Question

$1$ kg of a sample of water contains $222$ mg of $CaC{l}_2$ and $219$ mg of $Mg(HC{O}_3{)}_2$. Its permanent hardness and temporary hardness in ppm are respectively:

• A. $200,200$
• B. $200,150$
• C. $200,300$
• D. $150,220$

Answer 1

The correct option is B $200,150$

It is given that ${10}^3$ g of a sample of water contains $0.222$ g of $Ca{Cl}_2$.

${10}^6$ g of a sample of water contains $\frac{0.222}{{10}^3}\times {10}^6=222$ g of $Ca{Cl}_2$

$111$ g of $Ca{Cl}_2$ has hardness $=100$ ppm

$222$ g of $Ca{Cl}_2$ has hardness $=\frac{100}{111}\times 222=200$ ppm (permanent hardness)

It is given that ${10}^3$ g of sample of water contains $0.219$ g of $Mg(H{CO}_3{)}_2$.

${10}^6$ g of sample of water contains $\frac{0.219}{{10}^3}\times {10}^6=219$ g of $Mg(H{CO}_3{)}_2$

$146$ g of $Mg(H{CO}_3{)}_2$ has hardness $=100$ ppm

$219$ g of $Mg(H{CO}_3{)}_2$ has hardness = $\frac{100}{146}\times 219=150$ ppm (temporary hardness)

Hence, the permanent hardness and temporary hardness are $200$ ppm and $150$ ppm respectively.