Question

For the water quality characteristics in Table 1.0, soften the water using caustic soda (NaOH) and calculate;

(i) Chemicals required per day

(ii) Solids produced per day

Depth

Table 1.0 Water quality characteristics Parameter	Concentration
CO2	20 mg/L
Ca(HCO3)2	200 mg/L
MgSO4	100 mg/L
Flowrate	25,000 m3/day

NaOH equations

CO₂+2(NaOH)-->Na₂CO₃+H2O

Ca(HCO₃)₂+2(NaOH)-->Na₂CO₃+H2O

Mg(SO₄)+2(NaOH)-->Mg(OH)₂+Na₂SO₄

Answer 1

Lets calculate how much CO2 is in that 25,000 m3/day stream

20 mg/L is the same as 20 g/m3

so Amount of CO2 needed = 20 g/m3 * 25,000 m3/day = 500,000 g/ day or 500 kg/day of CO2

Do the same for Ca(HCO3)2

amount of Ca(HCO3)2 needed = 200 g/m3 * 25,000 m3/day = 5,000,000 g/day or 5 ton of Ca(HCO3)2 per day

now MgSO4 = 100 g/m3 * 25,000 m3/day = 2,500,000 g/day = 2.5 ton MgSO4 per day

B) Solids produced per day

CO2+2(NaOH)-->Na2CO3+H2O

Ca(HCO3)2+2(NaOH)-->Na2CO3+H2O

Mg(SO4)+2(NaOH)-->Mg(OH)2+Na2SO4

Solids are Na2CO3 and Mg(OH)2

Check out stoichimetrics

1 mol of CO2 : 1 mol of Na2CO3

1 mol of Ca(HCO3)2 : 1 mol of Na2CO3

1 mol of Mg(SO4) : 1 mol of Mg(OH)2

Calculate the amount of moles per unit... we need MW of each substance

1 mol of CO2 : 1 mol of Na2CO3

44 kg/kmol : 105.98 kg/kmol

or 2.4x

1 mol of Ca(HCO3)2 : 1 mol of Na2CO3

162 kg/kmol : 105.98 kg/kmol

or 0.65x

1 mol of Mg(SO4) : 1 mol of Mg(OH)2

120 kg/kmol : 58.3 kg/gmol

2.05x

Calculate now each substance produced

2.4x where x = 500 kg CO2/day

2.4*500 = 1200 kg of Na2CO3 per day

0.65x where x = 5 ton of Ca(HCO3)2 per day

0.65*5 = 3.25 ton of Na2CO3 per day

Total Na2CO3 = 1.2 ton + 3.25 ton = 4.45 ton of Na2CO3 per day

2.05x where x =2.5 ton MgSO4 per day

2.05*2.5 = 5.12 ton Mg(OH)₂ per day