Determine the lime and soda ash dose, in mg/L as CaCO_3, to soften the following

Question

Determine the lime and soda ash dose, in mg/L as CaCO_3, to soften the following water to a final hardness of 90.0 mg/L as CaCO_3. If the price of lime, purchased as CaO, is $61.70 per megagram (Mg), and the price of soda ash, purchased as Na_2 CO_3, is $172.50 per Mg, what is the annual chemical cost of treating 0.050 m^3/s of this water? Assume the lime is 90% pure and the soda ash is 97% pure. The ion concentrations reported below are all mg/L as CaCO_3. Ca^2+ = 137.0 Mg^2+ = 40.0 HCO_3^- = 197.0 CO_2 = 9.0

Explanation / Answer

Ans: Step 1:Before calculating the lime and soda ash dosages, express all concemtrations in terms of CaCO3.

Concentration of X as CaCO3= given Cx *Mw(caco3)/Mw(x)

thus,[Mg] as CaCO3= (40mg/L)*(50/12)= 166.66 mg/L as CaCO3

[HCO3-] =(197.0 mg/L)*(50/61)= 161.47 mg/L [HCO3-] as CaCO3

[CO2]=(9.0 mg/L)*(50/22)= 20.45mg/L [CO2] as CaCO3

Total Hardness= [Ca]+[Mg] = 137.0+40.0 = 177.0 as CaCO3

STEP 2: Now the following chemical equations are used to determine the lime and soda ash dosage requirements:

Lime dosage= [CO2] +[HCO3-] +[Mg] +[excess]

and Soda ash dosage= [Total Hardness] -[HCO3-] +[excess]

assuming [excess] to b zero and using the above equations,

Lime dosage= 20.45 + 161.47 + 166.66 + 0=348.58 mg/L as CaCO3

& soda ash dosage= 177.0 -161.47 + 0 = 15.53 mg/L as CaCO3

STEP 3: Covert lime and soda ash dosages expressed as CaCO3 to dosages expressed as CaO and as Na2CO3 respectively.

Equivalent weight of CaCO3 =50

Equivalent weight of CaO =28 and Equivalent weight of Na2CO3 =53

So, 348.58 mg/L lime as CaCO3 = 348.58 * (28/50)

                                                = 195.20 mg/L as Cao

& 15.53 mg/L soda ash as CaCO3 = 15.53 * (53/50)

                                                   = 16.46 mg/L as Na2CO3

STEP 4: Adjust dosages for the purity of the lime and soda ash used.

For this, ( % purity of chemical actually used)(Actual dosage required for chemical used) = (calculated dosage                                                                                                     of 100% pure chemical used )

Lime is 90% pure and soda ash is 97% pure

Therefore, Actual dosage of Lime = (195.20 mg/L as CaO * 100)/90 = 216.88 mg/L as CaO

Actual dosage of Soda ash required = (16.46 mg/L as Na2CO3 *100)/97 = 16.96 mg/L as Na2CO3

STEP 5 : Calculate the cost

Amount of lime required in Kg/ day = (216.88 mg/L) * (vol. of water treated in litres/day) / (0.85)

volume of water =0.050 m^3/sec= 4320000 l/day

thus, amount of lime = 1102260705.88 kg/day

Annual consumption in mg = 402325157646.2 * 10^6 mg/year of lime is uesd

therefore cost = 402325157646.2 * 10^6 *61.70$= $24,823,462,226,770 *10^6

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.