Question

An aqueous solution of sucrose, $C_{12}{H}_{22}{O}_{11}$, containing 34.2 g/L has an osmotic pressure of 2.38 atmospheres at ${17}^{\circ }C$. For an aqueous solution of glucose, $C_6{H}_{12}{O}_6$, to be isotonic with this solution at same temperature, it would have the density:

• A. 34.2 g/L
  
• B. 17.1 g/L
  
• C. 18.0 g/L
  
• D. 36.0 g/L

Answer 1

The correct option is C 18.0 g/L


Isotonic solutions have same osmotic pressure
Osmotic pressure $\pi =cRT=\frac{\rho RT}{M}=\frac{34.2RT}{342}=\frac{{\rho }_{glucose}RT}{M_{glucose}}=\frac{{\rho }_{glucose}RT}{180}$

$\Rightarrow {\rho }_{glucose}=\frac{34.2\times 180}{342}=18g/L$