Question

Osmotic pressure of 30% solution of glucose is 1.20 atm and that of 3.42% solution of cane sugar is 2.5 atm. The osmotic pressure of the mixture containing equal volumes of the two solutions will be:
A.2.5 atm
B.3.7 atm
C.1.85 atm
D.1.3 atm

Answer 1

Hint: We know that the process of flowing of solvent through a semipermeable membrane is termed as osmosis. The pressure that stops the solvent flow is the osmotic pressure of the solution. Here, we have to use the formula of osmotic pressure, that is, $\pi V = nRT$.

Complete step by step answer:
Here, osmotic pressure of two solutions namely glucose and cane sugar are given and we have to calculate the osmotic pressure of the solution which contains the equal volumes of two solutions.

We know the formula of osmotic pressure, that is, $\pi V = nRT$, where, $\pi $ is osmotic pressure, V is volume, n is moles of the solute, R is gas constant and T is temperature.

Let’s consider the osmotic pressure and volume of glucose to be ${\pi _1}$ and V1 respectively.
So, ${\pi _1}$=1.20 m

And similarly we consider the osmotic pressure and volume of cane sugar be ${\pi _2}$and V2 respectively

So, ${\pi _2}$=2.5 atm

Now, the final solution is obtained by mixing the solutions in equal volumes. So, the osmotic pressure of the final solution is the summation of osmotic pressure of both the solutions.

${\pi _f}{V_f} = {\pi _1}{V_1} + {\pi _2}{V_2}$…… (1)

Here, ${\pi _f}$ and Vf is the osmotic pressure and volume of the final solution respectively.
As equal volumes of both the solutions are taken, so, ${V_1} = {V_2} = V$ and final volume is 2V.

So, equation (1) becomes,

$2V{\pi _f} = {\pi _1}V + {\pi _2}V$

Now, we have to put the values of ${\pi _1}$ and ${\pi _2}$ in the above equation and solve for ${\pi _f}$.

${\pi _f} = \dfrac{{{\pi _1}V + {\pi _2}V}}{{2V}}$

$ \Rightarrow {\pi _f} = \dfrac{{1.20 + 2.5}}{2} = 1.85\,{\rm{atm}}$

Therefore, the osmotic pressure of the final solution is 1.85 atm.

Hence, the correct choice is option C.

Note: Always remember that osmotic pressure is an example of colligative property because it depends on the quantity of solute molecules rather than their identity. Experimentally it is found that osmotic pressure is proportional to the molarity of the solution at a given temperature T.