent to 2 milliosmol (Na+ and Cl+).
Q. 1 Molar solution of glucose has an osmotic pressure of 22.4 atmosphere at 0°C. Calculate the osmotic pressure of 0.1M sucrose and 0.1M NaCl at the same temperature. Assume 100% dissociation of NaCl.14
A. 1 molar solution exerts an osmotic pressure of 22.4 atmosphere.
So 0.1 Molar solution will exert an osmotic pressure of 2.24 atmosphere.
So 0.1M sucrose will have an osmotic pressure of 2.24 atmosphere.
In case of sodium chloride, each molecule of NaCl on dissociation gives Na+ ions and Cl ions. Each ion, i.e., Na+ and Cl will exert an independent osmotic pressure. Also the dissociation of sodium chloride is 100%.
So 0.1M solution of NaCl will exert an osmotic pressure of 2 × 2.24, i.e., 4.48 atmospheres.
Q. Calculate the osmolarities of:
  1. 0.1M NaCl solution
  2. 0.1M sucrose solution
A. The term milliosmol is used in connection with osmotic pressure.
0.1M solution of NaCl will have an osmotic pressure of 0.1 × 2 = 0.2 milliosmol (because each molecule of sodium chloride on ionization gives two ions).
Whereas 0.1M sucrose will have an osmotic pressure of 0.1 milliosmol.
 
Milliequivalent
1 milliequivalent is one thousandth of an equivalent and is the same as millimol as long as the valency is one.
For valence 1; 1 millimol = 1 milliequivalent
For valence 2; 1 millimol = 2 milliequivalent
For valence 3; 1 millimol = 3 milliequivalent
How to calculate millimols.
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Example:
78 mg of K+ ions per liter
= 78/39, i.e., 2 millimols
= 2 milliequivalent
= 2 milliosmols
15
Whereas
100 mg of Ca++ per liter
= 100/40, i.e., 2.5 millimols
= 2.5 milliosmols
= 5 milliequivalent
222 mg of CaCl2 per liter
= 222/111, i.e., 2 millimols of CaCl2
= 6 milliosmols.
 
Gibbs Donnan Equilibrium
Gibbs Donnan equilibrium is concerned with the distribution of electrolytes in systems separated by membranes which are impermeable to certain components. This resultant unequal distribution of diffusible ions due to the presence of nondiffusible ions on one side of the membrane is called Gibbs Donnan Effect.
Example: Consider a semipermeable membrane separating a solution of NaCl and Protein (NaR). The membrane is permeable to Na+ and Cl but not to R.
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When the equilibrium is attained, the product of concentrations of diffusible ions (Na+ and Cl) on one side of membrane is equal to the product of concentrations of same ions on the other side.
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The concentration of diffusible positive ion is greater on the side of membrane containing non-diffusible ion
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Donnan effect is of physiological significance in biological systems involving ion exchanges across permeable membranes when the fluid on one side of the membrane contains a non-diffusible component. This results in difference of concentration of diffusible ions which leads to junction potential 16across the membrane, which is a driving force for most of the body reaction. Donnan effect is also involved in absorption, secretion and maintenance of different electrolyte concentrations between various compartments of the body.
 
COLLOIDS
Graham classified substances into:
  1. Crystalloids Substances which pass through parchment or animal membrane.
  2. Colloids Substances which do not pass through parchment or animal membrane.
But now-a-days, the size of the molecule or particle determines whether they will form crystalloidal or colloidal solutions.
According to modern concept.
True solution
Colloidal solution
Suspension solution
where the size (diameter) of the particle is less than 1 mμ
where the size is between 1–20 mμ
where the size is more than 200 mμ
 
Properties of Colloidal Solutions
  1. Dialysis The process of separation of crystalloids from colloids by diffusion through a membrane by osmotic force is called dialysis. Dialysis has an important application in medicine in the artificial kidney. This device is inserted into the patient's circulation and diffusible material particularly urea passes out from the blood substituting for the action of the faulty kidneys.
  2. As the size of the colloidal particle is large, few particles are present in small concentration, the osmotic pressure of the colloidal solution will be very small. This is of prime importance in driving the passage of water and other substances through cell membranes.
  3. Precipitation Colloids possess net charge at the surface which arises from ionisable groups on the particle surface and also from absorption of ions and can be precipitated by neutralizing the charge.
    17
  4. Brownian motion.
  5. Tyndall effect.
 
SURFACE TENSION
The force with which the surface molecules are held in a solution is called surface tension. Some substances such as bile salts have the property of lowering the surface tension of the medium in which they are present. This effect is used in the absorption of fats from the intestine.
Other properties of surface tension are formation of drops of liquids falling through air; rise of liquid in a capillary tube and formation of meniscus at the surface of liquids. Surface tension decreases with increase in temperature.
 
Role of Surface Tension
Substance which lower the surface tension becomes concentrated in the surface layer whereas substances which increase surface tension are distributed in the interior of the liquid.
Soaps, oils, proteins and bile acids reduce the surface tension of water, while sodium chloride and inorganic salts increase the surface tension.
Surface tension leads to better adsorption.
 
ABSORPTION
Certain substances have the power of making water insoluble substances soluble in water without any apparent chemical alteration of the dissolved substance.
The substances having such quality are called hydrotropic substances.
Among the insoluble substances which are brought into the solution are fats, phospholipids, sterols, calcium carbonate, magnesium phosphate etc.
Substance which bring about the solubility are cholic acids, benzoic acid, hippuric acid, soaps of higher fatty acids, etc.
The biological importance of the solution of an insoluble substance in hydrotropic substances lie in the fact that the substances so dissolved are diffusible through membranes.18
 
VISCOSITY
Viscosity of a liquid is the resistance to flow. Viscosity of blood is 4.5 times more than water. Viscosity of blood is lowered in anemia, nephritis, leukemia, malaria, diabetes mellitus, jaundice, whereas excessive sweating and shock leads to increase of blood viscocity.