---
title: "Hardness from ion analysis with strontium"
subject: "Water Supply Engineering"
chapter: 4
key: "semester_5/water_supply_engineering:hardness-b81"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/hardness-b81
site: BCT Engineering
---

# Hardness from ion analysis with strontium

Water Supply Engineering · Chapter 4: Quality of Water

- Asked in: 2081 Bhadra, 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-b81
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-4

## Question

The analysis of a water sample shows the following results in mg/l: Na$^+$ = 15; K$^+$ = 25; Ca$^{++}$ = 10; Mg$^{++}$ = 18; Cl$^-$ = 35; HCO$_3^-$ = 72; SO$_4^{--}$ = 8; NO$_3^-$ = 15. The concentration of strontium (Sr) is equivalent to a hardness of 2.0 mg/l and carbonate alkalinity in this water is zero. Calculate the total hardness, carbonate hardness and non-carbonate hardness in mg/l as CaCO$_3$.

## Short answer

Multiply each hardness ion concentration by (50/equivalent weight); sum for total hardness. Alkalinity from HCO3- only. Total hardness = 101.02 mg/L, carbonate hardness = 59.00 mg/L, non-carbonate hardness = 42.02 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. Strontium contributes 2.0 mg/l as given. Na$^+$ and K$^+$ do not cause hardness.

#### Total hardness
| Ion | mg/l | Factor | Hardness (mg/l as CaCO$_3$) |
|---|---|---|---|
| Ca$^{2+}$ | 10 | 50/20.04 = 2.495 | 24.95 |
| Mg$^{2+}$ | 18 | 50/12.15 = 4.115 | 74.07 |
| Sr | | given | 2.00 |
| **Total** | | | **101.02** |

#### Alkalinity and carbonate hardness
Carbonate alkalinity is zero, so the alkalinity is due to HCO$_3^-$:

$$
\text{Alkalinity} = 72\times\frac{50}{61.02} = 59.00\ \text{mg/l as CaCO}_3
$$

Alkalinity is less than the total hardness, so CH = alkalinity. NCH $= 101.02-59.00 = 42.02$ mg/l.

**Answer: Total hardness = 101.02 mg/l; carbonate hardness = 59.00 mg/l; non-carbonate hardness = 42.02 mg/l (all as CaCO$_3$).**

## Check yourself

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

1. Which ions do not contribute to hardness?
   A. Na+ and K+
   B. Ca2+ and Mg2+
   C. Sr
   D. Ca2+ only
   Answer: A. Only divalent metallic ions cause hardness. (Key point: Non-hardness ions)

2. Total hardness = Ca (24.95) + Mg (74.07) + Sr (2.0) =
   A. 99.02
   B. 101.02 mg/l
   C. 87.5
   D. 123.4
   Answer: B. Sum of the three. (Key point: Total hardness)

## Related in Water Supply Engineering

- [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
- [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
- [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
- [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