PHYSICAL CHEMISTRY

LIQUID SOLUTIONS
 KEY CONCEPTS

Vapor Pressure. The pressure exerted by the vapors of a liquid which are in equilibrium with it at a
given temperature.

Note: It depends only on temperature and on nature of the liquid. It does NOT depend on the surface
area

Raoult's Law. The equilibrium vapor pressure of a volatile component is linearly proportional to the
mole fraction of that compoent in liquid phase.

For non-volatile solutes : P(solution) = xsolvent Po

or relative lowering of vapor pressure, (Po - P)/Po = xsolute .
A more useful form is (Po - P)/P = n/N
where n = total number of moles of all the free solute species in the solution finally (i.e. at equilibrium).

Three cases arise.

(i) Non-electrolyte is dissolved e.g. glucose or urea. These molecules do not dissociate into ions. If 0.1
mol of urea is dissolved in 50 moles of water, then n/N = 0.1/50 simply.

(ii) Strong electrolyte is dissolved e.g. NaCl, Ca(NO3 )2etc. These dissociate nearly completely into ions.
If 0.1 mol of NaCl is dissolved in 50 moles of water, then n/N = 0.2/50 since NaCl dissociates completely
in 0.1 mol Na+ ions and 0.1 mol Cl- ions. Similarly, for Ca(NO3 )2, n/N = 0.3/50 if 0.1 mol of it
dissociates completely into ions.

(iii) Weak electrolyte is dissolved e.g. HCOOH, CH3NH2 etc. In such cases, we should determine the
total number of moles of all the solute species at equilibrium. e.g. i f no moles of formic acid considered
non-volatile here) are dissolved in N moles of solvent then,
HCOOH  H+ + COOH-
no(1-) no no
Total number of moles at equilibrium no(1+). Hence, n/N = no(1+)/N.

Note : This factor, n (at equilibrium)/n(original) is referred to as van't Hoff factor.

Ideal Solutions. The solutions which obey Raoult's Law are called ideal solution. For ideality :
(i)Hmix= 0, (ii) Vmix = 0 as well for liquid-liquid solutions.

Non ideal solution (Deviations From Raoult's Law)

Positive deviation. When the observed vapor pressure is more than that expected by Raoult's law.

This is observed when Hmix> 0 i.e. energy is absorbed on mixing. Usually obtained by mixing of polar
liquids with non-polar ones. e.g. cyclohexane and ethanol.
 Negative deviation. When the observed vapor pressure is less than that expected by Raoult's law.
This is observed when Hmix< 0 i.e. energy is released on mixing. Attractive forces between unlike
molecules are greater than the forces of attraction between like molecules. e.g. chloroform and acetone.
(Curve 3 in Fig. 1 and 2).

P20 3
2

1 1
V. P. 
3 B. P.
P10 2

0 x 1
x is mole fraction of more 0 x 1
volatile component (2) x is mole fraction of more
Fig. 1 volatile component (2)
Fig. 2
Azeotropic Solutions. During distillation, the mole fraction of more volatile component in vapor state is
higher than that in liquid state. This makes distillation possible. However, there exist some solutions for
particular compositions of which the mole fraction of components in liquis and vapor state is same. Thus,
no advantage is derived by distilling such a mixture and it is termed as azeotropic.

Completely Immiscible Liquids : When they are distilled, they distil in the ratio of their vapor pressure

wB w B PB ·M B
at that temperature. e.g. When A and B are distilled wt ratio is given as w  
wA A PA ·M A
Completely Miscibile Liquids. They can be handled by Raoult's Law i.e.
yiP = xiPio
where P = Total pressure of vapors in equilibrium with the liquid solution,
Pio = vapor pressure of component i in pure state
yi = mole fraction of ith component in vapor state, xi = mole fraction of ith component in liquid state
This most fundamental expression may be arranged in many useful forms. e.g. for binary solutions :
P = x1(P10 - P20) + P20
or 1/P = 1/P20 + y1(1/P10 - 1/P20)
Note : Vapor pressure of an ideal solution is always between P10 and P20 (Curve1 in Fig. 1 and 2)
Bubble Point. When the first bubble of vapor appears in liquid solution.
Dew Point. When the first drop of liquid condenses from a mixture of vapors. OR when the last drop of
liquid remains and rest of the liquid is completely vaporised.
Colligative Properties. The properties which depend only on the number of moles of solute (and not
on their molecular weights or sizes) are referred to as colligative properties.
e.g. Lowring of vapor pressure, depression of freezing point, elevation of boiling point, osmotic pressure
etc.
P0  P n w/m
1. Relative lowering of vapour Pressure. 0 =  = xsolute
P nN w/mW/M

2. Elevation in Boiling Point, Tb. For dilute solutions, Tb = Kbm

where m is molality of the solution (i.e. total number of moles of all the solute particles per kg of solvent).
Kb is ebullioscopic or boiling point elevation constant which is given by
 R (Tb0 ) 2 M solvent
Kb=
1000H vap
Hvap is the enthalpy of vaporisation of solvent.

3. Depression in freezing Point (Tf). For dilute solutions, Tf = Kfm

R (Tf0 ) 2 M solvent
where, Kf =
1000H fusion

Osmosis. Spontaneous flow of solvent molecules through a semipermeable membrane from a pure
solvent to the solution (or from a dilute solution to a concentrated solution) is termed as osmosis.

