The osmotic pressure of blood at 27°C is 8.21atm. the amount of glucose should be used per litre for an intravenus injection so that it is isotonic with blood is

Given:

Osmotic pressure of solution, $\mathrm{\pi }=8.21 \mathrm{atm}$

Temperature, $\mathrm{T}=27℃=27+273=300\mathrm{K}$

Osmotic pressure of solution is given by the formula, $\mathrm{\pi }=\mathrm{CRT}$

C = Concentration in mole/litre

R = Universal Gas Constant = 0.0821 L(atm)/mol.K

$\mathrm{\pi }=\mathrm{CRT}$

$$\begin{gathered} \mathrm{C}=\frac{\mathrm{\pi }}{\mathrm{RT}} \\ =\frac{8.21}{0.0821\times 300} \\ =0.33 \mathrm{mole}/\mathrm{litre} \end{gathered}$$

Concentration = no. of moles/Volume 

Here volume is 1 litre.

Concentration = no. of moles = weight / molecular weight

Molecular formula of glucose = ${\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6$

Molecular weight of glucose = $6\times 12+1\times 12+6\times 16=180 \mathrm{gm}$

Concentration = weight/molecular weight

$0.33=\mathrm{weight}/180$

$\mathrm{weight}=0.33\times 180=60 \mathrm{gm}$

The amount of glucose should be used per litre for an intravenus injection so that it is isotonic with blood is 60 gm.