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chemistry analyze the amount of softener

(b) Analyze the amount of lime and soda needed for softening 50000 liter of water containing the following: Mg(HCO3)2: 52.00 mg/L, Ca(HCO3)2 : 35.2 mg/L, CaCl2 : 22.2 mg/L, KCl : 15.55 mg/L

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Impurities (mg/lit) Multiplication factor CaCO3 equivalent (mg/lit)
$Ca(HCO_3)_2 = 35.2\ mg/lit $ $\frac{100}{162}$ $ 35.2 \times \frac{100}{162} = 21.728$
$Mg(HCO_3)_2 = 52\ mg/lit $ $\frac{100}{146}$ $52 \times \frac{100}{146} = 35.616 $
$CaCl_2 = 22.2\ mg/lit $ $\frac{100}{111}$ $22.2 \times \frac{100}{111} = 20$
$KCl = 15.55\ mg/lit $ - -

$Lime = \frac{74}{100} [CaCO_3\ equivalent\ of\ Ca(HCO_3)_2 + 2 \times Mg(HCO_3)_2 ] \times \frac{Vol. of water}{1000} \times \frac{100}{\% purity} $

$ = \frac{74}{100} \times [21.728 + 2\times35.616] \times \frac{50,000}{1000} \times \frac{100}{90}$

$ = 3821.688 grams $


$ Soda = \frac{106}{100} \times [20 ] \times \frac{50,000}{1000} \times \frac{100}{95}$

$ = 1115.78 grams $

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