A #5*g# mass of polystyrene exerts an osmotic pressure of #1.21*kPa# at a temperature of #523*K#. What is the molecular mass of the polystyrene?

1 Answer
Jan 5, 2017

Answer:

#"Molecular mass of polystyrene"# #~=# #7.4xx10^2*g*mol^-1#

Explanation:

#Pi_"the osmotic pressure"# #=# #cRT#

And thus #Pi/(RT)=c#

#c=(1.21*cancel(kPa))/(1.01325*cancel(kPa*atm^-1))xx1/(0.0821*L*cancel(atm)*cancel(K^-1)*mol^-1xx523*cancelK)=0.0278*mol*L^-1#.

Note the dimensional consistency. I changed the pressure into units of atmospheres, because this gives us a better idea of dimensionality. Of course, #1*atm-=101.3*kPa#; such information should be given as supplementary material in any examination. Of course, you have to know how to use it and manipulate it.

And thus,
#(2.05*g)/("Molecular mass of polystyrene")xx1/(0.100*L)=0.0278*mol*L^-1#
So, finally, #"Molecular mass of polystyrene"=(2.05*g)/(0.0278*mol*L^-1)xx1/(0.100*L)=737*g*mol^-1#.

How many formula units of #"styrene, "C_7H_8,# compose this polymer?