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Question: Ion exchange resin \(R{H_2}\) can replace \(C{a^{2 + }}\) in hard water as \(R{H_2} + C{a^{2 + }} ...

Ion exchange resin RH2R{H_2} can replace Ca2+C{a^{2 + }} in hard water as
RH2+Ca2+→RCa+2H+R{H_2} + C{a^{2 + }} \to RCa + 2{H^ + }
One litre of hard water after passing through RH2R{H_2} has pH=2pH = 2. Hence, hardness is ppm of Ca2+C{a^{2 + }}is:
A.200200
B.100100
C.5050
D.125125

Explanation

Solution

An ion-exchange resin or ion-exchange polymer is a resin or polymer that acts as medium for ion exchange. It is usually white or yellowish, an insoluble matrix. It is fabricated from organic polymer substrate.

Complete step-by-step answer: The question above, we look into as,
According to the given reaction,
RH2+Ca2+→RCa+2H+R{H_2} + C{a^{2 + }} \to RCa + 2{H^ + }
Each of the mole of Ca2+C{a^{2 + }} ion is replaced by two moles of H+{H^ + }
Now,
11 Mole H+{H^ + } is replaced as →12=0⋅5 \to \dfrac{1}{2} = 0 \cdot 5mole of Ca2+C{a^{2 + }}
Now, it’s given as,
pH=2pH = 2
H+=10−2=0⋅01{H^ + } = {10^{ - 2}} = 0 \cdot 01
Here, it shows the replacement of H+{H^ + }
0⋅010 \cdot 01 Mole H+{H^ + } replaced =0⋅01×0⋅5=0⋅005 = 0 \cdot 01 \times 0 \cdot 5 = 0 \cdot 005moles of Ca2+C{a^{2 + }}
Here, it shows the replacement of
Ca2+C{a^{2 + }} Ca2+C{a^{2 + }}
$$$$Mass Ca2+C{a^{2 + }} replaced =0⋅005×40=0⋅2g=200mg = 0 \cdot 005 \times 40 = 0 \cdot 2g = 200mg
Concentration or hardness in ppm is calculated as,
=200mg/L =200ppm  = 200mg/L \\\ = 200ppm \\\

Hence, the correct option is (A).

The steps above explain the concept asked in the question given. The only thing that has to be focused here is the replacing of H+{H^ + } and how Ca2+C{a^{2 + }} is being replaced.

Additional information:
Now hard water is referred to as the water which has an excess amount of calcium and magnesium ions. The hard water can be easily detected by the amount of lather generated in it when it is being mixed with soap. Hard water produces a little amount of lather when it is mixed with soap. On the other hand soft water generates a lot of lather when it is being mixed with soap or detergent. When the calcium in hard water reacts with the soap or detergent it normally forms soap scum, and therefore more detergent is being used in the cleaning of the clothes.

Note: But the hard water not only does have disadvantages though it has an advantage as it has ample amounts of minerals such as calcium and magnesium. People with a deficiency of calcium or magnesium in their body can consume hard water to compensate for their deficiency.