If 1.02% of glycerin is isotonic with a 2% solution of glucose,...

For isotonic solutions, the osmotic pressures are equal, $\pi_1 = \pi_2$.

Since both glycerin and glucose are non-electrolytes, their van't Hoff factors are $i = 1$. Therefore, their molar concentrations are equal, $C_1 = C_2$.

Let the molar mass of glycerin be $M$. A $1.02\%$ solution of glycerin contains $1.02 \text{ g}$ in $100 \text{ mL}$ of solution, and a $2\%$ solution of glucose contains $2 \text{ g}$ in $100 \text{ mL}$ of solution.

Concentration of glycerin, $C_1 = \dfrac{1.02}{M \times 0.1}$

Concentration of glucose, $C_2 = \dfrac{2}{180 \times 0.1}$

Equating $C_1$ and $C_2$:

$\dfrac{1.02}{M} = \dfrac{2}{180}$

$M = \dfrac{1.02 \times 180}{2}$

$M = 1.02 \times 90 = 91.8 \text{ g/mol}$

Answer: 91.8