Question

One litre of a sample of hard water contains $55.5$ mg of $CaC{l}_2$ and $4.75$ mg of $MgC{l}_2$. The total hardness in terms of ppm of $CaC{O}_3$ is :

• A. $5$ ppm
• B. $10$ ppm
• C. $20$ ppm
• D. none of the above

Answer 1

The correct option is B $10$ ppm

$55.5$ g $CaC{l}_2\equiv 50$ g $CaC{O}_3$

$55.5$ mg $CaC{l}_2\equiv 50\times {10}^{-3}$ g $CaC{O}_3$

$47.5$ g $MgC{l}_2\equiv 50$ g $CaC{O}_3$

$47.5$ mg $MgC{l}_2\equiv 50\times {10}^{-3}$ g $CaC{O}_3$

Total $CaC{O}_3=(50+50)\times {10}^{-3}={10}^{-2}$ g/L

Hardness in terms of ppm $=\frac{{10}^{-2}}{1000}\times {10}^6$ mL $=10$ ppm