# 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?

Jan 5, 2017

$\text{Molecular mass of polystyrene}$ $\cong$ $7.4 \times {10}^{2} \cdot g \cdot m o {l}^{-} 1$

#### Explanation:

${\Pi}_{\text{the osmotic pressure}}$ $=$ $c R T$

And thus $\frac{\Pi}{R T} = c$

$c = \frac{1.21 \cdot \cancel{k P a}}{1.01325 \cdot \cancel{k P a \cdot a t {m}^{-} 1}} \times \frac{1}{0.0821 \cdot L \cdot \cancel{a t m} \cdot \cancel{{K}^{-} 1} \cdot m o {l}^{-} 1 \times 523 \cdot \cancel{K}} = 0.0278 \cdot m o l \cdot {L}^{-} 1$.

Note the dimensional consistency. I changed the pressure into units of atmospheres, because this gives us a better idea of dimensionality. Of course, $1 \cdot a t m \equiv 101.3 \cdot k P a$; 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,
$\frac{2.05 \cdot g}{\text{Molecular mass of polystyrene}} \times \frac{1}{0.100 \cdot L} = 0.0278 \cdot m o l \cdot {L}^{-} 1$
So, finally, $\text{Molecular mass of polystyrene} = \frac{2.05 \cdot g}{0.0278 \cdot m o l \cdot {L}^{-} 1} \times \frac{1}{0.100 \cdot L} = 737 \cdot g \cdot m o {l}^{-} 1$.

How many formula units of $\text{styrene, } {C}_{7} {H}_{8} ,$ compose this polymer?