# Solution

## In Text Questions 3

Question - 2.8 The vapour pressure of pure liquids A and B are 450 and 700 mm Hg respectively, at 350 K . Find out the composition of the liquid mixture if total vapour pressure is 600 mm Hg. Also find the composition of the vapour phase.

Answer: Given,POA = 450 mm Hg

POB = 700 mm Hg

PTotal = 600 mm Hg

For liquid A and B,

From Rault’s Law,

PTotal = PA + PB

= 600 mm Hg = POAXA+ POBXB

Since, XA + XB = 1

Hence, XB = 1 – XA

Thus, above equation can be written as

600 mm Hg = POAXA+ POB( - XA)

Or, 600 = 450 XA + 700(1 – XA)

Or, 600 = 450 XA + 700 – 700XA

Or, 600 – 700 = (450 – 700)XA

Or, -100 = -250XA

Or, XA = (100)/(250)=0.4

Since XB = 1 – XA

Hence, XB = 1 – 0.4 = 0.6

As PA = POAXA

So, PA = 450 xx 0.4 = 180 mm Hg

Similarly, PB = POAXB

So, PB = 700 xx 0.6 = 420 mm Hg

Now, In vapour phase,

Mole fraction of liquid A

i.e. X = (P_A)/(P_A+P_B)

Or, X_A=(180)/(180+420)=(180)/(600)=0.3

And mole fraction of liquid B

i.e. X_B=1-X_A=1-0.3=0.7

Thus, composition in liquid phase, is 0.4 and 0.6

And that in vapour phase, is 0.3 and 0.7

Question - 2.9 Vapour pressure of pure water at 298 K is 23.8 mm Hg. 50 g of urea (NH2 CONH2 ) is dissolved in 850 g of water. Calculate the vapour pressure of water for this solution and its relative lowering.

Answer:Weight of Urea (WB ) = 50 g

Molar mass (MB ) of Urea (NH2 CONH 2) = 14 + 1 x 2 + 12 +16 +14 + 1 x 2 = 60 g mol – 1

Weight of water (W A) = 850 g

Molar mass of water (M A) = 18 g mol – 1

Vapour pressure of water (P A o) = 23.8 mm Hg

Vapour pressure of water in the given solution P A = ?

Now, number of moles of urea =(W_B)/(M_B)

Or, nurea =(50g)/(60g\text(mol)^(-1))=0.83 mol

Now, number of moles of water =(W_A)/(M_B)

Or, nH2O =(850g)/(18g\text(mol)^(-1))=47.2 mol

Now, mole fraction of urea

Xurea = nurea ÷ (nurea + nH2O)

=(0.83text(mol))/(0.83text(mol)+47.2text(mol))

=(0.83)/(48.03)=0.017

Now, we know that

Xurea = (POA) ÷ (POA)

Or, 0.017=(23.8-P_A)/(23.8)

Or, 23.8-P_A=0.017xx23.8=0.40

Or, 23.8-0.40=P_A

Or, P_A=23.40 mm

Thus, vapour pressure of water in this solution is 23.40 mm of Hg and its relative lowering is 0.017

Question - 2.10 Boiling point of water at 750 mm Hg is 99.63°C. How much sucrose is to be added to 500 g of water such that it boils at 100°C.

Answer: Given, Elevation of boiling point

ΔTb = Tb - TOb

ΔTb = 100°C – 99.63°C

ΔTb = 0.37°C

Mass of water (W A) = 500 g

Molar mass (M B) of sucrose (C 12H22 O11 ) = 12 x 12 + 1 x 22 + 16 x 11 = 342 g mol – 1

Molal constant for water (Kb ) = 0.52 K kg mol – 1

Therefore, W B = ?

We know that,

ΔTb = (K_b\xx\W_B\xx1000)/(M_B\xx\W_A\gm)

Or, 0.37=(0.52xx\W_B\xx1000)/(342xx500)

Or, W_B=(0.37xx342xx500)/(0.52xx1000)

=(126.54)/(0.52xx2)=(63.27)/(0.52)=121.67 g

Thus, 121.67 g of sucrose to be added.

Question – 2.11 - Calculate the mass of ascorbic acid (Vitamin C, C6 H8 O 6) to be dissolved in 75 g of acetic acid to lower its melting point by 1.5°C. K f = 3.9 K kg mol-1.

Answer: Given, Lowering of melting point

ΔTf = 1.5°C

Kf = 39.5 kg mol-1

Molar mass of ascorbic acid (M B) = 176 g mol – 1

Thus, mass of ascorbic (WB ) = ?

We know that,

ΔTf = (K_f\xx\W_B\xx1000)/(M_B\xx\W_A\gm)

Or, 1.5=(3.9xx\W_B\xx1000)/(176xx75g)

=(176xx75xx1.5)/(3.9xx1000)

Or, W_B=5.077 g

Thus, required mass of ascorbic acid = 5.077 g

Question - 2.12 Calculate the osmotic pressure in pascals exerted by a solution prepared by dissolving 1.0 g of polymer of molar mass 185,000 in 450 mL of water at 37°C.

Answer: Given, Mass (W B) of polymer = 1 g

Molar mass (MB ) of polymer = 185000

Volume of water (V) = 450 mL = 0.45 L

Temperature (T) = 37 0C = 37+273 = 310 K

Osmotic pressure = ?

We know, R = 8.314 xx 103 Pa K k-1 mol-1

Number of moles of the polymer (n) =1/(185000) mol

We know that osmotic pressure (Π) =n/V\RT

Or, Π =1/(185000)xx1/(0.45)xx8.314xx10^3xx310

=(8314xx310)/(1850xx45)

=(2577340)/(83250)=30.95 Pa

Thus, Osmotic pressure = 30.95 Pa