Define vapour pressure of a liquid. What happens to the vapour pressure when (a) a volatile solute dissolves in the liquid and (b) the dissolved solute is non-volatile?

Every pure liquid exerts a vapour pressure in the space above it. This is the vapour pressure of the solvent over it at that particular temperature. It depends upon the nature of the solvent and the temperature.
(a) If a volatile solute is dissolved, vapour pressure of the solvent is increased.
(b) However, if a non-volatile solute is dissolved in it, the vapour pressure of the solution is lowered. This is because, in a solution, the percentage of the volatile solvent molecules, which only contributes towards vapour pressure is diminished.

Every pure liquid exerts a vapour pressure in the space above it. Thi
Fig. Decrease of vapour pressure when a non-volatile solute is added to the solvent.
Since, the solute molecules are non-volatile and show no measurable tendency to escape from the solution as vapour, consequently, the vapour pressure of a solution is always lower than that of its solvent.
Raoult’s gave a relation between the relative lowering of vapour pressure and the mole fraction of the solute. Mathematically:
fraction numerator straight p to the power of straight o minus straight p over denominator straight p to the power of straight o end fraction space equals space fraction numerator straight n over denominator straight n plus straight N end fraction space equals fraction numerator straight m divided by straight w over denominator begin display style straight m over straight w end style plus begin display style straight M over straight W end style end fraction

(mole fraction of the solute)
Using the above equation, we can determine the molecular weight of the solute, when the lowering in v.p. is known, when a known weight of the solute w, dissolved in a known wt. of the solvent W.p0 is the vapour pressure of the pure solvent and m and M are the molecular weights of solute and solvent respectively.

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Define vapour pressure of a liquid. What happens to the vapour pressure when (a) a volatile solute dissolves in the liquid and (b) non-volatile solute dissolvedin it?

Answer:

Liquids at a given temperature vapourise and under
equilibrium conditions the pressure exerted by the vapours of the liquid over the liquid phase is called vapour pressure.

When a volatile solute is dissolved into, solvent then the vapour state solute and the solvent.
total vapour pressure above such a solution will be equal to the sum of the pressure exerted by the vapours of both solute and solvent.

PTotal = pA0xA  + pB0 xB
Where 
Ptotal = total pressure of solution
pA0 = Vapour pressure of  pure component ApB0 = Vapour pressure of pure component BXA  = mole fraction of component AXB = mole fraction of pure component B

(b)
When  a non- volatile solute is dissovled then there is lowering in vapour pressure .
The lowering in vapour pressureisgiven by p° -p = p°xBp = vapour pressure of solution containing non- volatile solutep° = vapour pressure of pure solvent.

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Benzoic acid completely demerises in benzene. What will be the vapour pressure of solution containing 61 g of benzoic acid per 500 g benzene when the vapour pressure of pure benzene at the temperature of experiment is 66.6 torr?

C7H5COOH mol. mass = 12×6+5×1+12+2×16+1 = 122 g mol-1.C6H5COOH12(C6H5COO)2
No. of moles after dissociation
    1-α                 α/2
Total number of moles after association
                    = 1-α+α2 = 1-α2
     Mole fraction of benzoic acid (nA) = 61122=0.5
     Mole fraction of benzoic (nB) = 50078=6.4.
poA-pApoA = nAnA+nB66.6-pA66.6 = 0.50.5+6.4=0.56.9 = 0.072

or    66.6-pA = 66.6×0.72 = 4.79
or     66.9 - 4.79  = pA
                        pA = 61.8 torr
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Derive a relationship between mole fraction and vapour pressure of a compound of an ideal solution in the liquid phase and vapour phase.


