The osmotic pressure of a solution of $N a C l i s 0.10 a t m$ and that of a glucose solution is $0.20 a t m$ . The osmotic pressure of a solution formed by mixing $1 L$ of the sodium chloride solution with $2 L$ of the glucose solution is $x \times 10^{- 3} a t m . x$ is __________. (nearest integer)

167.00

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167.0

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167

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Solution

$F o r N a C l : π_{1} = i C_{1} R T \Rightarrow C_{1} = \frac{0.10}{2 R T} (i = 2)$

$For Glucose : π_{2} = C_{2} R T \Rightarrow C_{2} = \frac{0.20}{R T} (i = 1)$

When $1 L$ of $N a C l$ solution and $2 L$ glucose solution are mixed.

$∴ C_{1}^{'} = \frac{0.10}{2 R T} \times \frac{1}{3} a n d C_{2}^{'} = \frac{0.20}{R T} \times \frac{2}{3} = \frac{0.40}{3 R T}$

$∴ π_{T o t a l} = i C_{R}^{'} T + i C_{2}^{'} R T = 2 \times \frac{0.10}{6} + \frac{0.40}{3} = \frac{0.50}{3}$

$\begin{matrix} π_{T o t a l} ≃ 167 \times 10^{- 3} a t m \end{matrix}$

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The osmotic pressure of a solution of NaCl is 0.10 atm and that of a glucose solution is 0.20 atm. The osmotic pressure of a solution formed by mixing 1 L of the sodium chloride solution with 2 L of the glucose solution is x×10−3 atm. x is __________. (nearest integer)

For NaCl:π1=iC1RT⇒C1=0.102 RT (i=2) For Glucose:π2=C2RT⇒C2=0.20RT (i=1) When 1L of NaCl solution and 2 L glucose solution are mixed. ∴ C′1=0.102RT×13 and C′2=0.20RT×23=0.403 RT ∴ πTotal=iC′RT+iC′2RT=2×0.106+0.403=0.503 πTotal≃167×10−3 atm