Question

: The osmotic pressure of blood is $7.40atm$ at ${27^ \circ }C$. The number of mole of glucose to be used per litre of an intravenous injection that is to have the same osmotic pressure in blood is:
A.$0.3$
B.$0.2$
C.$0.1$
D.$0.4$

Answer 1

Hint: Colligative properties: It is defined as the ratio of number of solute particles to the number of solvent particles. It only depends on the number of ions and not on the nature of the solute.
Same osmotic pressure of substances means that the substances have equal osmotic pressures.

Complete step by step answer:
Let us first talk about colligative properties.
There are four colligative properties: Depression in freezing point, elevation in boiling point, osmotic pressure and lowering in vapour pressure.
Depression in freezing point: It is defined as the decrease in freezing point of a solvent in addition to non-volatile solute. It is directly proportional to the molality of the solution.
Elevation in boiling point: It is defined as an increase in boiling point of a solvent in addition to non-volatile solute. It is directly proportional to the molality of the solution.
Osmotic pressure: It is defined as the minimum pressure which needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane.
Relative lowering in vapour pressure: When non- volatile solutes are added to a solution then there is a decrease in its vapour pressure, which is known as relative lowering in vapour pressure.
In this question we have to work on osmotic pressure. Osmotic pressure is represented by $\pi $ and it is calculated as $\pi = \dfrac{n}{V}RT$, where $n$ is number of moles, $V$ is volume, $R$ is gas constant, $T$ is temperature and $\pi $ is osmotic pressure. Here in the question we have to find the number of moles of glucose to be used per litre of an intravenous injection that is to have the same osmotic pressure in blood. And we know that the same osmotic pressure of substances means that the substances have equal osmotic pressures. So the number of moles of glucose will be $n = \dfrac{{\pi V}}{{RT}}$, where the values of $\pi $ is $7.40atm$, $V$ is $1L$, $R$ is $0.0821$ and $T$ is ${27^ \circ }C = 300K$. The value of $n$ comes out to be $n = \dfrac{{7.40 \times 1}}{{0.0821 \times 300}} = 0.3$.

Hence option A is correct.

Note:
Van’t Hoff factor: It is defined as the ratio of actual number of particles in the solution after dissociation or association to the number of particles for which no ionization takes place. It is represented by $i$.