Question

One litre of a sample of hard water (\[{\text{d}} = 1\;{\text{g/mL}}\]) contains \[136\;{\text{mg}}\] of \[CaS{O_4}\] ​ and \[190\;{\text{mg}}\] of \[MgC{l_2}\] ​. What is the total hardness of water in terms of \[CaC{O_3}\] ​?
A.$100{\text{ppm}}$
B.$200{\text{ppm}}$
C.$300{\text{ppm}}$
D.None of the above

Answer 1

Hint: To answer this question you should recall the concept of hardness of water. Hardness is defined as the presence of salts in water which lead to difficulty in forming lather. You are required to know the molar masses of the minerals \[CaS{O_4}\], \[CaC{O_3}\], \[MgC{l_2}\].

Complete step by step answer:
-Hard water is the term given to the sample of water that has a very high mineral content (the term is the opposite of ‘soft water’). As water percolates into deposits of calcareous, gypsum or chalk that are primarily composed of carbonates of magnesium or calcium, bicarbonates and sulfates, hard water is formed.
-The hardness is a measure of the concentration of the multivalent cations present in that given sample of water. These multivalent cations are usually the metal complexes that have positive typically bearing a positive charge of 2. Most commonly found multivalent cations are like \[C{a^{2 + }}\] and \[M{g^{2 + }}\].
-We know that for calculation of hardness, according to the molar masses of the compounds:
\[136\;{\text{mg}}\] of \[CaS{O_4}\]= \[100\;{\text{mg}}\] of \[CaC{O_3}\]
\[190\;{\text{mg}}\] of \[MgC{l_2}\]​= \[2 \times 100\;{\text{mg}}\] of \[CaC{O_3}\].
So, as 1 litre of water contain \[100 + \left( {2 \times 100} \right) = 300\;{\text{mg}}\] of \[CaC{O_3}\]
\[\therefore {10^6}\;{\text{g water contains }}\dfrac{{300 \times {{10}^{ - 3}}}}{{1000}}\; \times {10^6} = 300\;{\text{ppm}}\].
Hence, the total hardness of water in terms of \[CaC{O_3}\]​ is $300{\text{ppm}}$.

Hence, the correct option is C.

Note:
Drinking hard water can have certain benefits to human health. However, in case of industrial and laboratory uses hard water is highly undesirable and can pose several major problems. For example, water hardness is controlled in industries in order to prevent costly breakdowns in cooling towers, boilers, and other water handling equipment.