At $27\,^oC$,the osmotic pressure of a solution containing $36\,g$ of glucose per liter is $4.92\,atm$. If the osmotic pressure of the solution is adjusted to $1.5\,atm$ at the same temperature,what will be its concentration?

  • A
    $0.045$
  • B
    $0.061$
  • C
    $1.236$
  • D
    $0.998$

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Solution $A$ is prepared by dissolving $1 \text{ g}$ of a protein (molar mass = $50000 \text{ g mol}^{-1}$) in $0.5 \text{ L}$ of water at $300 \text{ K}$. Its osmotic pressure is $x \text{ bar}$. Solution $B$ is made by dissolving $2 \text{ g}$ of the same protein in $1 \text{ L}$ of water at $300 \text{ K}$. The osmotic pressure of solution $B$ is $y \text{ bar}$. The entire solution of $A$ is mixed with the entire solution of $B$ at the same temperature. The osmotic pressure of the resultant solution is $z \text{ bar}$. $x, y$ and $z$ respectively are: $(R = 0.083 \text{ L bar mol}^{-1} \text{ K}^{-1})$

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