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

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.