A hot air balloon has a volume of 2.00 × 10³ m³ when fully inflated, and the air inside the balloon is always at atmospheric pressure of 1.01 × 10⁵ Pa because of the large opening used to fill the balloon and heat the air inside it. What is the mass of hot air inside the balloon if its temperature is 120°C? The universal gas constant is 8.314 J/mol•K. (Assume a molecular weight of 28.8 g/mol for air.) A) 1780 kg B) 5850 kg C) 203 kg D) 62.0 kg

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Quizplus · Accepted Answer

The mass of hot air inside the balloon can be calculated using the ideal gas law:PV = nRTwhere P is the pressure, V is the volume, n is the number of moles of gas, R is the universal gas constant, and T is the temperature.We can rearrange this equation to solve for n:n = PV/RTWe can then use the molar mass of air to convert the number of moles to mass:mass = n * molar massPlugging in the given values, we get:n = (1.01 × 10^5 Pa)(2.00 × 10^3 m^3)/(8.314 J/mol•K)(393 K) = 62.0 molmass = (62.0 mol)(28.8 g/mol) = 1780 kgTherefore, the mass of hot air inside the balloon is 1780 kg.

A Hot Air Balloon Has a Volume of 2