Derive the relationship to find the condition for isotonic solutions.

Explanation

For `1^(st)` solutions ,
Osmotic pressure, ` pi _(1= (n_(1)) /(V_(1)) RT `
Here `n_(1)` moles of non-volatile solute are dissolved in `V_(2)` L of solution . T is temperature of kelvin scale and ` r = 0 . 0 821 L atm K^(-1) mol^(-1)` (a constant)
For `2^(nd)` solution ,
Osmotic pressure, ` pi _(2) = (n_(2))/(V_(2)) RT `
Here `n_(2)` moles of non-volatile solute are dissolved in `V_(2)` L of solution .
For isotonic solutions `pi_(1) = pi_(2)`
`:. (n_(1))/( V_(1)) RT = (n_(2))/(V_(2)) RT `
or ` (n_(1))/( V_(1)) = (n_(2))/(V_(2))`
or `C_(1) = C_(2)`
where `C_(1) and C_(2)` are the concentration of 1st and 2nd solution in mol `L^(-1)`