Question

The osmotic pressure of blood is 7.65 atm, at 310K. An aqueous solution of glucose that will be isotonic with blood is of what wt./vol?

Answer 1

Hint: Isotonic solution will not allow any osmotic flow anyhow. And for wt/vol. ratio the molar mass is required which can be multiplied with molarity.

Complete step by step answer:
Let us define a few terms like tonicity and osmolarity.
The ability of an extracellular solution to direct water move inside or outside of a cell by osmosis is known as its tonicity. A solution's tonicity is related to its osmolarity, which is the total concentration of all solute particles in the solution. A solution with low osmolarity has fewer number of solutes per liter of solution, while a solution with high osmolarity has more solutes per liter of solution. When solutions of different osmolarities are separated by a membrane permeable to water, but non permeable to solute, water will move from lower osmolarity to higher osmolarity.
Three terms—hypotonic, isotonic, and hypertonic—are used to measure the osmolarity of a cell with respect to the osmolarity of the extracellular fluid around it.
We always use these terms considering only solutes that cannot cross the membrane.
If the extracellular fluid has lower osmolarity than the intracellular solution, it is hypotonic (hypo means less than) to the cell, and the net flow of water will be into the cell.
In the reverse case, if the extracellular fluid has a higher osmolarity with respect to the solution inside , it’s said to be hypertonic—hyper means greater than—to the cell, and water will move out to the higher solute concentration.
As we know from definition, an isotonic solution is a solution that has the same osmotic pressure, or solute concentration. If these two solutions are tried to be separated by a semipermeable membrane, water will flow in equally from and into each of the solutions.
and Osmotic pressure is defined as the pressure that is required to stop the flow of solvents through semi permeable membranes i.e. the minimum pressure required to stop the process of osmosis.
Now for the given question, let the concentration of the glucose solution be C moles/lts.

According to definition of osmotic pressure we know that,
$\pi $ = CRT [ R= 0.0821 l-atm /k/mol , T=310 K,$\pi $ = 7.65 atm. ]
$\Rightarrow $ 7.65 = C x 0.0821 x 310
$\Rightarrow $ C= \[\dfrac{7.65}{0.0821\times 310}\] = 0.300577 M = 0.300577 Moles/lt.

molar mass of glucose(\[{{C}_{6}}{{H}_{12}}{{O}_{6}}\] ) = 180 gm/ moles
wt/Vol conc. = 0.300577 $\dfrac{moles}{lt.}$ x 180 $\dfrac{gm}{mole}$
             = 0.300577 x 180 gm/lt = 54.1 gm/lt.
           =54.1 x ${{10}^{-3}}$ g $c{{m}^{-3}}$
        = 5.41 %
Therefore wt/vol. ratio of the glucose solution is 5.41%

Additional Information:
Colligative properties are those which depend upon the number of solute particles irrespective of the relative amount of particles present in the solution. Osmotic pressure is a colligative property as it depends upon the concentration of solute particles.

Note: Hypotonic, hypertonic, and isotonic all are relative terms. They describe how one solution is measured to another in terms of osmolarity. For example, if the fluid inside the membrane has a higher osmolarity, concentration of solute, than the surrounding fluid, the cell interior is hypertonic to the surrounding fluid, and the outside fluid is hypotonic to the cell inside.