Reverse Osmosis. If a pressure greater than the osmotic pressure is applied on the concentrated
solution, the solvent starts to flow from concentrated solution to dilute solution (or pure solvent). This is
reverse osmosis.One of its chief uses is desalination of sea water to get pure drinking water.

4. Osmotic Pressure (). The hydrostatic pressure built up on the solution which just stops osmosis.
Alternately, it may be defined as the pressure which must be applied to the concentrated solution in order
to stop osmosis.
For dilute solutions cRT = hg
where c is the total molar concentration of all the free species present in the solution, h is the height
developed by the column of the concentrated solution and is the density of the solution in the column.
On the basis of osmotic pressure, the solutions can be classified in three classes.

Isotonic solutions. Two solutions having same osmotic pressures at same temperature.
(This implies c1 = c2).

Hypertonic solution. When two solutions are being compared, then the solution with higher osmotic
pressure is termed as hypertonic. The solution with lower osmotic pressure is termed as hypotonic.

Important. Osmotic pressures can be determined quite accurately, hence it is used in the
determination of molecular weights of large proteins and similar substances.

Van't Hoff Factor (i)

Since colligative properties depends upon the number of particles of the solute, in some cases where the
solute associates or dissociates in solution, abnormal results for molecules masses are obtained.
Observed colligative property (actual)
i=
Theoretical colligative property
THE ATLAS
 EXERCISE I

Raoult’s law

Q.1 At 25°C, the vapour pressure of methyl alcohol is 96.0 torr. What is the mole fraction of CH3OH in a
solution in which the (partial) vapor pressure of CH3OH is 23.0 torr at 25°C?

Q.2 The vapour pressure of pure liquid solvent A is 0.80 atm. When a nonvolatile substance B is added to the
solvent its vapour pressure drops to 0.60 atm. What is the mole fraction of component B in the solution?

Q.3 The vapour pressure of pure water at 26°C is 25.21 torr. What is the vapour pressure of a solution
which contains 20.0 glucose, C6H12O6, in 70 g water?

Q.4 The vapour pressure of pure water at 25°C is 23.76 torr. The vapour pressure of a solution containing
5.40 g of a nonvolatile substance in 90.0 g water is 23.32 torr. Compute the molecular weight of the
solute.

Raoult’s law in combinaton with Dalton’s law of P.P. and V.P. lowering

Q.5 The vapour pressure of ethanol and methanol are 44.5 mm and 88.7 mm Hg respectively. An ideal
solution is prepared at the same temperature by mixing 60 g of ethanol with 40 g of methanol. Calculate
total vapour pressure of the solution.

Q.6 Calculate the mole fraction of toluene in the vapour phase which is in equilibrium with a solution of
benzene and toluene having a mole fraction of toluene 0.50. The vapour pressure of pure benzene is
119 torr; that of toluene is 37 torr at the same temperature.

Q.7 What is the composition of the vapour which is in equilibrium at 30°C with a benzene-toluene solution
with a mole fraction of benzene of 0.40? With a mole fraction of benzene of 0.60?
Pb =119 torr and Pt = 37 torr

Q.8 At 90°C, the vapour pressure of toluene is 400 torr and that of -xylene is 150 torr. What is the
composition of the liquid mixture that boils at 90°C, when the pressure is 0.50 atm? What is the composition
of vapour produced?

Q.9 Two liquids A and B form an ideal solution at temperature T. When the total vapour pressure above the
solution is 400 torr, the mole fraction of A in the vapour phase is 0.40 and in the liquid phase 0.75. What
are the vapour pressure of pure A and pure B at temperature T?

Q.10 Calculate the relative lowering in vapour pressure if 100 g of a nonvolatile solute (mol.wt.100) are
dissolved in 432 g water.

Q.11 What weight of the nonvolatile solute, urea needs to be dissolved in 100 g of water, in order to decrease
the vapour pressure of water by 25%? What will be the molality of the solution?

Q.12 The vapour pressure of an aqueous solution of glucose is 750 mm Hg at 373 K. Calculate molality and
mole fraction of solute.
Q.13 The vapour pressure of pure benzene at 25° C is 639.7 mm of Hg and the vapour pressure of a solution
of a solute in C6H6 at the same temperature is 631.7 mm of Hg. Calculate molality of solution.

Q.14 The vapour pressure of pure benzene at a certain temperature is 640 mm of Hg. A nonvolatile nonelectrolyte
solid weighing 2.175 g is added to 39.0 of benzene. The vapour pressure of the solution is 600 mm of
Hg. What is molecular weight of solid substance?

Q.15 The vapour pressure of water is 17.54 mm Hg at 293 K. Calculate vapour pressure of 0.5 molal
solution of a solute in it.

Q.16 Benzene and toluene form two ideal solution A and B at 313 K. Solution A (total pressure PA) contains
equal mole of toluene and benzene. Solution B contains equal masses of both (total pressure PB). The
vapour pressure of benzene and toluene are 160 and 60 mm Hg respectively at 313 K. Calculate the
value of PA/PB.

Boiling point elevation and freezing point depression

Q.17 When 10.6 g of a nonvolatile substance is dissolved in 740 g of ether, its boiling point is raised 0.284°C.
What is the molecular weight of the substance? Molal boiling point constant for ether is 2.11°C·kg/mol.

