Ch.6 - Gases

Problem 107c

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Chapter 6, Problem 107c

Olympic cyclists fill their tires with helium to make them lighter. Calculate the mass of air in an air-filled tire and the mass of helium in a helium-filled tire. Assume that the volume of the tire is 855 mL, that it is filled to a total pressure of 125 psi, and that the temperature is 25 °C. Also, assume an average molar mass for air of 28.8 g/mol. What is the mass difference between the two?

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Convert the volume of the tire from milliliters to liters by dividing by 1000.

Convert the pressure from psi to atm using the conversion factor: 1 atm = 14.696 psi.

Convert the temperature from Celsius to Kelvin by adding 273.15.

Use the ideal gas law, \( PV = nRT \), to calculate the number of moles of gas in the tire. Use R = 0.0821 L·atm/mol·K.

Calculate the mass of the air using the number of moles and the average molar mass of air (28.8 g/mol). Then, calculate the mass of helium using the number of moles and the molar mass of helium (4.00 g/mol). Finally, find the mass difference between the air-filled and helium-filled tire.

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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, represented as PV = nRT, relates the pressure (P), volume (V), and temperature (T) of a gas to the number of moles (n) and the ideal gas constant (R). This law is essential for calculating the number of moles of gas in the tire, which can then be converted to mass using the molar mass of the gas.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). In this question, the average molar mass of air (28.8 g/mol) and the molar mass of helium (approximately 4.0 g/mol) are crucial for determining the mass of the gases in the tire after calculating the number of moles using the Ideal Gas Law.

Pressure Conversion

Pressure conversion is necessary to ensure that the pressure used in calculations is in the correct units. In this case, the pressure of 125 psi must be converted to a compatible unit, such as atmospheres or pascals, to apply the Ideal Gas Law effectively. Understanding how to convert between pressure units is vital for accurate calculations.

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Pressure Conversion Example

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Textbook Question

Ammonium nitrate decomposes explosively upon heating according to the balanced equation: 2 NH4NO3(s)¡2 N2( g) + O2( g) + 4 H2O( g) Calculate the total volume of gas (at 125 °C and 748 mmHg) produced by the complete decomposition of 1.55 kg of ammonium nitrate.

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Textbook Question

Olympic cyclists fill their tires with helium to make them lighter. Calculate the mass of air in an air-filled tire and the mass of helium in a helium-filled tire. Assume that the volume of the tire is 855 mL, that it is filled to a total pressure of 125 psi, and that the temperature is 25 °C. Also, assume an average molar mass for air of 28.8 g/mol. Calculate the mass of air in an air-filled tire.

An ordinary gasoline can measuring 30.0 cm by 20.0 cm by 15.0 cm is evacuated with a vacuum pump. Assuming that virtually all of the air can be removed from inside the can and that atmospheric pressure is 14.7 psi, what is the total force (in pounds) on the surface of the can? Do you think that the can could withstand the force?

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Textbook Question

An 11.5-mL sample of liquid butane (density = 0.573 g/mL) is evaporated in an otherwise empty container at a temperature of 28.5 °C. The pressure in the container following evaporation is 892 torr. What is the volume of the container?

A scuba diver creates a spherical bubble with a radius of 2.5 cm at a depth of 30.0 m where the total pressure (including atmospheric pressure) is 4.00 atm. What is the radius of the bubble when it reaches the surface of the water? (Assume that the atmospheric pressure is 1.00 atm and the temperature is 298 K.)

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