Question

$100kg$ hard water contains $5g$ $MgS{O_4}$ . The hardness of water is:

Answer 1

Hint: Hardness of water is defined as the presence of the multivalent cations present in the water when the water seeps through limestone, gypsum or chalk which contains carbonates, sulfates and bicarbonates of calcium and magnesium. The hardness of water is estimated by the estimating the concentration of calcium and magnesium ions in water.

Complete step by step answer: The hardness of water is determined by the determination of the concentration of the bivalent cations that cause the hardness. As we can see, we have been provided only with magnesium ions in water, thus, we need to assume that only magnesium ions are present in the water and there are no traces of the presence of calcium ions.
$100kg$ of hard water contains = $5g$ $MgS{O_4}$
We need to find out the molarity of the solution. Thus, the mathematical equation of molarity is:
$M = \dfrac{n}{V}$
Where, $n = $ number of moles$ = \dfrac{w}{{{M_w}}}$
$w = $ Given weight $ = 5g$
${M_w} = $Molecular weight$ = 120g$
$V = $Volume of solution$ = 100L$
Thus, substituting the values, we have:
$M = \dfrac{n}{V} = \dfrac{{\dfrac{5}{{120}}}}{{100}} = 0.416mM$
Thus, the hardness of water is found to be $0.416mM$ or $416ppm$.

Note: The hardness of water can be differentiated into two types:
-Permanent hardness: It is usually caused by the presence of calcium sulfate/calcium chloride and/or magnesium sulfate/magnesium chloride in the water, which do not undergo precipitation when the temperature is increased. Ions that cause permanent hardness of water can be removed by using a water softener, or ion exchange column.
-Temporary hardness: Temporary hardness is a type of water hardness caused due to the presence of dissolved bicarbonate ions (calcium bicarbonate and magnesium bicarbonate). When dissolved, these type of minerals yield calcium and magnesium cations ($C{a^{2 + }},M{g^{2 + }}$ ) and carbonate and bicarbonate anions ($CO_3^{2 - }$ and $HCO_3^ - $ ).