Thursday, March 15, 2012


A (I)
Molecules of gases remain in continuous motion. While moving they collide with each other and with the
walls of the container. This results in change of their speed and redistribution of energy. So the speed and
energy of all the molecules of the gas at any instant is not the same. Thus, we can obtain only average value
of speed of molecules. If there are n number of molecules in a sample and their individual speeds are u1, u2,
u3, …….un, then average speed of molecules uav can be calculated as follows :
1 2 n
u = u +u +..........u
Maxwell and Boltzmann have shown that actual distribution of molecular speeds depends on
temperature and molecular mass of a gas. Maxwell derived a formula for calculating the number of molecules
possessing a particular speed. Fig.A(1) shows schematic plot of number of molecules vs. molecular speed
at two different temperatures T1 and T2 (Temperature T2 is higher thantemperature T1). The distribution of
speeds shown in the plot is called Maxwell-Boltzmann distribution of speeds.
Most probable
speed (u ) mp
Number of molecules
speed (u ) av
Root mean
square speed (u ) rms
ump uav urms
Curve at T2
at T1
T T 2 1 >
Fig.A(1) : Maxwell-Boltzmann distribution of speeds
The graph shows that number of molecules possessing very high and very low speed is very small.
Maximum in the curve represents speed possessed by maximum number of molecules. This speed is called
most probable speed, ump.This is very close to the average speed of the molecules. On increasing the
temperature most probable speed increases. Also, speed distribution curve broadens at higher temperature.
Broadening of curve shows that number of molecules moving at higher speed increases. Speed distribution
also depends upon mass of molecules. At the same temperature, gas molecules with heavier mass have
slower speed than lighter gas molecules. For example, at the same temperature lighter nitrogen molecules
move faster than heavier chlorine molecules. Hence, at any given temperature, nitrogen molecules have
higher value of most probable speed than the chlorine molecules. See the molecular speed distribution
curve of chlorine and nitrogen given in Fig. A(2). Though at a particular temperature the individual speed of
molecules keeps changing, the distribution of speeds remains same.
A (II)
u for chlorine mp
u for nitrogen mp
Molecular speed
Number of molecules
(0, 0)
Fig. A(2): Distribution of molecular speeds for chlorine and nitrogen at 300 K
We know that kinetic energy of a particle is given by the expression:
KineticEnergy 1 mu2
Therefore if we want to know average translational kinetic energy, 1 mu2
2 , for the movement of a gas
particle in a straight line, we require the value of mean of square of speeds, u2 , of all molecules. This is
represented as follows:
2 2 2
2 1 2 u u +u +..........u
= n
The mean square speed is the direct measure of the average kinetic energy of gas molecules. If we
take the square root of the mean of the square of speeds then we get a value of speed which is different
from most probable speed and average speed. This speed is called root mean square speed and is given
by the expression as follows:
rms u = u
Root mean square speed, average speed and the most probable speed have following
urms >uav > ump
The ratio between the three speeds is given below :
ump: uav : urms : : 1 : 1.128 : 1.224
6.5(e) Enthalpy of Dilution
It is known that enthalpy of solution is the enthalpy change associated with the addition of a specified
amount of solute to the specified amount of solvent at a constant temperature and pressure. This argument
can be applied to any solvent with slight modification. Enthalpy change for dissolving one mole of gaseous
hydrogen chloride in 10 mol of water can be represented by the following equation. For convenience we
will use the symbol Aq. for water
HCl(g) + 10 aq. → HCl.10 aq. H = –69.01 kJ / mol
Let us consider the following set of enthalpy changes:
(S-1) HCl(g) + 25 aq. → HCl.25 aq. H = –72.03 kJ / mol
(S-2) HCl(g) + 40 aq. → HCl.40 aq. H = –72.79 kJ / mol
(S-3) HCl(g) + õ aq. → HCl. õ aq. H = –74.85 kJ / mol
The values of H show general dependence of the enthalpy of solution on amount of solvent. As
more and more solvent is used, the enthalpy of solution approaches a limiting value, i.e, the value in
infinitely dilute solution. For hydrochloric acid this value of H in equation (S-3) written above.
