---
title: "Ca and Mg concentration, NCH, alkalinity: TH 400 ppm"
subject: "Water Supply Engineering"
chapter: 4
key: "semester_5/water_supply_engineering:hardness-bk79"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/hardness-bk79
site: BCT Engineering
---

# Ca and Mg concentration, NCH, alkalinity: TH 400 ppm

Water Supply Engineering · Chapter 4: Quality of Water

- Asked in: 2079 Baisakh, 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-bk79
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-4

## Question

Total hardness value obtained from the complete analysis of a water sample is found to be 400 ppm. The analysis further showed that the concentrations of the calcium and magnesium cat-ions causing hardness found to be equal. If value of carbonate hardness is 150 ppm, calculate (i) the concentration of calcium and magnesium, (ii) the value of total alkalinity in ppm and the value of NCH.

## Short answer

With Ca = Mg = x, 400 = (2.5 + 4.1)x, so Ca = Mg = 60.61 ppm. Total alkalinity equals carbonate hardness, 150 ppm as CaCO3. Non-carbonate hardness is 400 minus 150 = 250 ppm.

## Answer

Hardness is expressed in CaCO$_3$ equivalent. Using the standard factors, $TH = 2.5\,Ca + 4.1\,Mg$ (Ca and Mg in ppm). Here TH = 400 ppm, CH = 150 ppm.

#### (i) Concentration of calcium and magnesium
Let $Ca = Mg = x$.

$$
\begin{aligned} 400 &= 2.5x + 4.1x = 6.6x \\ x &= \frac{400}{6.6} = 60.61\ \text{ppm} \end{aligned}
$$

Ca = Mg = 60.61 ppm (as the ions). In CaCO$_3$ terms: Ca hardness = $2.5 \times 60.61 = 151.5$ ppm and Mg hardness = $4.1 \times 60.61 = 248.5$ ppm.

#### (ii) Total alkalinity and NCH
Carbonate hardness (150) is less than total hardness (400), so the alkalinity is fully used up in forming carbonate hardness:

$$
\text{Total alkalinity} = CH = 150\ \text{ppm as CaCO}_3
$$

$$
NCH = TH - CH = 400 - 150 = 250\ \text{ppm}
$$

**Answer: Ca = Mg = 60.61 ppm; total alkalinity = 150 ppm; NCH = 250 ppm.**

## Check yourself

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

1. Which relation links TH with Ca and Mg in ppm?
   A. TH = Ca + Mg
   B. TH = 2.5 Ca x 4.1 Mg
   C. TH = 4.1 Ca + 2.5 Mg
   D. TH = 2.5 Ca + 4.1 Mg
   Answer: D. The standard factors are 2.5 for Ca and 4.1 for Mg, giving hardness as CaCO3. (Key point: Hardness factors)

2. With Ca = Mg = x and TH = 400 ppm, what is x?
   A. 80 ppm
   B. 160 ppm
   C. 200 ppm
   D. 60.61 ppm
   Answer: D. 400 = 6.6x, so x = 60.61 ppm. (Key point: Equal Ca and Mg)

3. Why is total alkalinity 150 ppm?
   A. Alkalinity equals NCH
   B. CH is less than TH, so alkalinity is used up as CH
   C. Alkalinity equals TH
   D. Alkalinity is TH - CH
   Answer: B. When CH < TH, all alkalinity forms carbonate hardness, so alkalinity = CH. (Key point: Alkalinity from CH)

4. What is NCH?
   A. 550 ppm
   B. 250 ppm
   C. 150 ppm
   D. 400 ppm
   Answer: B. NCH = TH - CH = 400 - 150 = 250 ppm. (Key point: NCH)

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