Q.18 A solution containing 3.24 of a nonvolatile nonelectrolyte and 200 g of water boils at 100.130°C at
1atm. What is the molecular weight of the solute? (Kb for water 0.513°C/m)

Q.19 The molecular weight of an organic compound is 58.0 g/mol. Compute the boiling point of a solution
containing 24.0 g of the solute and 600 g of water, when the barometric pressure is such that pure water
boils at 99.725°C.

Q.20 An aqueous solution of a nonvolatile solute boils at 100.17°C. At what temperature will this solution
freeze? [Kf for water 1.86°C/m ]

Q.21 Pure benzene freeze at 5.45°C. A solution containing 7.24 g of C2H2Cl4 in 115.3 g of benzene was
observed to freeze at 3.55°C. What is the molal freezing point constant of benzene?

Q.22 A solution containing 6.35 g of a nonelectrolyte dissolved in 500 g of water freezes at – 0.465°C.
Determine the molecular weight of the solute.

Q.23 The freezing point of a solution containing 2.40 g of a compound in 60.0 g of benzene is 0.10°C lower
than that of pure benzene. What is the molecular weight of the compound? (Kf is 5.12°C/m for benzene)

Q.24 The elements X and Y form compounds having molecular formula XY2 and XY4. When dissolved in 20 gm
of benzene, 1 gm XY2 lowers the freezing point by 2.3°, whereas 1 gm of XY4 lowers the freezing point by
1.3°C. The molal depression constant for benzene is 5.1. Calculate the atomic masses of X and Y.

Q.25 Calculate the molal elevation constant, Kb for water and the boiling of 0.1 molal urea solution. Latent
heat of vaporisation of water is 9.72 kcal mol–1 at 373.15 K.

Q.26 Calculate the amount of ice that will separate out of cooling a solution containing 50g of ethylene glycol
in 200 g water to –9.3°C. (Kf for water = 1.86 K mol1 kg)
Q.27 A solution of 0.643 g of an organic compound in 50ml of benzene (density ; 0.879 g/ml) lowers its
freezing point from 5.51°C to 5.03°C. If Kf for benzene is 5.12 K, calculate the molecular weight of the
compound.

Q.28 The cryoscopic constant for acetic acid is 3.6 K kg/mol. A solution of 1 g of a hydrocarbon in 100 g of
acetic acid freezes at 16.14°C instead of the usual 16.60°C. The hydrocarbon contains 92.3% carbon.
What is the molecular formula?

Osmotic pressure

Q.29 Find the freezing point of a glucose solution whose osmotic pressure at 25oC is found to be 30 atm.
Kf(water) = 1.86kg.mol1.K.

Q.30 At 300 K, two solutions of glucose in water of concentration 0.01 M and 0.001 M are separated by
semipermeable membrane. Pressure needs to be applied on which solution, to prevent osmosis? Calculate
the magnitude of this applied pressure.

Q.31 At 10oC, the osmotic pressure of urea solution is 500 mm. The solution is diluted and the temperature
is raised to 25°C, when the osmotic pressure is found to be105.3 mm. Determine extent of dilution.

Q.32 The osmotic pressure of blood is 7.65 atm at 37°C. How much glucose should be used per L for an
intravenous injection that is to have the same osmotic pressure as blood?

Q.33 What would be the osmotic pressure at 17°C of an aqueous solution containing 1.75 g of sucrose
(C12H22O11) per 150 cm3 of solution?

Q.34 A 250 mL water solution containing 48.0 g of sucrose, C12H22O11, at 300 K is separated from pure
water by means of a semipermeable membrane. What pressure must be applied above the solution in
order to just prevent osmosis?

Q.35 A solution of crab hemocyanin, a pigmented protein extracted from crabs, was prepared by dissolving
0.750 g in 125 cm3 of an aqueous medium. At 4°C an osmotic pressure rise of 2.6 mm of the solution
was observed. The solution had a density of 1.00 g/cm3. Determine the molecular weight of the protein.

Q.36 The osmotic pressure of a solution of a synthetic polyisobutylene in benzene was determined at 25°C. A
sample containing 0.20 g of solute/100 cm3 of solution developed a rise of 2.4 mm at osmotic equilibrium.
The density of the solution was 0.88 g/cm3. What is the molecular weight of the polyisobutylene?

Q.37 A 5% solution (w/v) of cane-sugar (Mol. weight = 342) is isotonic with 0.877%(w/v) of urea solution.
Find molecular weight of urea.

Q.38 10 gm of solute A and 20 gm of solute B are both dissolved in 500 ml water. The solution has the same
osmotic pressure as 6.67 gm of A and 30 gm of B dissolved in the same amount of water at the same
temperature. What is the ratio of molar masses of A and B?

Van’t Hoff factor & colligative properties

Q.39 A storage battery contains a solution of H2SO4 38% by weight. What will be the Van't Hoff factor if the
Tf(experiment) in 29.08. [Given Kf = 1.86 mol–1 Kg]
Q.40 A certain mass of a substance, when dissolved in 100 g C6H6, lowers the freezing point by 1.28°C. The
same mass of solute dissolved in 100g water lowers the freezing point by 1.40°C. If the substance has
normal molecular weight in benzene and is completely ionized in water, into how many ions does it
dissociate in water? K f for H2O and C6H6 are 1.86 and 5.12K kg mol1.

Q.41 2.0 g of benzoic acid dissolved in 25.0g of benzene shows a depression in freezing point equal to 1.62K.
Molal depression constant (Kf) of benzene is 4.9 K.kg.mol1. What is the percentage association of the acid?