If we subtract the first equation from the second equation in the above set of equations, we obtain-
HCl.25 aq. + 15 aq. → HCl.40 aq. H = [ –72.79 – (–72.03)] kJ / mol = – 0.76 kJ / mol
The value of H is enthalpy of dilution, the heat withdrawn from the surroundings when additional
solvent is added to the solution. The enthalpy of dilution of a solution is dependent on the original concentration
of the solution and the amount of solvent added.
6.6(c) Entropy and Second Law of Thermodynamics
We know that for an isolated system the change in energy remains constant. Therefore, increase in entropy
in such systems is the natural direction of a spontaneous change. This, in fact is the second law of
thermodynamics. Like first law of thermodynamics, second law can also be stated in several ways. The
second law of thermodynamics explains why spontaneous exothermic reactions are so common. In
exothermic reactions heat released by the reaction increases the disorder of the surroundings and overall
entropy change is positive which makes the reaction spontaneous.
6.6(d) Absolute Entropy and Third law of Thermodynamics
Molecules of a substance may move in a straight line in any direction, they may spin like a top and the
bonds in the molecules may stretch and compress. These motions of the molecule are called translational,
rotational and vibrational motion respectively. When temperature of the system rises these motions become
more vigorous and entropy increases. On the other hand when temperature is lowered, the entropy decreases.
The entropy of any pure crystalline substance approaches zero as the temperature approaches
absolute zero. This is called third law of thermodynamics. This is so because there is perfect order in
a crystal at absolute zero. The statement is confined to pure crystalline solids because theoretical arguments
and practical evidences have shown that entropy of solutions and super cooled liquids is not zero at 0 K.
The importance of the third law lies in the fact that it permits the calculation of absolute values of entropy
of pure substance from thermal data alone. For a pure substance, this can be done by summing
increments from 0K to 298 K. Standard entropies can be used to calculate standard entropy changes by
a Hess’s law type of calculation.
7.12.1 Designing Buffer Solution
Knowledge of pKa, pKb and equilibrium constant help us to prepare the buffer solution of known pH. Let
us see how we can do this.
Preparation of acidic buffer
To prepare a buffer of acidic pH we use weak acid and its salt formed with strong base. We develop the
equation relating the pH, the equilibrium constant, Ka of weak acid and ratio of concentration of weak acid
and its conjugate base. For the general case where the weak acid HA ionises in water,
A (IV)
HA + H2O Ç H3O+ + A–
For which we can write the expression -
[H O+] [A– ] 3
a [HA] K =
Rearranging the expression we have,
[H O ] [HA] [A– ]
= Ka
Taking logarithm on both the sides and rearranging the terms we get -
[A– ] p pH log
a [HA] K = −
[A– ] pH= p log
a [HA] K + (A-1)
[Conjugate base,A– ] pH= p log
a [Acid,HA] K + (A-2)
The expression (A-2) is known as Henderson – Hasselbalch equation. The quantity
[A– ]
[HA] is
the ratio of concentration of conjugate base (anion) of the acid and the acid present in the mixture. Since
acid is a weak acid, it ionises to a very little extent and concentration of [HA] is negligibly different from
concentration of acid taken to form buffer. Also, most of the conjugate base, [A–], comes from the
ionisation of salt of the acid. Therefore the concentration of conjugate base will be negligibly different
from the concentration of salt. Thus, equation (A-2) takes the form:
pH= p log [Salt ]
a [Acid] K
In the equation (A-1), if the concentration of [A–] is equal to the concentration of [HA] then pH = pKa
because value of log 1 is zero. Thus if we take molar concentration of acid and salt (conjugate base) same,
the pH of the buffer solution will be equal to the pKa of the acid. So for preparing the buffer solution of the
required pH we select that acid whose pKa is close to the required pH. For acetic acid pKa value is 4.76,
therefore pH of the buffer solution formed by acetic acid and sodium acetate taken in equal molar
concentration will be around 4.76.
