The osmotic pressure of a solution containing 2.10 g of an unknown compound dissolved in 175.0 mL of solution at 25 °C is 1.93 atm. The combustion of 24.02 g of the unknown compound produced 28.16 g CO₂ and 8.64 g H₂O. What is the molecular formula of the compound (which contains only carbon, hydrogen, and oxygen)?

검증된 단계별 안내

Determine the molar mass of the unknown compound using the osmotic pressure formula: \( \Pi = \frac{n}{V}RT \), where \( \Pi \) is the osmotic pressure, \( n \) is the number of moles of solute, \( V \) is the volume of the solution in liters, \( R \) is the gas constant (0.0821 L atm K^{-1} mol^{-1}), and \( T \) is the temperature in Kelvin.

Convert the mass of the unknown compound (2.10 g) and the volume of the solution (175.0 mL) to appropriate units and plug them into the osmotic pressure equation to solve for the number of moles (\( n \)).

Calculate the molar mass of the compound by dividing the mass of the compound by the number of moles calculated in the previous step.

Analyze the combustion data to find the empirical formula. Convert the mass of CO2 and H2O produced into moles, and use these values to determine the moles of carbon and hydrogen in the original compound.

Use the molar mass found from the osmotic pressure data and the empirical formula from the combustion analysis to determine the molecular formula of the compound. Adjust the subscripts in the empirical formula to match the molar mass.

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주요 개념

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Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is directly proportional to the molarity of the solute and can be calculated using the formula π = iCRT, where π is the osmotic pressure, i is the van 't Hoff factor, C is the molarity, R is the ideal gas constant, and T is the temperature in Kelvin. Understanding this concept is crucial for determining the molar mass of the unknown compound from the given osmotic pressure.

Combustion Analysis

Combustion analysis is a method used to determine the elemental composition of organic compounds by burning them in excess oxygen and measuring the amounts of CO2 and H2O produced. The mass of CO2 and H2O generated allows for the calculation of the moles of carbon and hydrogen in the compound. This information is essential for deducing the empirical formula of the unknown compound, which can then be used to find its molecular formula.

Empirical and Molecular Formulas

The empirical formula represents the simplest whole-number ratio of elements in a compound, while the molecular formula indicates the actual number of atoms of each element in a molecule. To find the molecular formula, one must first determine the empirical formula and then use the molar mass obtained from osmotic pressure calculations to find the ratio between the empirical and molecular formulas. This distinction is vital for accurately identifying the unknown compound's composition.