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.

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