The hardness of a water sample containing $10^{-3} \mathrm{M} \mathrm{MgSO}_{4}$ expressed as $\mathrm{CaCO}_{3}$ equivalents (in ppm) is ______. (molar mass of $\mathrm{MgSO}_{4}$ is $120.38 \mathrm{~g} / \mathrm{mol}$)

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Hydrogen

The hardness of a water sample containing

1 0^{- 3} M MgSO_{4}

expressed as

CaCO_{3}

equivalents (in ppm) is ______.
(molar mass of

MgSO_{4}

120.38 g / mol

)

Answer: 100

Each mole of

MgS O_{4}

counts as one mole of

CaC O_{3}

for hardness. A

1 0^{- 3}

M solution holds

1 0^{- 3}

mol of

MgS O_{4}

per litre, equivalent to

1 0^{- 3} \times 100 = 0.1

g of

CaC O_{3}

per litre of water. Since a litre of water weighs about

1000

g, the hardness in parts per million is

\frac{0.1}{1000} \times 1 0^{6} = 100

ppm.

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Integer answer