Answer:
Magnesium sulphate is in two forms
Magnesium anhydrate and magnesium hepta hydrate
Density of MgSO4= 2.66 g/ml
Density of MgSO4. 7H2O= 1.68 g/ml
M. W of MgSO4= 120 kg/kmol
In order to form 1000 Kg 20wt% solution
A) the Kg of water required before addition of crystals for MgSO4 =(1000) (0.80)= 800 kg
Average density= (0.20) (2.66) +(0.80) (1) = 1.332 g/ml = 1332 Kg/m3
Volume of water required= (800/1332) = 600.60 litres
For hepta hydrate
Average density= (0.20) (1.68) +(0.80) (1) = 1.136 g/ml=
1136 kg/m 3
MgSO4. 7 H2O, mole fraction of water present =
7×18/(120+(7×18) )=0.512 = 51.2 mol%= 13.6 wt%
1000 kg of (20 wt%) solution required
Amount of pure MgSO4 needed= 1000(.20) = 200 Kg
But it contains 13.6% water hence total weight of
MgSO4. 7H2O= 200/(1-0.136) = 231.48 kg
Amount of water required= (1000-231.48) = 768.51 Kg
Volume of water required= 768.51/1136= 676.51 Litres
B) diameter of tank= 0.30 m
V= 3.142(d2)(H) /4
For pure MgSO4 , volume of water required=600.60 litres
H = 8.49 m
For hepta hydrate volume of water required=676.51 litres
H= 9.57 m
C) height of tank after addition of crystals
Total volume in case of pure MgSO4=
1000/(1332) = 0.7507= 750.7 litres
H= 10.62 m
Total volume of hepta hydrate =
1000/(1136) = 0.8802= 880.2 litres
H= 12.45 m
D) after dissolution of crystals
The volume after dissolution in case of pure MgSO4
= volume of water= 600.67 litres
H=8.49 m
in case of hepta hydrate
The volume after dissolution= ( volume of water + volume of water in MgSO4. 7H2O)
= (676.51+(231.48×0.136) = 707.99 Litres
H= 10.01 m
Part B question
A) Weight of house= 1×105 lb= 2.20 ×105
Force applied by house= (2.20×105) (9.81) = 2.15×106 N
Pressure of ballon= 1.05 atm= 1.063×105 Pa
Diameter= 9.5 inch= 0.2413 m
Area= (3.142) (0.2413) 2/4= 0.0457 m2
F= P×A= 4857.91 N
To float the house
Both forces should be equal
So force applied by 1 ballon= 4857.91 N
Total force required=2.15×106 N
Number of ballons required= (2.15×106) /4857.91=442.57=443 ballons
B) the ballon pressure must be greater than atmospheric pressure
If both pressures are equal then there will be no air flow
If outside pressure is higher, then air would flow from outside to inside of ballon causing deflation, hence pressure inside the ballon must be higher than outside
