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Which of the following pairs of ions makes the water hard?
A.${\text{N}}{{\text{a}}^{\text{ + }}}$, ${\text{S}}{{\text{O}}_{\text{4}}}^{{\text{2 + }}}$
B.${\text{C}}{{\text{a}}^{{\text{2 + }}}}$, ${\text{HC}}{{\text{O}}_{\text{3}}}^{\text{ - }}$
C.${\text{C}}{{\text{a}}^{{\text{2 + }}}}$, ${\text{N}}{{\text{O}}_{\text{3}}}$
D.${\text{N}}{{\text{H}}_{\text{4}}}^{\text{ - }}$, Cr

Answer
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Hint: Water contains many minerals present in it which is why we are using it for many purposes. These minerals are present in the form of ions (cations and anions). The ions found in water are Calcium, magnesium, sodium, bicarbonate, sulfate, chloride, nitrate, and small traces of potassium salts. The Hardness of water has some disadvantages as it does not foam with soap, causes dry skin, etc.

Complete step by step answer:
Water that we get through rainfall is soft (only sodium ions and some dissolved carbon dioxide ${\text{C}}{{\text{O}}_{\text{2}}}$ ) but when the water flows through the ground, it absorbs minerals from the ground, limestone, chalk, gypsum, etc., before it reaches us. These substances have Ca and Mg carbonates, bicarbonates, and sulfates. This is the reason for the hardness of the water.
Some of the minerals as mentioned in the above points are needed by the body. So we use it as drinking water.
The calcium and magnesium form multivalent cations in water.
These multivalent cations which have a charge more than +1, are the source of hardness
The water(that we get through rain has dissolved carbon dioxide also) on passing through the ground absorbs Calcium carbonate, Magnesium carbonate from minerals limestone, chalk, dolomite, etc and these react with water to produce ${\text{C}}{{\text{a}}^{{\text{2 + }}}}$ and ${\text{M}}{{\text{g}}^{{\text{2 + }}}}$ ions. These forms bicarbonates which dissolve in water making it hard.
The dissolved bicarbonate minerals produce this temporary hardness of the water.
Let us now check the options, option (A) has ${\text{N}}{{\text{a}}^{\text{ + }}}$ which does not cause hardness.
The option (B) and (C) have got ${\text{C}}{{\text{a}}^{{\text{2 + }}}}$. Let us now look at the other pair.
Option (B) has got ${\text{HC}}{{\text{O}}_{\text{3}}}^{\text{ - }}$ which is soluble in water and causes hardness.
Thus, the correct option is (B).

Note:There are two types of hardness- temporary hardness and permanent hardness. The hardness of water can be calculated as the grams of ${\text{CaC}}{{\text{O}}_{\text{3}}}$ present in ${10^6}$ grams or ${10^6}$ ml of water (parts per million). Here ${10^6}$ grams or ${10^6}$ mL are taken because the density of water is 1. ${\text{Hardness = }}\dfrac{{{\text{Grams of CaC}}{{\text{O}}_{\text{3}}}}}{{{\text{1}}{{\text{0}}^{\text{6}}}{\text{ mL of water}}}}$.