Question

A solution contain $8g$ of a carbohydrate in $100g$ of water has a density $1.025g/mL$ and an osmotic pressure of $5atm$ at ${27}^{\circ }C.$
What is the molar mass of the carbohydrate?

• A. $87gmo{l}^{-1}$
• B. $374gmo{l}^{-1}$
• C. $3740gmo{l}^{-1}$
• D. $870gmo{l}^{-1}$

Answer 1

The correct option is B $374gmo{l}^{-1}$

$8g$ of carbohydrate is present in $100g$ of water in solution
or $108g$ solution contains $8g$ of carbohydrate;

$V_{solution}=\frac{\text{Mass}}{\text{Density}}=\frac{108}{1.025}\times {10}^{-3}L$

$\pi =\frac{n}{V}\times R\times T$
$\pi \text{is the osmotic pressure}n=\text{No of moles}V\text{is volume in L}R\text{is ideal gas constant}T\text{is temperature in K}$
$\Rightarrow \frac{8}{M}\times \frac{1.025}{108}\times 1000\times 0.0821\times 300=5$
$M\approx 374g/mol$