Question

A 5% solution (w/v) of cane sugar (Mol. weight=342) is isotonic with 0.877% (w/v) of urea solution. Find molecular weight of urea (round off to nearest integer.)

Answer 1

Hint: Isotonic solutions have the same concentration and they have the same osmotic pressure at a given temperature. Osmotic pressure is directly proportional to concentration of solution at a given temperature. $\Pi =CRT$, Concentration is the number of moles of solute present in 1 liter of solution.

Complete answer:
-When solvent molecules move from lower concentration to higher concentration through semi permeable membranes, the process is called osmosis.
-Solvent molecule flow till equilibrium is attained. This flow of solvent molecules can be stopped by applying extra pressure.
-Extra pressure must be applied in order to stop flow of solvent molecules.
-Pressure that will just stop the flow of solvent molecules is called osmotic pressure.
-Movement of solvent molecules always occurs from lower concentration to higher concentration.
-Osmotic pressure is excess pressure that must be applied to stop the flow of solvent molecules.
-Osmotic pressure is a colligative property, it depends on the number of solute molecules.
-Osmotic pressure is proportional to concentration of solution at given temperature.
Solutions are said to be isotonic, if two solutions have the same osmotic pressure at given temperature.
-No osmosis occurs between such solutions when separated by semi permeable membranes
-Isotonic solutions have the same concentration.
$\begin{align}
 & \Rightarrow {{C}_{1}}={{C}_{2}} \\
 & \Rightarrow \dfrac{{{n}_{2}}}{{{V}_{1}}}=\dfrac{{{n}_{2}}^{'}}{{{V}_{2}}} \\
 &\Rightarrow \dfrac{{{w}_{2}}}{{{M}_{2}}{{V}_{1}}}=\dfrac{{{w}_{2}}^{'}}{{{M}_{2}}^{'}{{V}_{2}}} \\
 & \Rightarrow \dfrac{5g}{342\times 0.1\text{L}}=\dfrac{0.877}{{{M}_{2}}^{'}\times 0.1L} \\
 &\Rightarrow {{M}_{2}}^{'}=\dfrac{0.877\times 342}{5}=59.98g/mol \\
\end{align}$

Molecular weight of urea is 60g/mol.

Note:
$\%w/v$ is expressed as the mass of solute in grams present in 100ml of solution. Concentration is the number of moles of solute present in 1litre of solution. Isotonic solutions have the same concentration. -Two solutions having the same osmotic pressure at a given temperature are called isotonic solutions.