In the Dumas-bulb technique for determining the molarmass of an unknown liquid, you vaporize the sample of aliquid that boils below 100 °C in a boiling-water bath anddetermine the mass of vapor required to fill the bulb. Fromthe following data, calculate the molar mass of the unknownliquid: mass of unknown vapor, 1.012 g; volume of bulb,354 cm3; pressure, 98.93 kPa; temperature, 99 °C.

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Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature in Celsius.

Convert the volume from cm³ to liters by dividing the volume in cm³ by 1000.

Use the ideal gas law equation, PV = nRT, to solve for the number of moles (n) of the vapor. Here, P is the pressure in kPa, V is the volume in liters, R is the ideal gas constant (8.314 L·kPa/mol·K), and T is the temperature in Kelvin.

Rearrange the ideal gas law equation to solve for n: n = PV / RT.

Calculate the molar mass of the unknown liquid by dividing the mass of the vapor by the number of moles calculated in the previous step.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. In this context, it allows us to calculate the number of moles of vapor produced from the known pressure, volume, and temperature, which is essential for determining the molar mass of the unknown liquid.

Molar Mass Calculation

Molar mass is defined as the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the molar mass of the unknown liquid, we use the formula: Molar Mass = mass of vapor (g) / moles of vapor (mol), where moles are derived from the Ideal Gas Law.

Vaporization and Boiling Point

Vaporization is the process of converting a liquid into vapor, which occurs at the boiling point of the liquid. In the Dumas-bulb technique, the sample is vaporized in a boiling-water bath, ensuring that the temperature remains constant at the boiling point, which is crucial for accurate measurements of pressure and volume in the gas phase.

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