Hardness - Multivalent metal ions which will form precipitates with soaps. e.g. Ca 2+ + (soap) Ca(soap) 2 (s)

Water Softening (Precipitation Softening) (3^rd DC 178; 4^th DC 235)

1. Introduction Hardness

- Multivalent metal ions which will form precipitates with soaps.

e.g.

Ca²⁺ + (soap)

↔

Complexation reaction

a. Caused by ions of Ca²⁺ and Mg²⁺

- Hardness in water is caused by ions of Ca²⁺ and Mg²⁺

b. Other hardness constituents: Iron (Fe), manganese (Mn), strontium (Sr), aluminum (Al).

- Iron (Fe), manganese (Mn), strontium (Sr), aluminum (Al) also produce hardness.

c. Sources - Largely the result of geological formations of the water source.

Precipitation

: : : : : : : :

--- /// /// Top organic soil - microbial activity /// ///

CH2O + O2  CO2 + H2O organics

--- Subsoil

CO2 + H2O  H2CO3

--- Limestone formation – weathering

CaCO3(s) + H2CO3  Ca(HCO3)2

MgCO3(s) + H2CO3  Mg(HCO3)2

CaCO_3(s) + H⁺_(aq)

↔

60°C

Types of Hardness

 with respect to cations (metallic ion)

 with respect to anions (nonmetallic ion)

1) With respect to cations (metallic ion; Ca²⁺, Mg²⁺)

a. Calcium Hardness: Ca(HCO₃)₂, CaSO₄, CaCl₂ b. Magnesium Hardness: Mg(HCO₃)₂, MgSO₄, MgCl₂ Total Hardness (TH) = Calcium Hardness + Magnesium Hardness

2) With respect to anions (nonmetallic ion; HCO₃ ^-, SO₄^2-, Cl^-) a. Carbonate Hardness (CH)

b. Noncarbonate hardness (NCH)

Carbonate Hardness (Temporary Hardness) - heating the water removes it.

• Calcium bicarbonate Ca(HCO₃)₂ • Magnesium bicarbonate Mg(HCO₃)₂

Carbonate hardness = alkalinity, when alkalinity < TH Carbonate hardness = TH, when alkalinity > TH

where TH = total hardness

* Alkalinity - measured as the amount of acid required to titrate to PH 4.3. (e.g., HO^-, CO 3 2- , HCO 3

-)

Noncarbonate hardness (Permanent hardness) - not removed when water is heated

- will not precipitate when the water is boiled

• Calcium sulfates CaSO4

• Magnesium sulfates MgSO4

• Calcium chlorides CaCl2

• Magnesium chlorides MgCl2

Total Hardness (TH) = Carbonate Hardness (CH) + Noncarbonate hardness (NCH)

d. Expressed in mg/L as CaCO3

- The sum of calcium and magnesium concentrations expressed in mg/L as CaCO3.

eq. wt of CaCO3

Hardness (mg/L as CaCO3) = (mg/L of M²⁺) --- eq. wt of M²⁺

Hardness (mg/L as CaCO3)

= (meq/L Ca²⁺ + meq/L Mg²⁺) (ew. wt of CaCO3)

(eq. wt of CaCO3 = 50 mg/meq)

Note: EW = equivalent weight, mg/meq

meq mg mg --- --- = --- L meq L

Example: Given Ca²⁺ = 70 mg/L and Mg²⁺ = 9.7 mg/L

Determine calcium hardness, magnesium hardness, and total hardness as CaCO3.

(Solutions)

EW of Ca²⁺ = 20 mg/meq EW of Mg²⁺ =12.2 mg/meq EW of CaCO3 = 50 mg/meq

50 mg/meq CaCO3

Calcium hardness = (70 mg/L Ca²⁺) --- 20 mg/meq Ca²⁺

= 175 mg/L hardness as CaCO3

50 mg/meq CaCO3

Magnesium hardness = (9.7 mg/L Mg²⁺) --- 12.2 mg/meq Mg²⁺

= 40 mg/L hardness as CaCO3

Total hardness = (175 + 40) = 215 mg/L as CaCO3

Example: Given Ca²⁺ = 3.5 meq/L and Mg²⁺ = 0.795 meq/L.

Determine total hardness as CaCO3.

