If a certain natural gas supply contains 2.13% helium by mass,what amount of the natural gas must be processed,at 96.2% efficiency of helium recovery,to produce sufficient helium to inflate 24 party balloons to a volume of 5.3 L each at an internal gas pressure of 1.25 atm and a temperature of 23.7 °C?

Question

Quizplus · Accepted Answer

First, calculate the total volume of helium needed for the balloons: 24 balloons * 5.3 L/balloon = 127.2 L. Convert the temperature to Kelvin: 23.7 °C + 273.15 = 296.85 K. Use the ideal gas law (PV = nRT) to find the moles of helium needed, assuming R = 0.0821 L·atm/(mol·K): n = PV / RT = (1.25 atm * 127.2 L) / (0.0821 L·atm/(mol·K) * 296.85 K) ≈ 6.5 moles of He. The molar mass of helium is approximately 4 g/mol, so the mass of helium needed is 6.5 moles * 4 g/mol = 26 g. Since the recovery efficiency is 96.2%, the actual amount of helium needed is 26 g / 0.962 = 27.03 g. Given that helium is 2.13% of the natural gas by mass, the total mass of natural gas needed is 27.03 g / 0.0213 ≈ 1269 g or approximately 1.27 kg, which rounds to the closest option, 1.28 kg.

If a Certain Natural Gas Supply Contains 2