Question

A 0.6% urea solution would be isotonic with
A. $0.1M$ glucose solution.
B. $0.1M$ $KCl$solution
C. $0.6\% $ glucose solution
D. $0.6\% $ $NaCl$solution.

Answer 1

Hint: We know that the meaning of isotonic is that the osmotic pressure of the solutions will be equal. The osmotic pressure of a solution is given by
$ \Rightarrow \pi = iCRT$.
Here, $\pi = $osmotic pressure , $i = $ van’t hoff factor , $C = $concentration , $R = $ideal gas constant , $T = $temperature.

Complete step by step solution:
We know that urea is a non electrolyte. The molecular formula of urea is $N{H_2}CON{H_2}$. We are given a $0.6\% $ urea solution. That means it will contain $0.6g$ of urea in $100g$ of the solution. The density of the solution will be $1g/ml$. The volume of the solution will be $100ml = 0.1L$ The molecular mass of urea is $60$. Concentration of a solution is given by

$ \Rightarrow C = \dfrac{{moles}}{{volume(L)}} = \dfrac{{\dfrac{{0.6}}{{60}}}}{{0.1}} = 0.1M$.

For non electrolytes like urea the $i = $ van’t hoff factor will be one. So the osmotic pressure will be $ \Rightarrow \pi = iCRT = 0.1RT$. Now for a $0.1M$ glucose solution, the value of $i = $ van’t hoff factor will be one . So the osmotic pressure will be $ \Rightarrow \pi = iCRT = 0.1RT$.
For $0.1M$ $KCl$ solution the $i = $ van’t hoff factor will be two because it is a strong electrolyte. So
$ \Rightarrow \pi = iCRT = 0.2RT$. For $0.6\% $glucose solution, the molecular mass of glucose is $180g$, the osmotic pressure will be
$ \Rightarrow \pi = iCRT = \dfrac{{\dfrac{{0.6}}{{180}}}}{{0.1}}RT = 0.033RT < 0.1RT$.

For $0.6\% $ $NaCl$solution , the molecular mass of $NaCl$ is $58.5g$. The $i = $ van’t hoff factor will be two because it is a strong electrolyte. So

$ \Rightarrow \pi = iCRT = 2 \times \dfrac{{\dfrac{{0.6}}{{58.5}}}}{{0.1}}RT = 0.0205RT < 0.1RT$.

So from the above explanation and calculation it is clear to us that $0.6\% $ urea solution and $0.1M$ glucose solution are isotonic with each other because the osmotic pressure is same for them that is $ \Rightarrow \pi = iCRT = 0.1RT$.

So, the correct answer is option A.

Additional information:
Glucose has a molecular formula of ${C_6}{H_{12}}{O_6}$. It is a type of sugar. Osmotic pressure is a colligative property . The meaning of colligative property is that it will depend upon the number of moles of the solute of the solution.

Note: Always remember that the osmotic pressure of a solution is given by $ \Rightarrow \pi = iCRT$. $KCl$ and $NaCl$ are strong electrolytes. They get dissociated completely into their constituent ions. Urea and glucose are not strong electrolytes and the degree of dissociation is very low in urea and glucose.