Question

An electrolyte A gives 3 ions and B is a nonelectrolyte. If $0.1M$ solution of B produces an osmotic pressure P, then $0.05M$ solution of A will produce an osmotic pressure, assuming that the electrolyte is completely ionised:
A. $1.5P$
B. $P$
C. $0.5P$
D. $0.75P$

Answer 1

Hint: Osmotic pressure is the product of van’t Hoff factor, molar concentration, ideal gas constant and temperature. So, first we’ll find the osmotic pressure of A and then B by using the same formula. Then, we’ll divide both the pressures and the value of pressure of A can be calculated in terms of P. The van’t Hoff factor is the number of ions dissociated into the solution and R, T are constants.

Complete Step by step answer: An electrolyte is a substance that produces an electrically conducting solution when it is dissolved in a polar solvent such as water and non-electrolyte is a substance that does not dissociate into ions in aqueous or polar solvent. In this question, an electrolyte A gives 3 ions and B is a nonelectrolyte. The van’t Hoff factor $\left( i \right)$ is a measure of the effect of a solute on properties such as osmotic pressure, relative lowering in vapour pressure, boiling point elevation, etc. So, the value of i in electrolyte A is 3 and it is 1 in non-electrolyte B (as i is the ratio of actual concentration of the particles produced to the concentration of substance as calculated from its mass and in a non-electrolyte, both the concentrations remain the same).
Osmotic pressure is defined as the minimum pressure that needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane (the membrane which allows certain particles to enter). Osmotic pressure is given by the formula $\pi = icRT$ where $\pi $ is osmotic pressure, c is molar concentration of solute, R is an ideal gas constant and T is temperature.
For an electrolyte A, $\pi = icRT$
$\pi = 3 \times 0.05 \times RT$
$\Rightarrow \pi = 0.15RT$ $\left[ {eqn.1} \right]$
Now, for a non-electrolyte B, $\pi = icRT$
$P = 1 \times 0.1 \times RT$
$\Rightarrow P = 0.1RT$ $\left[ {eqn.2} \right]$
In both the cases the values of R and T are constant.
Now, we’ll divide eqn1. and 2,
$\dfrac{\pi }{P} = \dfrac{{0.15RT}}{{0.1RT}}$
$\Rightarrow \dfrac{\pi }{P} = 1.5$
$\Rightarrow \pi = 1.5P$

Therefore, option A is correct.

Note: Kindly remember that the value of van’t Hoff factor in most of the non-electrolytes in its aqueous form i.e., in a solution in which water is a solvent is taken as 1. So, we have assumed it as 1. Also, don’t forget that both R and T are constant as R is an ideal gas constant and Temperature $\left( T \right)$ is fixed in this question.