The osmotic pressure of blood is $7.65\text{atm}$ at $310\text{K}$. An aqueous solution of Glucose that will be isotonic with blood is what wt/vol?

Step1. Osmotic pressure

• “The flow of the solvent from its side to the solution side across a semipermeable membrane can be stopped if some extra pressure is applied on the solution. This pressure that just stops the flow of solvent is called the osmotic pressure of the solution.”
• Osmotic pressure is a colligative property.
• Isotonic solutions are the solutions that have the same osmotic pressure.

Step2. Formula for osmotic pressure

• The expression for osmotic pressure is as follows:-
• $\pi =iCRT$
• Here, $\mathrm{\pi }$ is the osmotic pressure, i, known as the van’t Hoff factor, to account for the extent of dissociation or association, $C$ is the concentration, $R$ is the gas constant, and $T$ is the temperature.

Step3. Calculation of concentration

$$\begin{gathered} 7.65\text{atm}=C\times 0.0821{\text{Latm K}}^{\text{-1}}{\text{mol}}^{\text{-1}}\times 310\text{K} \\ C=0.300577{\text{molL}}^{-1} \end{gathered}$$

Step4. Calculation of wt/Vol

Molar mass of glucose=$180.156{\text{gmol}}^{-1}$

$$\begin{gathered} \text{Wt/vol}=0.300577{\text{molL}}^{-1}{\text{×180.156 gmol}}^{\text{-1}} \\ {\text{=54.15 g L}}^{-1} \end{gathered}$$

Hence, the value of wt/vol is ${\text{54.15 g L}}^{-1}$.