Question

A $10kg$ of hard water sample contains $200{\text{millimoles}}$ of $MgS{O_4}$. Its concentration in $ppm$ is:
A.$20$
B.$240$
C.$320$
D.$400$

Answer 1

Molar Concentration: It is defined as the amount of substance per unit volume of solution.
Ppm (parts per million): It is also expressed in milligrams per litre. It is defined as mass of substance per unit volume of water.

Complete step by step answer:
Solute: The compound which is mixed in a given substance, is known as solute.
Solvent: The compound which is given and in which solute is mixed, is known as solvent.
Here in the question we are given a $10kg$ of hard water sample containing $200{\text{millimoles}}$ of $MgS{O_4}$. As the amount of magnesium sulphate is given in millimoles so its amount in moles will be $200 \times {10^{ - 3}}$. Now moles is defined as the mass of substance divided by its molar mass. Here the substance is magnesium sulphate whose molar mass is $24 + 32 + 4 \times 16 = 120$. So the mass of substance will be
$\Rightarrow$ $200 \times {10^{ - 3}} = \dfrac{{{\text{mass of substance}}}}{{120}}$
So, mass of substance$= 24grams$.
As ppm is defined as mass per unit volume. Here mass of the substance is $24grams$. And we have to find concentration in $10litres$ so ppm will be $24 \times 10 = 240$.

So, option B is correct.

Additional information:
Other molar concentration measuring terms are as:
Molarity: It is defined as the number of moles in the given volume of the solution. The unit of the molarity is as: $mol/litre$.
Molality: It is defined as the number of moles of solute per kilogram of solvent. The unit of molality is: $mol/kg$.
Normality: It is defined as the gram equivalent weight per unit litre of solution. The unit of normality is: $eq/litre$.
Equivalent mass: It is defined as the mass of one equivalent.

Note:
Hard water is defined as the water which contains magnesium and calcium salts of chlorides and sulphates. Hard water is not suitable for washing purposes because with soap it forms foam which is not soluble.