Q.42 A decimolar solution of potassium ferrocyanide is 50% dissociated at 300K. Calculate the osmotic
pressure of the solution.(R=8.314 JK1 mol1)

Q.43 The freezing point of a solution containing 0.2 g of acetic acid in 20.0g of benzene is lowered by 0.45°C.
Calculate the degree of association of acetic acid in benzene. (Kf for benzene = 5.12 K mol1 kg)

Q.44 0.85 % aqueous solution of NaNO3 is apparently 90% dissociated at 27°C. Calculate its osmotic
pressure. (R= 0.082 l atm K1 mol1 )

Q.45 A 1.2% solution (w/v) of NaCl is isotonic with 7.2% solution (w/v) of glucose. Calculate degree of
ionization and Van’t Hoff factor of NaCl.
 PROFICIENCY TEST
Q.1 Fill in the blanks with appropriate items :
1. Lowering of vapour pressure is ______ to the mole fraction of the solute.
2. The ratio of the value of any colligative property for NaCl solution to that of equimolal solution of sugar
is nearly______.
3. Semipermeable membrane allows the passage of ________through it.
4. A binary solution which has same composition in liquid as well as vapour phase is called______.
5. The molal elevation constant of solvent is also called _____.
6. The 0.1 M aqueous solution of acetic acid has boiling point _______ than that of 0.1 M aqueous
solution of KCl.
7. For ideal solutions, the plot of total vapour pressure v/s composition is ______.
8. A solution of CHCl3 and acetone shows________deviation.
9. Gases which react with water are generally _________ soluble in it.
10. Assuming complete dissociation, Van’t Hoff’s factor for Na2SO4 is equal to ________.
11. The osmotic pressure of a solution _______ with increase in temperature.
12. Water will boil at 101.5°C at pressure of _______76 cm of Hg.
13. Vant’s Hoff’s factor ‘i’ for dimerisation of CH3COOH in benzene is_________.

nB
14. = RT is known as_________.
V
15. The molal elevation constant is the ratio of the elevation in boiling point to _________.
Q.2 True or False Statements :
16. Relative lowering of vapour pressure is a colligative property.
17. Lowering of vapour pressure of a solution is equal to the mole fraction of the non-volatile solute present in it.
18. The components of an azeotropic solution can be separated by simple distillation.
19. Vapour pressure of a liquid depends on the size of the vessel.
20. Addition of non-volatile solute to water always lowers it vapour pressure.
21. Reverse osmosis is generally used to make saline water fit for domestic use.
22. A 6% solution of NaCl should be isotonic with 6% solution of sucrose.
23. A real solution obeys Raoult’s law.
24. Boiling point is a characteristic temperature at which vapour pressure of the liquid becomes higher than
the atmospheric pressure.
25. Molal depression constant is independent of the nature of solute as well as that of solvent.
26. The real solutions can exhibit ideal behaviour at high concentrations.
27. The osmotic pressure decreases on addition of solvent to the solution.
28. For urea the value of Vant’s Hoff’s factor ‘i’ is equal to 1.
29. The unit of kb is kg K–1 mol–1.
30. 0.1 M solution of urea would be hypotonic with 0.1 M solution of NaCl.
 EXERCISE II

Q.1 An aqueous solution containing 288 gm of a non-volatile compound having the stoichiometric composition
CxH2xOx in 90 gm water boils at 101.24°C at 1.00 atmospheric pressure. What is the molecular formula?
Kb(H2O) = 0.512 K mol–1 kg
Tb(H2O) = 100°C

Q.2 The degree of dissociation of Ca(NO3)2 in a dilute aqueous solution containing 7 gm of the salt per
100 gm of water at 100°C is 70%. If the vapour pressure of water at 100°C is 760 mm. Calculate the
vapour pressure of the solution.

Q.3 The addition of 3 gm of substance to 100 gm CCl4(M = 154 gm mol–1) raises the boiling point of CCl4
by 0.60°C of Kb (CCl4) is 5.03 kg mol–1 K. Calculate
(a) the freezing point depression
(b) the relative lowering of vapour pressure
(c) the osmotic pressure at 298 K
(d) the molar mass of the substance
Given Kf(CCl4) = 31.8 kg mol–1K and  (density) of solution = 1.64 gm/cm3

Q.4 A 10% solution of cane sugar has undergone partial inversion according to the reaction:
Sucrose + Water  Glucose + Fructose. If the boiling point of solution is 100.27°C.
(a) What is the average mass of the dissolved materials?
(b) What fraction of the sugar has inverted? Kb(H2O) = 0.512 K mol–1 kg

Q.5 If 20 ml of ethanol (density = 0.7893 gm/ml) is mixed with 40 ml water (density = 0.9971 gms) at 25°C,
the final solution has density of 0.9571 gm/ml. Calculate the percentage change in total volume of mixing.
Also calculate the molality of alcohol in the final solution.

Q.6 Mixture of two liquids A and B is placed in cylinder containing piston. Piston is pulled out isothermally so
that volume of liquid decreases but that of vapour increases. When negligibly small amount of liquid was
remaining, the mole fraction of A in vapour is 0.4. Given PA =0.4 atm and PB = 1.2 atm at the experimental
temperature. Calculate the total pressure at which the liquid has almost evaporated. (Assume ideal
behaviour).

