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Ch.6 - Gases
Tro - Chemistry: A Molecular Approach 6th Edition
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoTro 6th EditionCh.6 - GasesProblema 117c
Capitolo 6, Problema 117c

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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Concetti chiave

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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.
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01:15
Ideal Gas Law Formula

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.
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Molar Mass Concept

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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