Final answer:
The cylinder pressure per gallon for the helium is approximately 409 psi/gallon.
Step-by-step explanation:
The cylinder pressure per gallon for the helium can be calculated using the ideal gas law. The ideal gas law equation is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.In this case, we have the pressure (100 psi) and the volume (30 balloons). We need to convert the volume from balloons to gallons. Assuming each balloon has a volume of 4.00 L, we multiply 30 balloons by 4.00 L/balloon to get 120 L. Convert this volume to gallons by dividing by 3.785 L/gallon, which gives us 31.7 gallons.Now that we have the pressure in psi and the volume in gallons, we can rearrange the ideal gas law equation to solve for the cylinder pressure per gallon, P/gallon. P/gallon = (PV)/(nRT) = (100 psi)(31.7 gallons) / [(1 mole)(0.0821 L.atm/mol.K)(298 K)]. Calculating this expression gives us approximately 409 psi/gallon.