Two solutions are isotonic if they have the same osmotic pressure at the same temperature . Osmotic pressure ($\Pi$) is given by $\Pi = CRT$, where $C$ is the molar concentration ($\frac{n}{V}$). For isotonic solutions: $C_1 = C_2$ (assuming effectively equal densities for dilute solutions, molarity $\approx$ molality for calculation purposes or volumes cancel out for equal mass percentages).

Step 1: Identify given values. Solution 1: Mass of compound ($w_1$) = 1 g; Molecular weight ($M_1$) = ? Solution 2: Mass of sucrose ($w_2$) = 5 g; Molecular weight of sucrose ($C_{12}H_{22}O_{11}$) = 342 g/mol .

Step 2: Apply the isotonic condition. Since $\frac{n_1}{V} = \frac{n_2}{V}$ (for same volume of solution containing these percentages), $\frac{w_1}{M_1} = \frac{w_2}{M_2}$

Step 3: Calculate $M_1$. $\frac{1}{M_1} = \frac{5}{342}$ $M_1 = \frac{342}{5} = 68.4 \text{ g/mol}$

The molecular weight of the compound is 68.4.