Answer:

for any solution the partial vapour pressure of each volatile component in the solution is directly proportional to its mole fraction.
pA ∝ xA

Where only solvent is volatile
pA a xA where p A is vapour pressure of solvent having mole fractionxA,
But xA + xB = 1
xA = 1 – xB where xB is mole fraction of non-volatile solute B
pA = p0A (1 – xB)
= p0A – p0A x B
Total vapour pressure
p = pA+pB   = pA = p0A+p0A×BxB = p0A-pAp0A
Solution containing non-volatile solute : For a solution of non-volatile solid in a liquid the vapour pressure contribution by the non-volatile solute is negligible. Therefore the partial vapour pressure of a solution containing a non-volatile solute is equal to the product of the vapour pressure of the pure liquid (solvent p0A) and its mole fraction in solution.
PA = P0A x xB ....(i)
xB is the mole fraction of the non-volatile solute
B, then xA + xB = 1
xA = 1 – xB ....(ii)
Substituting the value of xA fromeq. (ii) into eq. (i), we get, pA = p0A (1 – xB) = p0A – p0x B
p0A-pAp0A=xB.

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Discuss the various types of plots between the partial vapour pressure and the mole fractions of two components of the completely miscible liquids in a solution.

When the partial vapour pressures of different (two) miscible liquids are plotted against their compositions (mole fractions), following three types of vapour pressure-composition (p – x) curves are obtained.
(a) Type-I: When the vapour pressures of the mixture lie between the vapour pressure of pure components : In such cases the solution obeys the Raoult’s law (ideal solution) i.e., the partial vapour pressure of each component (pc) is obtained by the relation.

When the partial vapour pressures of different (two) miscible liquids
Fig. Solution obeying Raoult’s law.
Where xc is the mole fraction of that component and p0c the vapour pressure of that component in pure form. In such cases, p-x curve is always a straight line. The total vapour pressure of the solution is equal to the sum of the partial vaour pressures of all components.
Examples: Solution of benzene-toluene, chlorobenzene bromobenzene, hexane-heptane.
(b) Type-II : When the observed vapour pressure of the solution is greater than that of calculated vapour pressure from the Raoult’s law : In such cases partial vapour pressure of each component is found to be more than expected on the basis of the Raoult’s law. The total vapour pressure of the solution is also greater than the vapour pressure corresponding to the ideal solution. At a certain composition the total vapour pressure of the solution will be the highest (maximum) which is greater than the vapour pressure of either of the pure liquids (components) at this components the boiling point of the solution will be lowest. This type of deviation from Raoult’s law is known as positive deviation and the system exhibits a maximum value of vapour pressure at certain composition. At this composition both the liquids boil at same (constant) temperature (minimum boiling azeotropes). In figure point C, corresponds the composition of the two liquids which boils at lowest temperature. For example, alcohol-water mixture having the composition of 95.59% alcohol and 4.41 water boils at 78.130C. This composition is called azeotropic mixture.

When the partial vapour pressures of different (two) miscible liquids
Fig.p-x curve showing maximum in the total vapour pressure curve.
Example: Ethanol-water solution. Acetone-carbon disulphide solution. Chloroform-ethanol solution.
(c) Type-III: When the observed vapour pressure of the solution is less than that of calculated from Raoults law: In such cases the partial vapour pressure of any component is found to be less than the expected vapour pressure on the basis of Raoult’s law. Similarly, the total vapour pressure of the solution is also less than that of expected value according to Raoult’s law. At a certain composition the total vapour pressure of such solution will be lowest (minimum). At this composition the boiling point of the solution will be highest (maximum) and both the component will boil at same temperature without the change in the composition. Such composition corresponds to the maximum boiling azeotropic mixture. For example a mixture of 20.24% of HCl and 79.76% water forms an azeotropic mixture which boils at 1100C, without the change in composition. In figure, point C, corresponds the composition of azeotropic mixture. This type of deviation in Raoult’s law is known as negative deviation.
Example : Solution of water-HCl, chloroform-benzene, acetone-aniline.

When the partial vapour pressures of different (two) miscible liquids
Fig.  p-x curve showing minimum in the total vapour pressure curve.

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