Question

Ion exchange resin $R{H_2}$ can replace $C{a^{2 + }}$ in hard water as
$R{H_2} + C{a^{2 + }} \to RCa + 2{H^ + }$
One litre of hard water after passing through $R{H_2}$ has $pH = 2$. Hence, hardness is ppm of $C{a^{2 + }}$is:
A.$200$
B.$100$
C.$50$
D.$125$

Answer 1

Hint: 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,
$R{H_2} + C{a^{2 + }} \to RCa + 2{H^ + }$
Each of the mole of $C{a^{2 + }}$ ion is replaced by two moles of ${H^ + }$
Now,
$1$ Mole ${H^ + }$ is replaced as $ \to \dfrac{1}{2} = 0 \cdot 5$mole of $C{a^{2 + }}$
Now, it’s given as,
$pH = 2$
${H^ + } = {10^{ - 2}} = 0 \cdot 01$
Here, it shows the replacement of ${H^ + }$
$0 \cdot 01$ Mole ${H^ + }$ replaced $ = 0 \cdot 01 \times 0 \cdot 5 = 0 \cdot 005$moles of $C{a^{2 + }}$
Here, it shows the replacement of
$C{a^{2 + }}$$C{a^{2 + }}$
\[\]Mass $C{a^{2 + }}$ replaced $ = 0 \cdot 005 \times 40 = 0 \cdot 2g = 200mg$
Concentration or hardness in ppm is calculated as,
$
  = 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 ${H^ + }$ and how $C{a^{2 + }}$ 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.