Question

The osmotic pressure of blood is 7.65atm at 310K.an aqueous solution of glucose that will be isotonic with blood is ---wt/vol.

Answer 1

Hint: Isotonic solutions have the same concentration and they have the same osmotic pressure at a given temperature. Osmotic pressure is directly proportional to concentration of solution at a given temperature. $$\mathrm{\Pi }=CRT$$, molecular mass of glucose is 180.

Complete answer:
-Only solvent molecules can permeate through semi permeable membranes. When a semipermeable membrane is placed between solution and solvent, solvent molecules flow through the membrane from pure solvent to solution.
-When solvent molecules move from lower concentration to higher concentration through semi permeable membranes, the process is called osmosis.
-Extra pressure must be applied in order to stop flow of solvent molecules.
-Movement of solvent molecules always occurs from lower concentration to higher concentration.
-Osmotic pressure is excess pressure that must be applied to stop the flow of solvent molecules.
-Osmotic pressure is a colligative property, it depends on the number of solute molecules.
- Solutions are said to be isotonic, if two solutions have same osmotic pressure at given temperature
-No osmosis occurs between such solutions when separated by semi permeable membranes.
As given in data, osmotic pressure of blood $\mathrm{\Pi }=7.65$ atm
R=Gas constant=$0.082$
$T=310K$
$\begin{array}{rl}& \mathrm{\Pi }=CRT\\ & \Rightarrow 7.65=C\times 0.082\times 310\\ & \Rightarrow C=0.3009M\\ & \end{array}$
As concentration is the number of moles of solute present in 1 liter of solution.
Number of moles of glucose=$${\displaystyle \frac{Weight\text{ of Glucose}}{Molar\text{ mass of Glucose}}}={\displaystyle \frac{Weight\text{ of Glucose}}{180}}$$
$\begin{array}{rl}& \Rightarrow C={\displaystyle \frac{Weight\text{ of Glucose}}{180\times 1}}\\ & \Rightarrow Weight\text{ of Glucose = }0.3009\times 180=54.162g/liter\end{array}$

An aqueous solution of glucose having wt/vol as 54g/L will be isotonic with blood.

Note:
Osmotic pressure of fluid inside the blood cell is equivalent to 0.9% of sodium chloride solution. 5% of glucose solution in isotonic with blood cells. -Two solutions having same osmotic pressure at a given temperature are called isotonic solutions Osmotic pressure can be calculated using following formula: $\mathrm{\Pi }={\displaystyle \frac{w_2}{M_2\times V}}RT$