Ch.10 - Gases

Problem 53

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Chapter 10, Problem 53

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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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.

Convert the volume from cm³ to liters by dividing by 1000, since 1 L = 1000 cm³.

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 atm, V is the volume in liters, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.

Calculate the molar mass of the unknown liquid by dividing the mass of the vapor (in grams) by the number of moles (n) obtained from the ideal gas law calculation.

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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 unknown liquid, 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 liquid, we use the formula: Molar Mass = mass of vapor (g) / moles of vapor (n), where n is derived from the Ideal Gas Law.

Conversions and Units

Understanding unit conversions is crucial in this problem, particularly converting pressure from torr to atmospheres and temperature from Celsius to Kelvin. Accurate conversions ensure that the calculations align with the standard units used in the Ideal Gas Law, leading to correct results.

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Conversion Factors

Related Practice

(a) Calculate the density of NO₂gas at 0.970 atm and 35 °C.

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Textbook Question

(b) Calculate the molar mass of a gas if 2.50 g occupies 0.875 L at 685 torr and 35 °C

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Textbook Question

Calculate the molar mass of a vapor that has a density of 7.135 g/L at 12°C and 743 torr.

Textbook Question

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.

Textbook Question

Magnesium can be used as a “getter” in evacuated enclosures to react with the last traces of oxygen. (The magnesium is usually heated by passing an electric current through a wire or ribbon of the metal.) If an enclosure of 0.452 L has a partial pressure of O2 of 3.5×10−6 torr at 27°C, what mass of magnesium will react according to the following equation?

Textbook Question

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?