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Question: Given, \({\text{1 L}}\) of pond water contains \({\text{20 mg}}\) of \(C{a^{ + 2}}\) and \({\text{12...

Given, 1 L{\text{1 L}} of pond water contains 20 mg{\text{20 mg}} of Ca+2C{a^{ + 2}} and 12 mg{\text{12 mg}} of Mg+2M{g^{ + 2}} ions. What is the volume of a 2N Na2CO3{\text{2N }}N{a_2}C{O_3} solution required to soften 5000 L{\text{5000 L}} of pond water?
A) 500 L{\text{500 L}}
B) 50 L{\text{50 L}}
C) 5 L{\text{5 L}}
D) None of these

Explanation

Solution

The calcium and magnesium ion concentration is given which can be related to the volume of sodium carbonate solution. One can calculate the volume required of sodium carbonate with respect to one liter by using milliequivalent formula relation and then convert that value for five thousand liters.

Complete step by step answer:

  1. First of all we will see what data has been given in the question. The calcium ion and magnesium ion have been given which can make the compounds calcium carbonate and magnesium carbonate respectively.
  2. Now that we need to find out the volume required of sodium carbonate to soften the five thousand liter amount of pond water we can relate these two in the concentration terms as follows,
    Milli equivalents of calcium ion Ca+2C{a^{ + 2}}
    + Milliequivalents of magnesium ions Mg+2M{g^{ + 2}} = Milli equivalents of sodium carbonate Na2CO3N{a_2}C{O_3}
  3. Now we have 20 mg{\text{20 mg}} of calcium ion which has a mass of 40{\text{40}} and has two charges on the atom and 12 mg{\text{12 mg}} of Mg+2M{g^{ + 2}} ions which has a mass of 24{\text{24}} we can write the equation as,
    2040×2+1224×2=2×V\dfrac{{20}}{{40}} \times 2 + \dfrac{{12}}{{24}} \times 2 = 2 \times V
    Where V is the volume required of sodium carbonate.
    Now let's calculate this value,
    1+1=2×V1 + 1 = 2 \times V
    By taking the V value on one side we get,
    V=22=1mLV = \dfrac{2}{2} = 1mL
  4. Therefore, we need 1 mL{\text{1 mL}} of sodium carbonate solution to soften the one liter of pond water. Hence, for the softening of 5000 L{\text{5000 L}} pond water, we need,
    Sodium carbonate needed =5000×0.0011 = \dfrac{{5000 \times 0.001}}{1}
    Sodium carbonate needed =5 L = 5{\text{ L}}
    Therefore, the volume of a 2N Na2CO3{\text{2N }}N{a_2}C{O_3} solution required to soften 5000 L{\text{5000 L}} pond water is 5 L{\text{5 L}} which shows option C as the correct choice.

Note: Sodium carbonate is an inorganic compound that is white and water-soluble salt that gives an alkaline solution when dissolved in water. Sodium carbonate is commonly known as the washing soda and is generally used for cleaning products and in the production of glass.