Q.7 1.5 g of a monobasic acid when dissolved in 150g of water lowers the freezing point by 0.165°C. 0.5 g
of the same acid when titrated, after dissolution in water, requires 37.5 ml of N/10 alkali. Calculate the
degree of dissociation of the acid (Kf for water = 1.86°C mol–1).

Q.8 Sea water is found to contain 5.85% NaCl and 9.50% MgCl2 by weight of solution. Calculate its normal
boiling point assuming 80% ionisation for NaCl and 50% ionisation of MgCl2 [Kb(H2O) = 0.51kgmol1K].

Q.9 The latent heat of fusion of ice is 80 calories per gram at 00C. What is the freezing point of a solution of
KCl in water containing 7.45 grams of solute in 500 grams of water, assuming that the salt is dissociated
to the extent of 95%?

Q.10 A complex is represented as CoCl3 · x NH3. It's 0.1 molal solution in aq. solution shows Tf = 0.558°C.
Kf for H2O is 1.86 K mol–1 kg . Assuming 100% ionisation of complex and coordination no. of Co is six,
calculate formula of complex.
Q.11 The molar volume of liquid benzene (density = 0.877 g ml1) increases by a factor of 2750 as it vaporizes
at 20°C and that of liquid toluene (density = 0.867gml1) increases by a factor of 7720 at 20°C has a
vapour pressure of 46.0 torr. Find the mole fraction of benzene in the vapour above the solution.

Q.12 At 100oC, benzene & toluene have vapour pressure of 1375 & 558 Torr respectively. Assuming these
two form an ideal binary solution, calculate the composition of the solution that boils at 1 atm & 100oC.
What is the composition of vapour issuing at these conditions?

Q.13 Calculate the boiling point of a solution containing 0.61g of benzoic acid in 50g of carbon disulphide
assuming 84% dimerization of the acid. The boiling point and Kb of CS2 are 46.2°C and
2.3 K kg mol–1, respectively.

Q.14 At 25OC, 1 mol of A having a vapor pressure of 100torr and 1 mol of B having a vapor pressure of
300 torr were mixed. The vapor at equilibrium is removed, condensed and the condensate is heated
back to 25OC. The vapors now formed are again removed, recondensed and analyzed. What is the
mole fraction of A in this condensate?

Q.15 Phenol associates in benzene to a certain extent to form a dimer. A solution containing 20 × 10–3 kg
phenol in 1 kg of benzene has its freezing point depressed by 0.69 K. Calculate the fraction of phenol
that has dimerised. Kf for benzene = 5.12 kg mol–1K.

Q.16 30 ml of CH3OH (d = 0.7980 gm cm–3) and 70 ml of H2O (d=0.9984 gm cm–3) are mixed at 25°C to
form a solution of density 0.9575 gm cm–3. Calculate the freezing point of the solution. Kf (H2O) is
1.86 kg mol–1 K. Also calculate its molarity.

Q.17 Dry air was drawn thorugh bulbs containing a solution of 40 grams of urea in 300 grams of water, then
through bulbs containing pure water at the same temperature and finally through a tube in which pumice
moistened with strong H2SO4 was kept. The water bulbs lost 0.0870 grams and the sulphuric acid tube
gained 2.036 grams. Calculate the molecular weight of urea.

Q.18 Vapour pressure of C6H6 and C7H8 mixture at 500C is given by P (mm Hg) = 180 XB + 90, where XB
is the mole fraction of C6H6. A solution is prepared by mixing 936g benzene and 736g toluene and if the
vapours over this solution are removed and condensed into liquid and again brought to the temperature
of 500C, what would be mole fraction of C6H6 in the vapour state?

Q.19 When the mixture of two immicible liquids (water and nitrobenzene) boils at 372 K and the vapour
pressure at this temperature are 97.7 kPa (H2O) and 3.6 kPa (C6H5NO2). Calculate the weight % of
nitrobenzene in the vapour.

Q.20 The vapour pressure of a certain liquid is given by the equation:

313.7
Log10P = 3.54595  + 1.40655 log10 T where P is the vapour pressure in mm and T = Kelvin
T
Temperature. Determine the molar latent heat of vaporisation as a function of temperature. Calculate the
its value at 80 K.

Q.21 A very dilute saturated solution of a sparingly soluble salt A3B4 has a vapour pressure of 20 mm of Hg
at temperature T, while pure water exerts a pressure of 20.0126 mm Hg at the same temperature.
Calculate the solubility product constant of A3B4 at the same temperature.
Q.22 The molar volume of liquid benzene (density = 0.877g ml-1) increases by a factor of 2750 as it vaporises
at 20oC while in equilibrium with liquid benzene. At 27oC when a non-volatile solute (that does not
dissociate) is dissolved in 54.6 cm3 of benzene vapour pressure of this solution, is found to be 98.88 mm
Hg.Calculate the freezing point of the solution.
Given : Enthalpy of vaporization of benzene(l) = 394.57 J/gm
Molal depression constant for benzene = 5.0 K kg. mol1 .
Freezing point of benzene = 278.5 K.

Q.23 If the apparent degree of ionization of KCl (KCl =74.5 gm mol–1) in water at 290 K is 0.86. Calculate
the mass of KCl which must be made up to 1 dm3 of aqueous solution to the same osmotic pressure as
the 4.0% solution of glucose at that temperature.

