A 160.0-L helium tank contains pure helium at a pressure of 1855 psi and a temperature of 298 K. How many 3.5-L helium balloons can be filled with the helium in the tank? (Assume an atmospheric pressure of 1.0 atm and a temperature of 298 K.)

Verified step by step guidance

Convert the pressure in the tank from psi to atm using the conversion factor: 1 atm = 14.7 psi.

Use the ideal gas law \( PV = nRT \) to calculate the number of moles of helium in the tank. Use the converted pressure in atm, the volume of the tank in liters, the temperature in Kelvin, and the ideal gas constant \( R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \).

Calculate the volume of helium at atmospheric pressure using the ideal gas law again, with the number of moles calculated in the previous step, atmospheric pressure, and the same temperature.

Determine the volume of helium available at atmospheric pressure by using the ratio of the initial and final pressures and volumes.

Divide the total volume of helium at atmospheric pressure by the volume of one balloon (3.5 L) to find the number of balloons that can be filled.

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. This law is essential for understanding how gases behave under different conditions and allows us to calculate the amount of gas in a given volume at a specific pressure and temperature.

Conversion of Units

In this problem, it is crucial to convert pressure from psi to atm and volume from liters to a consistent unit. Understanding how to convert between different units of measurement ensures accurate calculations and comparisons, particularly when dealing with gas laws and conditions.

Stoichiometry of Gases

Stoichiometry in the context of gases involves calculating the relationships between the volumes of gases and their moles. By knowing the volume of helium available and the volume of each balloon, we can determine how many balloons can be filled, applying the principles of gas behavior and conservation of mass.

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