Question

Consider a balloon that will expand without restriction until it pops. If the balloon can hold a maximum of 5.0 L gas before it pops, and you're filling the balloon at a mass flow rate of 3.0g/s of hydrogen gas, determine how long you can fill the balloon before it pops if the gas and the surrounding atmosphere are at 26°C. Take the outside pressure to be 0.97 atm.

A) 1.58 hours
B) 3.17 hours
C) 5.34 hours
D) 6.34 hours

Answer 1

The calculation shows that the balloon will pop in 0.1328 seconds, which is much less than a second and indicates that none of the provided options (in hours) are correct.

Step-by-step explanation:

The student has asked how long you can fill a balloon with hydrogen gas at a mass flow rate of 3.0g/s before it pops, given that the balloon can hold a maximum of 5.0 L of gas and the surrounding conditions are 26°C and 0.97 atm. To solve this, we first need to convert the mass flow rate of hydrogen into a volume flow rate, making use of the ideal gas law, PV = nRT, where P is pressure, V is volume, n is number of moles, R is the gas constant, and T is temperature in Kelvin.

To find the number of moles (‘n’), we use the molar mass of hydrogen (approximately 2.016 g/mol):

• Mass flow rate = 3.0 g/s,Molar mass of H2 = 2.016 g/mol,Moles per second = Mass flow rate / Molar mass

Moles per second = 3.0 g/s / 2.016 g/mol = 1.4881 mol/s

Kelvin = 26 + 273.15 = 299.15 K

• V = nRT / P

Volume rate = 1.4881 mol/s × 0.0821 L atm/mol K × 299.15 K / 0.97 atm

Volume rate = 37.639 L/s

• Max volume = 5.0 L
• Time = Max volume / Volume rate

Time = 5.0 L / 37.639 L/s = 0.1328 seconds

Since the options provided are in hours and the calculated time is significantly less than a second, none of the choices of A) 1.58 hours, B) 3.17 hours, C) 5.34 hours, or D) 6.34 hours are correct.