A similar analysis of a buffer made with a weak base and its conjugate acid leads to the result,
pOH= p log [Conjugate acid,BH ]
b [Base,B] K
+ (A-3)
pH of the buffer solution can be calculated by using the equation pH + pOH =14. We know that
pH + pOH = pKw and pKa + pKb = pKw. On putting these values in equation (A-3) it takes the form as
follows :
w w
p - pH= p p log [Conjugate acid,BH ]
a [Base,B] K K K
− +
pH= p log [Conjugate acid,BH ]
a [Base,B] K
+ (A-4)
A (V)
If molar concentration of base and its conjugate acid (cation) is same then pH of the buffer solution
will be same as pKa for the base. pKavalue for ammonia is 9.25; therefore a buffer of pH close to 9.25 can
be obtained by taking ammonia solution and ammonium chloride solution of equal molar concentration.
For a buffer solution formed by ammonium chloride and ammonium hydroxide, equation (A-4) becomes:
pH=9.25 log [Conjugate acid,BH ]
pH of the buffer solution is not affected by dilution because ratio under the logarithmic term remains
A (VI)
14.5 Hormones
Hormones are molecules that act as intercellular messengers. These are produced by endocrine glands in
the body and are poured directly in the blood stream which transports them to the site of action.
In terms of chemical nature, some of these are steroids, e.g., estrogens and androgens; some like
insulin and endorphins are poly peptides, and amino acid derivatives such as epinephrine and nor epinephrine.
Hormones have several functions in the body. They help to maintain the balance of biological activities
in the body. The role of insulin in keeping the blood glucose level within the narrow limit is an example of
this function. Insulin is released in response to the rapid rise in blood glucose level. On the other hand
hormone glucagon tends to increase the glucose level in the blood. The two hormones together regulate
the glucose level in the blood. Epinephrine and norepinephrine mediate responses to external stimuli.
Growth hormones and sex hormones play role in growth and development. Thyroxine produced in the
thyroid gland is an iodinated derivative of amino acid tyrosine. Abnormally low level of thyroxine leads to
hypothyroidism which is characterised by lethargy and obesity. Increased level of thyroxine causes
hyperthyroidism. Low level of iodine in the diet may lead to hypothyroidism and enlargement of the thyroid
gland. This condition is largely being controlled by adding sodium iodide to commercial table salt (“Iodised”
Steroid hormones are produced by adrenal cortex and gonads ( testes in male and ovaries in
females).Hormones released by the adrenal cortex play very important role in the functions of the body.
For example glucocorticoids control the carbohydrate metabolism, modulate inflammatory reactions, and
are involved in reactions to stress. The mineralocorticoids control the level of excretion of water and salt
by the kidney. If adrenal cortex does not function properly then one of the results may be Addison’s
disease characterised by hypoglycemia, weakness and increased susceptibility to stress. The disease is
fatal unless it is treated by glucocorticoids and mineralocorticoids. Hormones released by gonads are
responsible for development of secondary sex characters. Testosterone is the major sex hormone produced
in males. It is responsible for development of secondary male characteristics (deep voice, facial hair,
general physical constitution) and estradiol is the main female sex hormone. It is responsible for development
of secondary female characteristics and participates in the control of menstrual cycle. Progesterone is
responsible for preparing the uterus for implantation of fertilised egg.
16.4.3 Antioxidants in Food
These are important and necessary food additives. These help in food preservation by retarding the action
of oxygen on food. These are more reactive towards oxygen than the food material they are protecting.
The two most familiar antioxidants are butylated hydroxyl toluene (BHT) and butylated hydroxy anisole
(BHA). The addition of BHA to butter increases its shelf life from months to years.
Some times BHT and BHA along with citric acid are added to produce more effect. Sulphur dioxide
and sulphite are useful antioxidants for wine and beer, sugar syrups and cut pealed or dried fruits and

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