The molar mass of a volatile substance was determined by the Dumas-bulb method described in Exercise 10.53. The unknown vapor had a mass of 0.846 g; the volume of the bulb was 354 cm3, pressure 752 torr, and temperature 100°C. Calculate the molar mass of the unknown vapor.

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Convert the pressure from torr to atm using the conversion factor: 1 atm = 760 torr.

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

Use the ideal gas law equation, PV = nRT, to solve for the number of moles (n) of the gas. Rearrange the equation to n = PV / RT.

Substitute the known values into the ideal gas law equation: P (in atm), V (in liters), R (ideal gas constant, 0.0821 L·atm/mol·K), and T (in Kelvin).

Calculate the molar mass by dividing the mass of the vapor (in grams) 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 the vapor using the given pressure, volume, and temperature, which is essential for determining its molar mass.

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 vapor, we use the formula: Molar Mass = mass of the vapor (g) / number of moles (mol), which we can derive from the Ideal Gas Law.

Dumas Method

The Dumas method is a technique used to determine the molar mass of volatile substances by measuring the mass of vapor produced in a controlled environment. It involves heating the substance to vaporize it, capturing the vapor in a bulb, and measuring the pressure, volume, and temperature to calculate the molar mass using the Ideal Gas Law.

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In the Dumas-bulb technique for determining the molar mass of an unknown liquid, you vaporize the sample of a liquid that boils below 100°C in a boiling-water bath and determine the mass of vapor required to fill the bulb. From the following data, calculate the molar mass of the unknown liquid: mass of unknown vapor, 1.012 g; volume of bulb, 354 cm3; pressure, 742 torr; temperature, 99°C.

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Calcium hydride, CaH2, reacts with water to form hydrogen gas:

CaH2(𝑠)+2 H2O(𝑙)⟶Ca(OH)2(𝑎𝑞)+2 H2(𝑔)

This reaction is sometimes used to inflate life rafts, weather balloons, and the like, when a simple, compact means of generating H2 is desired. How many grams of CaH2 are needed to generate 145 L of H2 gas if the pressure of H2 is 825 torr at 21°C?