# Hardness and Alkalinity Numerical | Water Supply Engineering

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### 1. Formula

 Alkalinity due to B– as CaCo3 = alkalinity as B– x eq. wt. of CaCo3 / eq. wt. of B– Hardness due to M++ as CaCo3 = hardness as M++ (mg/lit) x eq. wt. of CaCo3 / eq. wt. of M++ Total Hardness = Carbonate hardness + Non carbonate hardness [H+] = antilog10 [-pH] ,

If, TH > A

then, CH = A

NCH = TH-CH

NCH = TH-A

If, TH =<A

then, CH= TH

NCH=0

### 2. Hardness and Alkalinity Numerical

1. The analysis of water from a well showed the following results in mg/lit;

Ca= 65, Mg=51, Na=101.5, K= 21.5,

HCO3 = 248, SO4 = 221.8, Cl = 79.2

Find the total hardness, carbonate hardness and non-carbonate hardness.

Solution:

Hardness due to M++ as CaCo3 = hardness as M++ (mg/lit) x eq. wt. of CaCo3 / eq. wt. of M++

Total hardness = [ 65x 50/20 +51 x 50/12.2] mg/lit as CaCo3.

= 371.52 mg/lit as CaCo3

Alkalinity due to B as CaCo3 = alkalinity as B– x eq. wt. of CaCo3 / eq. wt. of B

= 248 x 50/61

= 203.28 mg/lit

In this case.

If, TH > A

then, CH = A

NCH = TH-CH

= 371.52-203.28

= 168 mg/lit

The analysis of a sample of water shows the following results in mg/lit:

 Ca Mg Na K No3 Cl HCo3 7 12 20 30 12 40 68

The concentration of Sr (Stroncium) is eq. to the hardness of 2.52 mg/lit as CaCo3 and the carbonate alkalinity in this water is zero. Calculate the total hardness and NCH in mg/lit as CaCo3.

Solution,

Total hardness = Ca++ x 50./20 +Mg++ x 50/12.2 +2.52

= 7×50/20 + 12×50/12.2 +2.52

= 69.2 mg/lit as CaCo3.

Bicarbonate alkalinity= 68 x 50/61 =55.74 mg/lit as CaCo3

In this case,

TH>A

CH= A

NCH = TH-CH

=69.2-55.74

= 13.46 mg/lit as CaCo3

3. The total hardness value obtained from the complete analysis of a water sample is found to be 150 mg/lit. The analysis further showed that the concentrations of all the three principal cations causing hardness are numerically the same. If the value of carbonate hardness is 77 mg /lit, calculate;

1) the value of NCH

2) the concentrations of principal cations; and

3) the value of total alkalinity in mg/lit.

Solution:

Total Hardness = Carbonate hardness + Non Carbonate Hardness

NCH = 150 – 77 = 73 mg/lit

Let, P is the concentration of principle cations.

Now, TH= P x 50/20 + P x 50/12.2 + P x 50/43.8

Principle concentrations (P)= 19.38 mg/lit

In this case, NCH is greater than zero so total hardness is greater than
alkalinity.

When, TH > A

then, CH = A = 77 mg/lit as CaCo3

NCH = TH-CH

 Read Also: Quantity of Water Numerical

4. The hardness of a water sample was found to be 300 mg/lit as CaCo3. The hardness was found due to Ca and Mg ions being equal in Water. The analysis showed the concentration of HCO3, was 150 mg/lit,

ii) the concentration of Ca and Mg

ii) the value of alkalinity of water.

iii) the CH and NCH; and

Solution:

i. Let, P is the concentration of principal cations.

Hardness due to M++ as CaCo3 = hardness as M++ (mg/lit) x eq. wt. of CaCo3 / eq. wt. of M++

Total Hardness = [50P/20 + 50P/12.2] mg/lit as CaCo3

300 = 6.6 P

Therefore, P = 45.45 mg/lit

ii) Bicarbonate alkalinity

Bicarbonate alkalinity = 150 x 50/61 = 122.95 mg/lit as CaCO3

Total alkalinity = CA + BA = 0 + 122.95 = 122.95 mg/lit

iii) Here, Total hardness > Total alkalinity

Carbonate hardness = Total alkalinity = 122.95 mg/lit

Total Hardness = Carbonate hardness + Non Carbonate Hardness NCH

= 300-122.95

= 177.05 mg/lit as CaCO

5. If 400 ml of water with a pH 6 is mixed with 700 ml of water with a pH of 8, what will be the resultant pH of the mixture?

Given,

Va = 400 ml, (PH)a = 6

Vh = 700 ml, (pH)b = 8

Total volume of solution = 1100 ml

[H+] = antilog10 [-pH] ,

pH = log10 1/[H+]

[Hla = 10-6 moles/lit,

Conc. of [H+]a in 400 ml = 10-6 x 400 / 1100 = 3.64×10-7 moles/lit

Conc. of [H+lb in 700 ml = 10-8 x 700/1100 = 6.36×10-9 moles/lit

Concentration mix
= 3.64 x 10-7 + 6.36 x 10-9

= 3.7036 x 10-7 moles/lit

pH= 6.43

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Madhu Krishana Poudel is a distinguished Civil Engineer with extensive experience in site supervision, estimation, and AutoCAD 2D and 3D design. Holding a Bachelor's degree in Civil Engineering from Pokhara University, his work and expertise have earned recognition in reputable sources such as USA Today, Time, Wikipedia, and TheRichest, establishing his credibility and trustworthiness in the construction industry.
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