An artificial cell is made by encapsulating $0.2 \, \text{M}$ glucose solution within a semipermeable membrane. The osmotic pressure developed when the artificial cell is placed within a $0.05 \, \text{M}$ solution of NaCl at 300 K is ______ $ \times 10^{-1} \, \text{bar} $. (Nearest Integer)
Given: $R = 0.083 \, \text{L bar mol}^{-1} \text{K}^{-1}$
Assume complete dissociation of NaCl.

Question

$W$ g of a non-volatile electrolyte solid solute of molar mass $M\,\text{g mol}^{-1}$ when dissolved in $100\,\text{mL}$ water decreases vapour pressure of water from $640\,\text{mm Hg}$ to $600\,\text{mm Hg}$. If aqueous solution of the electrolyte boils at $375\,\text{K}$ and $K_b$ for water is $0.52\,\text{K kg mol}^{-1}$, then the mole fraction of the electrolyte $(x_2)$ in the solution can be expressed as ___.
(Given: density of water $=1\,\text{g mL}^{-1}$, boiling point of water $=373\,\text{K}$)

Answer 1

For the dissociation of NaCl:
\[ \text{NaCl} \rightarrow \text{Na}^+ + \text{Cl}^- \]
The initial concentration of NaCl is 0.05 M.
Due to dissociation, the effective concentration ($C_1$) becomes 0.05 M (from Na$^+$) + 0.05 M (from Cl$^-$) = 0.1 M.
The concentration of glucose ($C_2$) is 0.2 M.
The osmotic pressure is calculated using the formula:
\[ \pi = (C_2 - C_1)RT \]
Explanation 87
Substituting the values:
\[ \pi = (0.2 \, \text{M} - 0.1 \, \text{M}) \times 0.083 \, \text{L bar/mol K} \times 300 \, \text{K} = 24.9 \times 10^{-1} \, \text{bar} \]
The nearest integer value for the osmotic pressure is 25 bar.

Correct Answer: 25

Solution and Explanation

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