(Solution)

Total hardness = (3.5 meq/L + 0.795 meq/L) (50 mg/meq CaCO3)

= 215 mg/L as CaCO3

Hard Water Classification Table 3-13 (DC 179); Table 4-14 (4^th DC 236)

Hardness Range Description mg/L as CaCO3

---

0 - 75 Soft

75 -100 Moderately hard

100 - 300 Hard

>300 Very Hard

---

● Hardness >300 mg/L as CaCO₃ is considered excessive for public water supply - results in

a. high soap consumption

b. scale in heating vessels and pipes

● Mg²⁺ in excess of ~40 mg/L as CaCO3 forms scale on heat exchange elements in hot water heaters

 Goal of water treatment (softening) is 75–120 mg/L as CaCO3 (3^rd DC, 179)

From other literature

--- a. High (excessive) hardness >300 mg/L as CaCO3

b. Hard 150 - 300 mg/L as CaCO3

(100 - 300 mg/L as CaCO3)

c. Moderate hardness 60-120 mg/L as CaCO3

(75 -150 mg/L as CaCO3) - is considered moderately hard

d. Soft 0 - 75 mg/L as CaCO3

e. Acceptable 80-100 mg/L as CaCO3

- acceptable for a public water supply

- but magnesium content should not exceed 40 mg/L as CaCO3 ---

2. Chemistry of Water Softening Lime-soda ash processes

a. The lime-soda ash water-softening process uses:

Lime, Ca(OH) 2 (or CaO) and Soda ash, Na2CO3

to precipitate hardness as:

Calcium carbonate, CaCO3(s) Magnesium hydroxide, Mg(OH)2(s)

b. Chemical reactions:

a. CO2

- is not hardness but it consumes lime and must therefore be considered in calculating the amount required.

CO2 + Ca(OH)2 ↔ CaCO 3(s) + H2O (1)

b. Carbonate hardness

- is precipitated by lime.

Ca(HCO3)2 + Ca (OH)2 ↔ 2CaCO3 (s) + 2H2O (2)

Mg(HCO3)2 + Ca(OH)2 ↔ CaCO3 (s) + MgCO3 + 2H2O (3)

MgCO3 + Ca(OH)2 ↔ Mg (OH)2 (s) + CaCO 3(s) (4)

Note: - 1 mole of lime is needed for each mole of calcium bicarbonate (Rxn 2) - 2 moles of lime are required for each mole of magnesium bicarbonate (Rxns 3 and 4). c. Noncarbonate hardness - requires the addition of soda ash for precipitation MgSO 4 + Ca(OH) 2 ↔ Mg(OH) 2(s) + CaSO4 (5)

CaSO4 + Na2CO3 ↔ CaCO 3(s) + Na2SO4 (6)

MgCl2 + Ca(OH) 2 ↔ Mg(OH) 2(s) + CaCl2 (7)

CaCl2 + Na2CO3 ↔ CaCO 3(s) + 2 NaCl (8)

Note:

- 1 mole of lime Ca(OH)2 and 1 mole of soda ash Na2CO3 are needed to each mole of MgSO4 or MgCl 2

- 1 mole of soda ash Na2CO3 is needed to each mole of CaSO4 or CaCl 2

Solubility of CaCO3(s) and Mg(OH)2(s)

- Precipitation softening cannot produce water completely free of hardness because of:

a. Solubility of CaCO3(s) and Mg(OH)2 (s)

= (0.6 meq/L of CaCO3) + (0.2 meq/L of Mg(OH)2)

= (30 mg/L CaCO3) + (10 mg/L of Mg(OH) 2 as CaCO3)

Total limiting hardness = 40 mg/L as CaCO3

- The minimum practical limits of precipitation softening = 30 mg/L of CaCO 3 and10 mg/L of Mg(OH)2 expressed as CaCO3

Goal is 75 – 120 mg/L hardness as CaCO3

Deviations from the theoretical hardness removal by the lime-soda ash treatment.

- Limited completion of the chemical reactions by physical considerations;

e.g., inadequate mixing, limited detention time in settling basins

Advantages of Lime-Soda ash Softening

a. Hardness is taken out of solution

b. Lime added is also removed.

- when soda ash is applied, Na⁺ remains in the finished water.

- noncarbonate hardness requiring soda ash is generally a small portion of the total hardness.

c. TDS (total dissolved solids) is reduced

- Lime also precipitates the soluble Fe and Mn - TDS may be significantly reduced.

d. Disinfection

- Excess lime treatment provides disinfection

e. Aids in coagulation

- Excess lime treatment provides aids in coagulation for removal of turbidity

Schemes of lime-soda ash softening

- three different basic schemes may be used to provide a finished water with the desired hardness.

a. Excess lime treatment b. Selective calcium removal c. Split treatment

Excess Lime Treatment

1) Carbonate hardness associated with Ca²⁺ can be effectively removed to the practical limit of CaCO3 solubility (30 mg/L) by stoichiometric additions of lime.

