---
title: "Ca and Mg concentration, alkalinity (300 mg/l hardness)"
subject: "Water Supply Engineering"
chapter: 4
key: "semester_5/water_supply_engineering:hardness-ca-mg-equal-300"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/hardness-ca-mg-equal-300
site: BCT Engineering
---

# Ca and Mg concentration, alkalinity (300 mg/l hardness)

Water Supply Engineering · Chapter 4: Quality of Water

- Asked in: 2071 Shrawan, 8 marks; 2073 Chaitra, 8 marks (asked 2 times)
- 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-ca-mg-equal-300
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-4

## Question

The hardness of a water sample was found to be 300 mg/l as CaCO$_3$. The hardness was found due to Ca and Mg ions only. The concentrations of these ions are equal in water. The water analysis showed the concentration of HCO$_3^-$ was 150 mg/l. Calculate (i) the concentrations of Ca and Mg, (ii) alkalinity of water and (iii) carbonate hardness and non-carbonate hardness of water.

## Short answer

Let Ca = Mg = x mg/L. Total hardness = x(50/20.04 + 50/12.15) = 6.610x = 300, so x = 45.38 mg/L. Alkalinity = 150 × (50/61.02) = 122.91 mg/L as CaCO3. Carbonate hardness = alkalinity = 122.91 mg/L; non-carbonate hardness = 300 – 122.91 = 177.09 mg/L.

## 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.

#### (i) Concentration of Ca and Mg
Let Ca = Mg = $x$ mg/l.

$$
\begin{aligned}
\text{TH} &= x\left(\frac{50}{20.04}+\frac{50}{12.15}\right) = x(2.495+4.115) = 6.610x = 300\\
x &= 45.38\ \text{mg/l}
\end{aligned}
$$

Ca$^{2+}$ = Mg$^{2+}$ = 45.38 mg/l.

#### (ii) Alkalinity
Only HCO$_3^-$ is present (no CO$_3^{2-}$ or OH$^-$), so

$$
\text{Alkalinity} = 150\times\frac{50}{61.02} = 122.91\ \text{mg/l as CaCO}_3
$$

#### (iii) Carbonate and non-carbonate hardness
The alkalinity (122.91) is less than the total hardness (300), so carbonate hardness equals alkalinity.

$$
\begin{aligned}
\text{CH} &= 122.91\ \text{mg/l}\\
\text{NCH} &= \text{TH}-\text{CH} = 300-122.91 = 177.09\ \text{mg/l}
\end{aligned}
$$

**Answer: Ca = Mg = 45.38 mg/l; alkalinity = 122.91 mg/l as CaCO$_3$; CH = 122.91 mg/l; NCH = 177.09 mg/l.**

## Check yourself

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

1. Hardness of an ion as CaCO3 is found by:
   A. concentration x 50 / equivalent weight
   B. concentration x equivalent weight / 50
   C. concentration / 50
   D. concentration x 100 / atomic weight
   Answer: A. 50 is the equivalent weight of CaCO3. (Key point: Conversion)

2. With Ca = Mg = x and TH = 300, x is:
   A. 22.7 mg/l
   B. 45.38 mg/l
   C. 60 mg/l
   D. 150 mg/l
   Answer: B. TH = x(2.495+4.115) = 6.610x, so x = 300/6.610 = 45.38. (Key point: Ca and Mg)

## Related in Water Supply Engineering

- [Ca and Mg concentration, NCH, alkalinity: TH 400 ppm](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ahardness-bk79) — Water Supply Engineering, chapter 4
- [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
- [Alkalinity and Ca, Mg: TH 280, CH 75](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ahardness-s73) — Water Supply Engineering, chapter 4
- [Hardness from ion analysis (Ca 65, Mg 35)](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ahardness-c71) — 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
- [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×