Q. Analysis of water gave the following results H_{2}SO_{4} = 196Mg/L; MgSO_{4} = 24Mg/L, CaSO_{4} = 272Mg/L and NaCl = 25Mg/L. Water is to be supplied to the town of the population of one lake only. The daily consumption of water is 50 Litre per head. Calculate the cost of the cost of Lime soda required for the softening of hard water for town for the month of April 2002. If the cost of lime is Rs.5/per Kg and soda is Rs.8/per Kg.
Ans. Calculation of CaCO_{3} equivalents
constituent
amount
multiplication
CaCO_{3} equivalent
Requirement
H_{2}SO_{4}
196
100/98
196*100/98 = 200 Mg/L
L + S
MgSO_{4}
24
100/120
24*100/120 = 20 Mg/L
CaSO_{4}
272
100/136
272*100/120 = 20Mg/L
S
NaCl
25

Does not create hardness
Amount of Lime required: = 74/100[H_{2}SO_{4 }+ MgSO_{4}]*Vol. Of water
= 74/100[200 + 20]*50*100000
= 814*10^{6} mg = 814 kg/day
Amount of soda required: = 106/100[H_{2}SO_{4 }+ MgSO_{4 }+CaSO_{4}]*Vol. Of water
= 106/100[200 + 20 + 200]*50*100000
= 2226*10^{6}
= 2226Kg/day
Cost of lime and soda for the month of April 30 days
Cost of lime = 814*30*5 = Rs. 122100
Cost of soda = 2226*30*8 = Rs. 534240