Ca(HCO3)2 + Ca(OH)2  2CaCO3(s) + 2H2O

2) Precipitation of Mg²⁺ calls for a surplus of approximately 1.25 meq/L (30 mg/L) of CaO above stoichiometric requirements.

3) The practice of excess-lime treatment reduces the total hardness to about 40 mg/L as CaCO3

i.e., 30 mg/L of CaCO3 as CaCO3

10 mg/L of Mg(OH)2 as CaCO3

4) After excess-lime treatment, the water is scale forming and must be neutralized to remove caustic alkalinity (OH^-).

- Recarbonation and soda ash are regularly used to stabilize the water

5) CO2 neutralizes excess lime as follows:

Ca(OH) 2 + CO2  CaCO3(s) + H2O excess lime

- this reaction precipitates calcium hardness and reduces the pH from near 11 to about 10.2.

6) Further recarbonation of the clarified water converts a portion (say 1/2) of the remaining carbonate ions to bicarbonate by the reaction.

CaCO 3(s) + CO 2 + H2O  Ca(HCO3) 2

- the final pH is in the range 9.5 to 8.5, depending on the desired carbonate to bicarbonate ratio.

Bar Diagram (Bar Graph)

- purpose is to visualization of the chemical composition - data may be expressed in meq/L (milliequivalents per liter).

a) Top row of the bar graph consists of major cations arranged in the order of Ca²⁺, Mg²⁺, Na⁺, K⁺.

b) Bottom row of the aligned in the sequence of OH⁻, CO32−

, HCO3 −

, SO42−

, Cl^-, NO3-

.

c) The sum of the positive meq/L must equal the sum of the negative meq/L for a given water sample in equilibrium.

Ion Balance or I Cations -  Anions l

Charge Balance = --- x 100 Cations + ΣAnions

< 5% OK

Example: WATER SOFTENING - Excess Lime Treatment

The water defined by the analysis given below is to be softened by excess lime treatment in a two-stage system.

Given chemical Analysis Data: CO2 = 8.8 mg/L; Ca ²⁺ =70.0 mg/L; Mg²⁺ = 9.7 mg/L; Na⁺ = 6.9 mg/L; HCO3−

=115.0 mg/L as CaCO3; SO42-

= 96.0 mg/L; Cl⁻ = 10.6 mg/L

1. Sketch a bar graph for:

a) the raw water,

b) softened water after chemical addition and settling, but before recarbonation and filtration,

c) softened water after 1^st stage recarbonation,

d) softened water after 2^nd stage recarbonation and filtration assuming that one-half of the alkalinity is in the bicarbonate form.

2. List the hypothetical combinations of chemical compounds in the raw water.

3. Calculate the quantity of softening chemicals required in lb/MG of water.

4. Calculate the theoretical quantity of CO2 needed to provide finished water with ½ of the alkalinity converted to bicarbonate ion.

(SOLUTIONS)

1. Express the concentrations in meq/L

a. Sketch a meq/L bar graph for the raw water.

b.

Species Conc.

(mg/L)

MW (g/mol)

z MW/z = eq.wt (mg/meq)

mg/L

--- = meq/L mg/meq

Total (meq/L)

CO₂ 8.8 44 2 22.0 0.4 0.4

Cations

Ca ²⁺ 70.0 40.1 2 20.0 3.5

Mg²⁺ 9.7 24.3 2 12.2 0.795

Na⁺ 6.9 23.0 1 23.0 0.3 4.595

Anions HCO₃⁻ (as Ca CO₃)

115 100 2 50.0 2.3

SO₄ ²⁻ 96.0 96.0 2 48.0 2.0

Cl⁻ 10.6 35.5 1 35.3 0.3 4.6

b. Check ion balance

Ion Balance or I ΣCations - ΣAnions l

Charge Balance = --- x 100 ΣCations + ΣAnions

I 4.595 - 4.6 l

= --- x 100 = 0.05 % < 5% Ion Balance is OK 4.595 + 4.6

2. Sketch a bar graph for the raw water. - See the bar graph below: 1) Raw water

3. Calculate the softening chemicals required.

1) List the combination and concentration (meq/L) of chemical compounds from the bar graph (Raw water)

Compound (meq/L)

