Let the plasma cell wall of shark is a semipermeable membrane. When these cells were kept in a series of `NaCl` solution of different concentration at `25^(@)C` these cells remain intact in `0.7%` `((w)/(w))` `NaCl` solution, shrank in more concetrated solution and swelled in dilute solution. What is the osmotic pressure of the cell cytoplasm at `25^(@)C`? given `K_(f)` of water `=1.86kgmol^(-1)K` and water freezes from the `0.7%((w)/(w))` salt solution at `-0.418^(@)C`. Assume solution is dilute in each case. Give your answer to nearest integer. `(R=0.0atm(L)/(molK))`

Answer

5

Explanation

In `0.7%` solution no osmosis was there. Here the exerted extra pressure is osmotic pressure
`NaClhArrNa^(+)+Cl^(-)`
Have van't Hoff factor `i=1+(2-1)alpha=(1+alpha)`
`DeltaT_(f)=(K_(f)W_(1)1000)/(m_(1)W_(2))(1+alpha)`
or `(1+alpha)=`
`(DeltaT_(f)M_(1)W_(1)1000)=(0.418xx58.5xxW_(2))/(1.86xx1000xxW_(1))`
as it is `0.7%` solution of NaCl`because(W_(2))/(W_(1))=(99.3)/(0.7)`
`because(1+alpha)=1.86`
Assuming dilute solution `100gm` `H_(2)O=100mLH_(2)O`
`becausepiV="in" RT` or `pi=`
`((1+alpha)xxnRT)/(V)=((1+alpha)W_(1)RT)/(M_(1)V)`
or `pi=(1.86xx0.7xx0.08xx298)/(58.5xx0.1)=5.30atm`