Question

The $ {\text{R}}{{\text{H}}_{\text{2}}} $ (ion exchange resin) can replace $ {\text{C}}{{\text{a}}^{{\text{2 + }}}} $ ions in hard water as:
 $ {\text{R}}{{\text{H}}_{\text{2}}} + {\text{C}}{{\text{a}}^{{\text{2 + }}}} \to {\text{RCa}} + {\text{2}}{{\text{H}}^{\text{ + }}} $
If $ {\text{1L}} $ of hard water after passing through $ {\text{R}}{{\text{H}}_{\text{2}}} $ has $ {\text{pH = 3}} $ , then hardness in parts per million of $ {\text{C}}{{\text{a}}^{{\text{2 + }}}} $ is:
(A) 80
(B) 10
(C) 40
(D) 100

Answer 1

Hint: We know that ion exchange resins are used to remove permanent hardness from water. Water is said to be hard when it consists of the carbonates or sulphates of either calcium or magnesium. To answer this question, you need to recall the formula for the pH of a solution.

Formula used: $ {\text{pH}} = \log \left[ {{{\text{H}}^ + }} \right] $
Where, $ \left[ {{{\text{H}}^ + }} \right] $ denotes the concentration of hydrogen ions in the given solution.

Complete step by step solution
After one liter of hard water is passed through the ion exchange resin we are given the pH of the solution as 3. In the ion exchange resin, the calcium ions present in the hard water are replaced by the hydrogen ions and thus the hardness is removed. The reaction that occurs in the ion- exchange resin is given to us as:
 $ {\text{R}}{{\text{H}}_{\text{2}}} + {\text{C}}{{\text{a}}^{{\text{2 + }}}} \to {\text{RCa}} + {\text{2}}{{\text{H}}^{\text{ + }}} $
From the reaction, we can see that one calcium ion replaces two hydrogen ions in the resin. Or in other words we can say, that the concentration of hydrogen ions present in the solution after the process will be half that of the calcium ions present initially in the solution.
So, the concentration of hydrogen ions can be calculate using the pH of the solution as:
  $ {\text{pH}} = \log \left[ {{{\text{H}}^ + }} \right] $
 $ \Rightarrow \left[ {{{\text{H}}^ + }} \right] = {10^{ - {\text{pH}}}} = {10^{ - 3}}{\text{M}} $
As discussed above, the concentration of calcium ions in the water will be $ = 2 \times {10^{ - 3}}{\text{M}} $
So, the ppm of calcium ions $ = \dfrac{{2 \times 40 \times {{10}^{ - 3}}}}{{1000}} \times {10^6} = 80{\text{ ppm}} $
The correct answer is A..

Note
The pH of a solution is known as the power of Hydrogen and it tells the nature of a solution, whether acidic or basic, on the basis of the concentration of hydrogen ions in the solution.