An exhausted zeolite bed was revived by 250 L of NaCl solution containing `50gL^(-1)` of NaCl solution. How many litres of hard water of hardness 250 ppm can be softened on the zeolite bed?

Explanation

Let `V_(1)` be the volume of hard water and `V_(2)` be the volume of `NaCl` solution containing `x g L^(-1)` used for the regeneration of the zeolite. Then hardness (H) is given by:
Hardness`(H)=(50xx x xxV_(2)10^(3))/(58.3xxV_(1))` `{:(Ew of CaCO_(3)=50),(Mw of NaCl=85.5):}`
In the prioblem `x=50gL^(-1),V_(2)=250L, H=250 ppm`,
`V_(1)=?`
So, `250=(50xx50xx250xx10^(3))/(58.5xxV_(1))`
`thereforeV_(1)=42735L`