CO2 0.4

Ca(HCO3)2 2.3

CaSO₄ 1.2

MgSO ₄ 0.8

NaCl 0.3

Lime Required

CO2: CO2 + Ca(OH)2  CaCO 3(s) + H2O (1) 0.4 0.4

Ca(HCO₃)₂: Ca(HCO₃)₂ + Ca (OH)₂  2CaCO_{3 (s)} + 2H₂O (2)

2.3 2.3

MgSO 4: MgSO 4 + Ca(OH) 2  Mg(OH) 2(s) + CaSO4 (5) 0.8 0.8 0.8

--- (meq/L) 3.5 3.5

Soda Ash Required

CaSO₄: CaSO₄ + Na₂CO₃  CaCO _3(s) + Na₂SO₄ (6) Raw water 1.2 1.2

Produced w/Lime 0.8 0.8

_____________________________________________________

(meq/L) 2.0 2.0

Calculate eq.wt of lime and soda ash

MW z eq.wt (mg/meq) Quick Lime CaO 56.1 2 28.0

Soda Ash Na₂CO₃ 106 2 53.0

Lime (as CaO) required = stoichiometric requirement + excess lime

= (3.5 meq/L)(28 mg/meq) + (1.25 meq/L)(28 mg/meq) = 133 mg/L CaO

= (133 mg/L)(8.34 lb/MG per mg/L) = 1100 lb/MG

Soda ash required = (2.0 meq/L)(53 mg/meq) = 106 mg/L Na₂CO₃

= (106 mg/L)(8.34 lb/MG per mg/L) = 884 lb/MG

(c) Sketch an meq/L bar graph for the water after lime and soda ash additions and settling, but before recarbonation

1) Calculate solubilities (in meq/L)

mg/L eq.wt (mg/meq) meq/L

CaCO₃ as Ca CO₃ 30 50 0.6

Mg(OH)₂ as Ca CO₃ 10 50 0.2

After the addition of softening chemicals

CATIONS (meq/L)

Ca ²⁺ Excess lime, Ca(OH)₂ 1.25 Ca ²⁺ Solubility of Ca CO3 0.6 Mg²⁺ Solubility of Mg(OH) ₂ 0.2 Na⁺ Present in raw water 0.3 Na⁺ From Na2CO3 added 2.0

M⁺, not including excess lime 3.1

ANIONS (meq/L)

OH^- Excess lime, Ca(OH)₂ 1.25 OH^- Solubility of Mg(OH) 2 0.2 CO₃^2- Solubility of Ca CO₃ 0.6 SO4 2- Present in raw water 2.0 Cl^- Present in raw water 0.3

M^-, not including excess lime 3.1 See the bar graph (2)

Recarbonation

1) converts the excess OH⁻ to CO32−

Ca(OH)2 + CO2  CaCO3(s) + H2O

Excess OH⁻ = OH⁻ from excess lime + OH⁻ from Mg(OH) 2

= 1.25 meq/L + 0.2 meq/L = 1.45 meq/L

1.45 meq 22 mg

= --- (--- CO2 ) = 31.9 mg/L of CO2 L meq

- Draw a bar graph for the softened water after recarbonation and filtration assuming that

2) After second-stage processing, final recarbonation convert ½ of remaining CO32−

to HCO3-

CaCO 3 + CO 2 + H2O  Ca(HCO3) 2

0.6 0.6

MgCO 3 + CO 2 + H2O  Mg(HCO3) 2

0.2 0.2

22 mg

(½)(0.8 meq/L)(--- CO2 ) = 8.8 mg/L of CO2 meq

Total CO2 Reacted = 31.9 + 8.8 = 40.7 mg/L

= 40.7 mg/L (8.34 lb/MG per mg/L)

= 340 lb CO2 / MG

(d) Draw a bar graph for the softened water after recarbonation and filtration.

CATIONS

(meq/L)

Ca ²⁺ Solubility of Ca CO3 0.6

Mg²⁺ Solubility of Mg(OH) ₂ 0.2 Na⁺ Present in raw water + From Na2CO3

added

2.3 ΣM⁺, not including excess lime 3.1 ANIONS

(meq/L)

CO₃^2- Solubility of Ca CO₃ 0.4

HCO₃- From Ca(HCO₃) ₂ and Mg(HCO₃) ₂ 0.4 SO₄ ^2- Present in raw water 2.0

Cl^- Present in raw water 0.3

ΣM^-, not including excess lime 3.1

A single-stage calcium carbonate softening plant

A two-stage excess lime softening plant

Homework #7 is due one week from today!

A split-treatment softening plant

CO₂