Question

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?

Answer 1

`"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?