Q.24 An ideal solution was prepared by dissolving some amount of cane sugar (nonvolatile) in 0.9 moles of
water. The solution was then cooled just below its freezing temperature (271 K), where some ice get
separated out. The remaining aqueous solution registered a vapour pressure of 700 torr at 373 K.
Calculate the mass of ice separated out, if the molar heat of fusion of water is 6 kJ.

Q.25 The freezing point depression of a 0.109 M aq. solution of formic acid is –0.21°C. Calculate the
equilibrium constant for the reaction,
HCOOH (aq) l H +(aq) + HCOOH– (aq)
Kf for water = 1.86 kg mol–1 K

Q.26 10 gm of NH4Cl (mol. weight = 53.5) when dissolved in 1000 gm of water lowered the freezing point by
0.637°C. Calculate the degree of hydrolysis of the salt if its degree of dissociation of 0.75. The molal
depression constant of water is 1.86 kg mol–1 K.

Q.27 The freezing point of 0.02 mol fraction solution of acetic acid (A) in benzene (B) is 277.4K. Acetic acid
exists partly as a dimer 2A = A2. Calculate equilibrium constant for the dimerisation. Freezing point of
benzene is 278.4 K and its heat of fusion Hf is 10.042 kJ mol1.

Q.28 A saturated solution of a sparingly soluble salt, MCl2 has a vapour pressure of 31.78 mm of Hg at 30°C,
while pure water exerts a pressure of 31.82 mm of Hg at the same temperature. Calculate the solubility
product of the compound at this temperature.

Q.29 The vapour pressure of two pure liquids, A and B that form an ideal solution are 300 and 800 torr
respectively, at temperature T. A mixture of the vapour of A and B for which the mole fraction of A is
0.25 is slowly compressed at temperature T. Calculate
(a) the composition of the first drop of the condensate,
(b) the total pressure when this drop is formed,
(c) the composition of the solution whose normal boiling point is T,
(d) the pressure when only the last bubble of vapour remains, and
(e) the composition of the last bubble.

Q.30 Tritium, T (an isotope of H) combines with fluorine to form weak acid TF, which ionizes to give T+.
Tritium is radioactive and is a –emitter. A freshly prepared aqueous solution of TF has pT (equivalent of
pH) of 1.5 and freezes at –0.3720C. If 600ml of freshly prepared solution were allowed to stand for
24.8 years. Calculate (i) ionization constant of TF. (ii) Number of –particles emitted.
(Given Kf for water = 1.86 kg mol K–1, t1/2 for tritium = 12.4 years)
 EXERCISE III

Q.1 For an ideal binary liquid solution with PA > PB , which relation between XA (mole fraction of A in liquid
phase) and YA(mole fraction of A in vapour phase) is correct?
YA X A YA X A
(A) YA < YB (B) XA > XB (C) Y  X (D) Y  X
B B B B
Q.2 Mole fraction of A vapours above the solution in mixture of A and B (XA = 0.4) will be
[Given : PA = 100 mm Hg and PB = 200 mm Hg]
(A) 0.4 (B) 0.8 (C) 0.25 (D) none of these
Q.3 The exact mathematical expression of Raoult’s law is

P 0  Ps n P 0  Ps N P 0  Ps n P 0  Ps
(A)  (B)  (C)  (D) =n×N
P0 N P0 n Ps N P0

Q.4 A mixture contains 1 mole of volatile liquid A ( PA =100 mm Hg) and 3 moles of volatille liquid
B ( PB = 80 mm Hg). If solution behaves ideally, the total vapour pressure of the distillate is
(A) 85 mm Hg (B) 85.88 mm Hg (C) 90 mm Hg (D) 92 mm Hg
Q.5 Which of the following aqueous solution will show maximum vapour pressure at 300 K?
(A) 1 M NaCl (B) 1 M CaCl2 (C) 1 M AlCl3 (D) 1 M C12H22O11
Q.6 The Van’t Hoff factor for a dilute aqueous solution of glucose is
(A) zero (B) 1.0 (C) 1.5 (D) 2.0
Q.7 The correct relationship between the boiling points of very dilute solution oif AlCl3 (T1K) and
CaCl2 (T2K) having the same molar concentration is
(A) T1 = T2 (B) T1 > T2 (C) T2 > T1 (D) T2  T1
Q.8 A 0.001 molal solution of a complex [MA8] in water has the freezing point of –0.0054°C. Assuming
100% ionization of the complex salt and Kf for H2O = 1.86 km–1, write the correct representation for
the complex
(A) [MA8] (B) [MA7]A (C) [MA6]A2 (D) [MA5]A3
Q.9 The vapour pressure of a solution of a non-volatile electrolyte B in a solvent A is 95% of the vapour
pressure of the solvent at the same temperature. If the molecular weight of the solvent is 0.3 times the
molecular weight of solute, the weight ratio of the solvent and solute are
(A) 0.15 (B) 5.7 (C) 0.2 (D) 4.0
Q.10 At a given temperature, total vapour pressure in Torr of a mixture of volatile components A and B is
given by
PTotal = 120 – 75 XB
hence, vapour pressure of pure A and B respectively (in Torr) are
(A) 120, 75 (B) 120, 195 (C) 120, 45 (D) 75, 45
Q.11 Assuming each salt to be 90 % dissociated, which of the following will have highest boiling point?
(A) Decimolar Al2(SO4)3
(B) Decimolar BaCl2
(C) Decimolar Na2SO4
(D) A solution obtained by mixing equal volumes of (B) and (C)
Q.12 The vapour pressure of a solvent decreased by 10 mm of Hg when a non-volatile solute was added to
the solvent. The mole fraction of solute in solution is 0.2, what would be mole fraction of the solvent if
decrease in vapour pressure is 20 mm of Hg
(A) 0.2 (B) 0.4 (C) 0.6 (D) 0.8

