100 mL of a water sample contains 0.81 g of calcium bicarbonate and 0.73 g of magnesium bicarbonate. The hardness of this water sample expressed in terms of equivalents of $C a C O_{3}$ is (molar mass of calcium bicarbonate is $162 g m o l^{- 1}$ and magnesium bicarbonate is $146 g m o l^{- 1}$ )

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5,000 ppm

1,000 ppm

100 ppm

10,000 ppm

answer is D.

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Detailed Solution

$n_{e q} (C a C O_{3}) = n_{e q} [C a {(H C O_{3})}_{2}] + n_{e q} [m g {(H C O_{3})}_{2}] \frac{W}{100} \times 2 = \frac{W_{1}}{162} \times 2 + \frac{W_{2}}{146} \times 2$
Hardness of water = $\frac{W}{100} \times 10^{6}$

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