Question

Benzoic acid (molecular weight $=122$ g mol${}^{-1}$) associates to form dimer when dissolved in benzene and the osmotic pressure of a solution of $5$ g of benzoic acid in $100$ ml benzene is $5.73$ atm at ${10}^{o}C$. What is the percentage association of benzoic acid?

• A. $8\%$
• B. $80\%$
• C. $40\%$
• D. $20\%$

Answer 1

Answer: (B)

$80\%$

The formula for osmotic pressure is given below:

$\pi =i\times CRT$,

where $\pi$ is the osmotic pressure, $i$ is the van't Hoff factor, $C$ is the concentration, $R$ is the molar gas constant and $T$ is the temperature.

Given that,

$\pi =5.73$ atm and $5$ g of benzoic acid at $283$ K.

$5.73=i\times \frac{\frac{5}{122}}{\frac{100}{1000}}\times 0.082\times 283$ $⟹5.73=i\times 9.511\Rightarrow i\approx 0.6$

Now, $i=1-\frac{\alpha }{2}=0.6\Rightarrow \alpha =0.8$

Hence, the percentage association of benzoic acid is $80\%$.