Q.13 Elevation of boiling point of 1 molar aqueous glucose solution (density = 1.2 g/ml) is
(A) Kb (B) 1.20 Kb (C) 1.02 Kb (D) 0.98 Kb

Q.14 What will be the molecular weight of CaCl2 determined in its aq. solution experimentally from depression
of freezing point?
(A) 111 (B) < 111 (C) > 111 (D) data insufficient

Q.15 1.0 molal aqueous solution of an electrolyte A2B3 is 60% ionised. The boiling point of the solution at 1
1
atm is ( K b( H 2O)  0.52 K kg mol )
(A) 274.76 K (B) 377 K (C) 376.4 K (D) 374.76 K

Q.16 Which of the following plots represents an ideal binary mixture?

(A) Plot of Ptotal v/s 1/XB is linear (XB = mole fraction of 'B' in liquid phase).
(B) Plot of Ptotal v/s YA is linear (YB = mole fraction of 'A' in vapour phase)
1
(C) Plot of P v/s YA is linear
total

1
(D) Plot of P v/s YB is non linear
total

Q.17 Pressure over ideal binary liquid mixture containing 10 moles each of liquid A and B is gradually decreased
isothermally. If PAo =200 mm Hg and PBo =100 mm Hg, find the pressure at which half of the liquid is
converted into vapour.
(A) 150 mm Hg (B) 166.5 mm Hg (C) 133 mm Hg (D) 141.4 mm Hg

Q.18 The lowering of vapour pressure in a saturated aq. solution of salt AB is found to be 0.108 torr. If vapour
pressure of pure solvent at the same temperature is 300 torr. Find the solubility product of salt AB
(A) 10–8 (B) 10–6 (C) 10–4 (D) 10–5
Q.19 Which of the following represents correctly the changes in thermodynamic properties during the formation
of 1 mol of an ideal binary solution.

(A) (B) (C) (D)

Q.20 FeCl3 on reaction with K4[Fe(CN)6] in aqueous solution gives blue

colour. These are separated by a semipermeable membrane AB as
shown. Due to osmosis there is
(A) blue colour formation in side X.
(B) blue colour formation in side Y.
(C) blue colour formation in both of the sides X and Y.
(D) no blue colour formation.
 EXERCISE IV

OBJECTIVE

Q.1 The van’t Hoff factor for 0.1 M Ba(NO3)2 solution is 2.74. The degree of dissociation is
(A) 91.3% (B) 87% (C) 100% (D) 74%

Q.2 In the depression of freezing point experiment, it is found that

(I) The vapour pressure of the solution is less than that of pure solvent.
(II) The vapour pressure of the solution is more than that of pure solvent.
(III) Only solute molecules solidify at the freezing point.
(IV) Only solvent molecules solidify at the freezing point.
(A) I, II (B) II, III (C) I, IV (D) I, II, III

Q.3 During depression of freezing point in a solution, the following are in equilibrium
(A) liquid solvent-solid solvent (B) liquid solvent-solid solute
(C) liquid solute-solid solute (D) liquid solute-solid solvent

Q.4 A 0.004 M solution of Na2SO4 is isotonic with a 0.010 M solution of glucose at same temperature. The
apparent degree of dissociation of Na2SO4 is
(A) 25% (B) 50% (C) 75% (D) 85%

Q.5 The elevation in boiling point, when 13.44 g of freshly prepared CuCl2 are added to one kilogram of
water, is [Some useful data, Kb (H2O) = 0.52 kg K mol–1, mol. wt. of CuCl2 = 134.4 gm]
(A) 0.05 (B) 0.1 (C) 0.16 (D) 0.21

SUBJECTIVE
Q.6 A very small amount of a nonvolatile solute (that does not dissociate) is dissolved in 56.8 cm3 of benzene
(density 0.889 g cm3), At room temperature, vapour pressure of this solution is 98.88 mm Hg while
that of benzene is 100 mm Hg. Find the molality of this solution. If the freezing temperature of this
solution is 0.73 degree lower than that of benzene. What is the value of molal freezing point depression
constant of benzene?

Q.7 A solution of a nonvolatile solute in water freezes at 0.30°C. The vapor pressure of pure water at
298K is 23.51mmHg and Kf for water is 1.86 degree/molal. Calculate the vapor pressure of this solution
at 298K.

Q.8 To 500 cm3 of water, 3×10–3 kg of acetic acid is added. If 23% of acetic acid is dissociated, what will
be the depression in freezing point ? Kf and density of water are 1.86 K kg–1 mol–1 and 0.997 g cm–3
respectively.

