Q53 / 180 · KCET 2010 · Chemistry

The empirical formula of a non-electrolyte is $\mathrm{CH}_{2} \mathrm{O}$. A solution containing $6 \mathrm{~g}$ of the compound exerts the same osmotic pressure as that of $0.05 \mathrm{M}$ glucose solution at the same temperature. The molecular formula of the compound is

  • A
    $\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}$
  • B
    $\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{3}$
  • C
    $\mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{5}$
  • Correct answer
    D
    $\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{4}$

Solution

Solutions having same osmotic pressure, at a given temperature, have same concentration. Concentration of compound $=$ concentration of glucose $$ \begin{aligned} &\frac{6}{\mathrm{M} \times 1}=0.05 \\ &\mathrm{M}=\frac{6}{0.05}=120 \\ &\text { Empirical formula mass }\left(\mathrm{CH}_{2} \mathrm{O}\right)=12+2+16 \\ &\mathrm{n}=\frac{\text { molecular mass }}{\text { empirical formula mass }} \\ &=\frac{120}{30}=4 \end{aligned} $$ Hence, molecular formula $=\left(\mathrm{CH}_{2} \mathrm{O}\right)_{4}=\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{4}$

Hence, the correct answer is option: 'D'.

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