Solution
In Text Questions
Part 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