Q.9 The vapour pressure of two miscible liquids (A) and (B) are 300 and 500 mm of Hg respectively. In a
flask 10 mole of (A) is mixed with 12 mole of (B). However, as soon as (B) is added, (A) starts
polymerising into a completely insoluble solid. The polymerisation follows first-order kinetics. After 100
minute, 0.525 mole of a solute is dissolved which arrests the polymerisation completely. The final vapour
pressure of the solution is 400 mm of Hg. Estimate the rate constant of the polymerisation reaction.
Assume negligible volume change on mixing and polymerisation and ideal behaviour for the final solution.
Q.10 Match the boiling point with Kb for x, y and z, if molecular weight of x, y and z are same
b.pt. Kb
x 100 0.68
y 27 0.53
z 253 0.98

Q.11 1.22 g of benzoic acid is dissolved in (i) 100 g acetone (Kb for acetone = 1.7) and (ii)100 g benzene
(Kb for benzene = 2.6). The elevation in boiling points Tb is 0.17°C and 0.13°C respectively.
(a) What are the molecular weights of benzoic acid in both the solutions?
(b) What do you deduce out of it in terms of structure of benzoic acid?

Q.12 72.5 g of phenol is dissolved in 1 kg of a solvent (kf = 14) which leads to dimerization of phenol and
freezing point is lowered by 7 kelvin. What percent of total phenol is present in dimeric form?
 ANSWER
EXERCISE I

Q.1 0.24 Q.2 0.25 Q.3 24.5 torr Q.4 57.24 g/mol

Q.5 66.13 mm Hg Q.6 0.237 Q.7 0.682, 0.318; 0.829, 0.171

Q.8 92 mol% toluene; 96.8 mol % toluene Q.9 PA = 213.33 torr, PB = 960.0 torr

Q.10 0.04 Q.11 111.1g, 18.52 molal Q.12 0.741 m, 0.013

Q.13 0.162 m Q.14 65.25 Q.15 17.38 Q.16 0.964

Q.17 106 g/mol Q.18 64.0 g/mol Q.19 100.079°C Q.20 – 0.62°C

Q.21 5.08°C/m Q.22 50.8 g/mol Q.23 2050 g/mol Q.24 x = 25.6, y = 42.6

Q.25 Kb= 0.512 kg mol K–1, Tb = 373.20 K Q.26 38.71 g Q.27 156.06

Q.28 C6H 6 Q.29 Tf = –2.28oC Q.30 P = 0.2217 atm should be applied

Q.31 (Vfinal = 5.Voriginal) Q.32 54.2 g Q.33 0.81 atm Q.34 13.8 atm

Q.35 5.4 × 105 g/mol Q.36 2.4 × 105 g/mol Q.37 59.99

Q.38 MA/MB = 0.33 Q.39 i = 2.5 Q.40 3 ions Q.41  = 99.2%

Q.42 7.482 ×105 Nm–2 Q.43 94.5 % Q.44 4.64 atm Q.45 0.95; 1.95

PROFICIENCY TEST

1. proportional 2. 2 : 1 3. solvent molecules 4. azeotropic mixture

5. Ebullioscopic constant 6. lesser 7. straight line with slope  0

8. negative 9. more 10. 3 11. increases

12. greater than 13. less than 1

14. Van’t Hoff’s solution equation 15. molality 16. T

17. F 18. F 19. F 20. T

21. T 22. F 23. F 24. F

25. F 26. F 27. T 28. T

29. F 30. T
 EXERCISE II

Q.1 C44 H88 O44 Q.2 746.24 mm/Hg

Q.3 (a) 3.79°C, (b) 0.018, (c) 4.65 atm, (d) 251.5 Q.4 (a) 210, (b) 64.1%

Q.5 % change in volume = 3.05, 8.604 m Q.6 0.66 atm Q.7 18.34%

Q.8 Tb = 102.3oC Q.9 Tf = -0.73oC Q.10 [Co(NH3)5Cl]Cl2 Q.11 0.73

Q.12 xb = 0.2472, Yb = 0.4473 Q.13 46.33°C Q.14 xa" = 0.1

Q.15  = 0.7333 Q.16 –19.91°C, 7.63 M Q.17 M = 53.8

Q.18  Q.19 20.11 %

Q.20 Hv at 80 K is 1659.1 calorie; Hv = R [2.303 × 313.7 + 1.40655T

Q.21 5.4 × 10–13 Q.22 Tf = 277.5 K Q.23 8.9 gm

Q.24 12.54 Q.25 Ka= 1.46×10–4 ` Q.26 h = 0.082 Q.27 K = 3.36

Q.28 4.9 × 10–5 M3

Q.29 (a)0.47, (b) 565 torr, (c) xA=0.08, xB= 0.92, (d) 675 torr, (e) x'A= 0.11, x'B= 0.89

Q.30 (i) Ka = 7.3 × 10–3 (ii) 4.55 × 1022

EXERCISE III

Q.1 C Q.2 C Q.3 C Q.4 B Q.5 D Q.6 B Q.7 B

Q.8 C Q.9 B Q.10 C Q.11 A Q.12 C Q.13 D Q.14 B
Q.15 D Q.16 C Q.17 D Q.18 C Q.19 C Q.20 D

EXERCISE IV

Q.1 B Q.2 C Q.3 A Q.4 C

Q.5 C Q.6 0.1452, 5.028 K m–1
Q.7 23.44 mm Hg Q.8 0.229 Q.9 1.0 × 10–4

Q.10 Kb(x) = 0.68, Kb(y) = 0.53, Kb(z) = 0.98

Q.11 (a)122, (b) It means that benzoic acid remains as it is in acetone while it dimerises in benzene
O H O
as C C
O H O
Q.12 35% phenol is present in dimeric form