A solution containing 10.2g glycerine per litre is isotonic with a 2 percent solution of glucose. What is the molecular mass of glycerine?

Isotonic solution

• Two solutions having the same osmotic pressure across a semipermeable membrane is referred to as isotonic solution. It has the same osmolarity (solute concentration), as another solution.
• A solution is isotonic when its effective mole concentration is the same as that of another solution.
• The osmotic pressure of glycerine and glucose is same here, then

${\pi }_{Glycerine}={\pi }_{Glucose}$

$\frac{n_1}{V_1}RT=\frac{n_2}{V_2}RT$

$i.e,\frac{n_1}{V_1}=\frac{n_2}{V_2}$

Where, $n_1$ is the no. of moles of glycerine

$V_1$ is volume of glycerine

$n_2$ is the no. of moles of glucose

$V_2$ is volume of glucose

• The number of moles is given by $\frac{givenmass}{molecularweight}$
• 2% solution means 2 gram glucose in 100 gm solution, density of water =$1gmperc{m}^3$

$\frac{W_{Glycerine}}{M_{Glycerine}}\times \frac{1}{V_1}=\frac{W_{Glucose}}{M_{Glucose}}\times \frac{1}{V_2}$

$\frac{10.2}{M_{Glycerine}}\times \frac{1}{1000}=\frac{2}{180}\times \frac{1}{100}$

$M_{Glycerine}=\frac{10.2\times 180\times 100}{2\times 1000}$

$=91.8gm$

Hence, the molecular mass of glycerine =91.8 gm