Final answer:
Using the Ideal Gas Law, PV = nRT, and converting the given mass of helium to moles, the calculated volume of a helium-filled balloon at 31°C and 2.12 atm is 147.8 liters.
Step-by-step explanation:
To find the volume of the balloon that is filled with helium, we will use the Ideal Gas Law, which is PV = nRT. We need to first convert the temperature from Celsius to Kelvin. The temperature in Kelvin is 31°C + 273.15 = 304.15 K. We also need to convert the mass of helium to moles using the molar mass of helium, which is approximately 4.0026 g/mol.
Therefore, the number of moles of helium (n) is 48.3 g / 4.0026 g/mol = 12.07 mol. The pressure (P) is given as 2.12 atm, and we know the universal gas constant (R) is 0.0821 L°atm/mol°K. Plugging the values into the Ideal Gas Law equation:
PV = nRT
V = nRT / P
V = (12.07 mol)(0.0821 L°atm/mol°K)(304.15 K) / 2.12 atm
V = 147.8 liters. Thus, the volume of the helium-filled balloon is 147.8 liters.