Question

The analyses results of a water sample are given below. The non-carbonate hardness of the water (in mg/L) as CaCO\(_3\) is ......... (in integer).
Ca\(^{2+}\) = 150 mg/L as CaCO\(_3\)
Mg\(^{2+}\) = 40 mg/L as CaCO\(_3\)
Fe\(^{2+}\) = 10 mg/L as CaCO\(_3\)
Na\(^+\) = 50 mg/L as CaCO\(_3\)
K\(^+\) = 10 mg/L as CaCO\(_3\)
CO\(_3^{2-}\) = 120 mg/L as CaCO\(_3\)
HCO\(_3^{-}\) = 30 mg/L as CaCO\(_3\)
Cl\(^{-}\) = 50 mg/L as CaCO\(_3\); Other anions were not analysed.

Hint:

To calculate non-carbonate hardness, subtract the carbonate hardness from the total hardness. Carbonate hardness is the minimum of alkalinity and total hardness, and non-carbonate hardness accounts for the hardness due to other ions.

Answer 1

Total Hardness (TH) Calculation:
Total hardness as CaCO₃ is calculated by summing the hardness contribution of each ion:
\[ \text{Total Hardness (TH)} = 150 + 40 + 10 = 200 \, \text{mg/L as CaCO}_3 \]
Alkalinity Calculation:
Alkalinity as CaCO₃ is the sum of the contributions from the ions that contribute to alkalinity:
\[ \text{Alkalinity} = 100 + 50 = 150 \, \text{mg/L as CaCO}_3 \]
Carbonate Hardness (CH) Calculation:
The carbonate hardness (CH) is given by the minimum of alkalinity and total hardness:
\[ \text{CH} = 150 \, \text{mg/L as CaCO}_3 \]
Non-Carbonate Hardness (NCH) Calculation:
The non-carbonate hardness (NCH) is given by:
\[ \text{NCH} = \text{TH} - \text{CH} = 200 - 150 = 50 \, \text{mg/L as CaCO}_3 \]
Final Answer:
Thus, the non-carbonate hardness of the water is: \[ \boxed{50 \, \text{mg/L as CaCO}_3} \]