---
title: "Hardness from ion analysis (Ca 65, Mg 35)"
subject: "Water Supply Engineering"
chapter: 4
key: "semester_5/water_supply_engineering:hardness-c71"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/hardness-c71
site: BCT Engineering
---

# Hardness from ion analysis (Ca 65, Mg 35)

Water Supply Engineering · Chapter 4: Quality of Water

- Asked in: 2071 Chaitra, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/water_supply_engineering/hardness-c71
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-4

## Question

The analysis of water showed the following results in mg/l: Ca = 65; Mg = 35; Na = 101.5; K = 21.5; HCO$_3$ = 248; SO$_4$ = 221.8. Find the total hardness, carbonate hardness and non-carbonate hardness.

## Short answer

Ca hardness is 162.18 and Mg hardness is 144.03 mg/l as CaCO3, so total hardness is 306.21. Bicarbonate alkalinity is 203.21 mg/l as CaCO3, giving carbonate hardness 203.21 and non-carbonate hardness 103.00 mg/l as CaCO3.

## Answer

Hardness (or alkalinity) due to an ion $= \text{concentration (mg/l)}\times\dfrac{50}{\text{equivalent weight}}$ as CaCO$_3$. Equivalent weights: Ca = 20.04, Mg = 12.15, Sr = 43.81, HCO$_3$ = 61.02, CO$_3$ = 30. Na$^+$, K$^+$ and SO$_4^{2-}$ do not contribute to hardness or alkalinity.

#### Total hardness
$$
\begin{aligned}
\text{Ca hardness} &= 65\times\frac{50}{20.04} = 162.18\\
\text{Mg hardness} &= 35\times\frac{50}{12.15} = 144.03\\
\text{TH} &= 306.21\ \text{mg/l as CaCO}_3
\end{aligned}
$$

#### Carbonate hardness
Alkalinity due to HCO$_3^-$ $= 248\times\dfrac{50}{61.02} = 203.21$ mg/l as CaCO$_3$. It is less than TH, so

$$
\text{CH} = 203.21\ \text{mg/l},\qquad \text{NCH} = 306.21-203.21 = 103.00\ \text{mg/l}
$$

**Answer: Total hardness = 306.21 mg/l; carbonate hardness = 203.21 mg/l; non-carbonate hardness = 103.00 mg/l (as CaCO$_3$).**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is the hardness of an ion expressed as CaCO3?
   A. Concentration / 50 x valency
   B. Concentration x 50 / equivalent weight
   C. Concentration x 100 / equivalent weight
   D. Concentration x equivalent weight / 50
   Answer: B. Each ion's concentration is scaled by 50 (equivalent weight of CaCO3) divided by its own equivalent weight. (Key point: Hardness conversion)

2. Which of the listed ions contribute to total hardness?
   A. All listed ions
   B. Ca, Mg and Na
   C. Ca and Mg only
   D. Ca, Mg and SO4
   Answer: C. Hardness is caused by multivalent cations such as Ca and Mg; Na, K and SO4 do not contribute. (Key point: Ions that cause hardness)

3. What is total hardness here?
   A. Sum of Ca and Mg hardness = 306.21 mg/l
   B. HCO3 alkalinity = 203.21 mg/l
   C. Ca hardness only = 162.18 mg/l
   D. Sum of all ions = 692.8 mg/l
   Answer: A. TH = 162.18 + 144.03 = 306.21 mg/l as CaCO3. (Key point: Total hardness)

4. Alkalinity (203.21) is less than TH (306.21). What are CH and NCH?
   A. CH = 103.00, NCH = 203.21
   B. CH = 203.21, NCH = 509.42
   C. CH = 203.21, NCH = 103.00
   D. CH = 306.21, NCH = 0
   Answer: C. When alkalinity is below TH, CH equals the alkalinity and NCH = TH - CH = 103.00 mg/l. (Key point: Carbonate vs non-carbonate)

## Related in Water Supply Engineering

- [Hardness from ion analysis with strontium](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ahardness-b81) — Water Supply Engineering, chapter 4
- [Hardness of well water with strontium 25.26 mg/l](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ahardness-bk81) — Water Supply Engineering, chapter 4
- [Ca and Mg concentration, alkalinity (300 mg/l hardness)](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ahardness-ca-mg-equal-300) — Water Supply Engineering, chapter 4, asked 2×
- [Hardness with Ca, Mg, Sr equal, TH 150](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ahardness-as70) — Water Supply Engineering, chapter 4
- [Non-carbonate hardness: TH 150, CH 60](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ahardness-c72) — Water Supply Engineering, chapter 4, asked 2×
- [Non-carbonate hardness: TH 160, CH 70](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ahardness-b78) — Water Supply Engineering, chapter 4, asked 2×

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