QUESTION 1:
Calculate the osmotic pressure of a solution 0.1 molar of sucrose (Mw = 342) at 20oC.
SOLUTION:
From the formulae,
Molality = moles/kilogram of solvent
Molarity = moles/liter of solution
The grams of sucrose in the solutions are 34.2 and the total weight of the solution is
34.2 + 1000 grams of solvent = 1034.2
Assuming a density is 1
0.1 moles : 1034.2 = M : 1000 grams of solution
M = 100/1034.2 = 0.097
p = (0.097)(0.0820578 liter atm mol-1 K-1)(293) = 2.34 atm
QUESTION 2:
A mixture of water and acetone at 756 mm boils at 70oC. Calculate the percentage composition of the mixture using the following table:
SOLUTION:
According to Raoult's law,
P = xacetone Po acetone + xwater Powater
= 756/760 =0.995 atm
Substituting the values at 70oC ,
P = xacetone 1.58 + xacqua 0.312 = 0.995
We also know that,
So, xacetone 1.58 + 0.312 (1 - xacetone) = 0.995
xacqua 1.58 + 0.312 - 0.312 xacetone = 0.995
xacetone 1.26+ 0.312 = 0.995
xacetone = (0.995 - 0.312) / 1.26 = 0.54
So, xwater = 1 - 0.54 = 0.46
Considering that we have 100 moles of solution, 54 moles of acetone and 46 moles of water is present in the sample.
54 moles of acetone is 54 x 58 =3132 grams
and 46 moles of water is 46 x 18 = 828 grams
So, % water = (828)(100)/3132 + 828) = 21%
% acetone = 100-21 = 79%
QUESTION 3:
The addition of 114 grams of sucrose to 1000 grams of water lowers the vapor pressure of water from 17.540 to 17.435. Calculate the molecular weight of sucrose.
SOLUTION:
The difference in pressure: 17.540 - 17.435 = 0.105
Then,
0.105 = 17.540 x2 = nsolute/(nsolvent + nsolute)
nsolvent = 1000/mw water = 1000/18 = 55.55 moles
0.105 = 17.540 x2 = 17.540 nsolute/(55.55 + nsolute)
by solving this,
nsolute = 0.335 moles and
MW = 114/0.335 = 340
The calculated molecular weight (340) is very close to the true molecular weight of sucrose 342
QUESTION 4:
Calculate the osmotic pressure at 20o of a suspension containing 60g/l of solid particles each particle having a mass of 10-9 grams (1 nanogram).
SOLUTION:
Formula: p = MRT ( T = 278 + 20 = 298 oK and R = 0.0823)
The number of particles in one liter of solution is = 60/10-9 = 6 x 1010
1 mole of any substance contains an Avogadro number of particles (6 x 1023)
The number of moles in one liter of suspension = 6 x 1010/6 x 1023 = 10-13
which is equal to the molarity of the suspension.
So, p = (0.0823)(298) (10-13) = 24.5 x 10-13 atm
QUESTION 5:
Calculate the vapor pressure of a mixture containing 252 g of n-pentane (Mw = 72) and 1400 g of n-heptane (Mw = 100) at 20oC. The vapor pressure of n-pentane and n-heptane are 420 mm Hg and 36 mm Hg respectively.
SOLUTION:
From Raoult's law, P = Po x
Here,
P = vapor pressure of the component in the mixture.
Po= vapor pressure of the pure component.
x = Molar fraction of the component in the mixture.
Calculation of mole fraction:
Mole fraction = moles of one component / Total moles in solution
Moles n-pentane = 252/72 = 3.5
Moles n-eptano = 1400/100 = 14
Totals = 3.5 + 14 = 17.5 moles
xn-pentane = 3.5/17.5 = 0.2 , xn-eptane = 14/17.5 = 0.8
So, Pn-pentane = 0.2 x 420 = 84 mm Hg ; Pn-eptane = 0.8 x 36 = 28.8 mm Hg
and the vapor pressure of mixture is, Pmixture = 84 + 28.8 = 112.8 mm
QUESTION 6:
Calculate the boiling point (at 1 atm) of a solution containing 116 g of acetone (Mw = 58) and 72 g of water (Mw = 18) by using the following table:
SOLUTION:
A liquid starts to boil when its vapor pressure matches the atmospheric pressure (1 atm in this case).
According to Raoult's law
P = xacetone Po acetone + xwater Powater = 1 atm
Calculate the molar fractions:
Mole fraction = moles of one component / Total moles in solution
molesacetone = 116/58 = 2 ; moleswater = 72/18 = 4
So, Total moles = 2 + 4 = 6
Substituting the given values,
xacetone = 2/4 = 1/3 ; xwater = 4/6 = 2/3
So, P = 2/3 Po acetone + 1/3 Powater= 1 atm
By trials, using the table, we can find the values of vapor pressure which satisfies the above equation. The best result is obtained by using the values at 80oC :
P = 2/3 0.456 + 1/3 2.12 = 1.01 atm
So, the boiling point is about 80oC.
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