An organic compound has a composition of 93.46 % C and 6.54...

An organic compound has a composition of $93.46 \%$ C and $6.54 \%$ H by mass. A solution of 0.090 g of this compound in $1.10 \mathrm{g}$ of camphor melts at $158.4^{\circ} \mathrm{C}$. The melting point of pure camphor is $178.4^{\circ} \mathrm{C} . \mathrm{K}_{\mathrm{f}}$ for camphor is $37.7^{\circ} \mathrm{C} / \mathrm{m} .$ Assuming ideal solution behavior, what is the molecular formula of the solute? Show your calculations.

Key Concepts

Empirical Formula Determination

This concept involves converting the mass percentages of elements in a compound into moles and then finding the simplest whole?number ratio to write the empirical formula. It is essential in organic analysis, as it provides the basic stoichiometric composition from elemental analysis data without knowing the actual molecular weight of the compound.

Colligative Properties and Freezing Point Depression

Colligative properties are those solution features that depend only on the number of solute particles present, not on their identity. Freezing point (or melting point) depression is a colligative property where the presence of a non?volatile solute lowers the temperature at which a solvent freezes or melts. This change in freezing/melting point, together with the cryoscopic constant (Kf) of the solvent, can be used to determine the molal concentration and, in turn, the molar mass of the solute.

Molality and Molar Mass Determination

Molality is a measure of the concentration of a solution defined as the number of moles of solute per kilogram of solvent. By using the freezing point depression data, one can calculate the molality of the solute. Once the moles of solute are determined from molality and the mass of the solvent, the molar mass of the solute can be deduced by dividing its mass by the calculated number of moles. Comparing the obtained molar mass to the empirical formula mass enables the determination of the molecular formula as an integer multiple of the empirical formula.

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