Question

Washing soda ( $N{a_2}C{O_3}.10{H_2}O$ ) is widely used in softening of hard water. If 1L of hard water requires 0.0286g of washing soda, the hardness of $CaC{O_3}$ in ppm is:
(A) 10
(B) 5
(C) 8
(D) 6

Answer 1

Hint:We will note the data provided in the question. We will write the reaction of the calcium sulphate with the sodium carbonate. Then we will calculate the mass of each entity. Then we will calculate the mill equivalents of washing soda. From it we can calculate the millimoles of the $CaC{O_3}$ in $1l$ . Once we get the moles we calculate the mass of $CaC{O_3}$ . From there we will get the ppm value.

Complete step-by-step solution:Step1. We are provided with the washing soda and $1l$ of hard water. The$0.0286g$ of washing soda is needed to soften the $1l$ of hard water.

Step2. The hard water contains the sulphates of calcium. The washing soda or we can say that the sodium carbonate reacts with the calcium sulphate and forms calcium carbonate and removes the hardness of water. The reaction is the double displacement reaction. The reaction is given below
$CaS{O_4} + N{a_2}C{O_3} \to CaC{O_3} + N{a_2}S{O_4}$

Step3. The molecular mass of washing soda is $286g$ and of $CaC{O_3}$ is $100g$
We will find the milli equivalents of washing soda.
milli equivalents = $\dfrac{{0.0286}}{{286}} \times {10^3} = 0.1$

Step4. Now from reaction the one mole of washing soda will form a mole of sodium carbonate. The milli moles of $CaC{O_3}$ is $0.1$ in $1l$ of water.

Step5. Now calculate the mass of $CaC{O_3}$ in $1l$ of water.
Mass = $0.1 \times \dfrac{{100}}{{{{10}^3}}} = 0.01g$

Step6. Ppm stands for parts per million.
Formula of ppm is $mass \times \dfrac{{{{10}^6}}}{{volume(ml)}}$
Ppm= $\dfrac{{0.01 \times {{10}^6}}}{{{{10}^3}}} = 10$
Hence there is 10 parts of $CaC{O_3}$ per million

Hence the option(A) is the correct option.

Note:Washing soda is transparent crystalline solid. It is only a few metal carbonates that are soluble in water. It is basic in nature. It is used to remove dirt, oil from clothes. Many types of detergent, glass and soap are manufactured using it.