Ideal gas law: 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.)

Question

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, 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 molecular weight of air to convert the number of moles to mass:mass = n * molecular weightPlugging in the given values, we get:n = (1.01 × 10^5 Pa * 2.00 × 10^3 m^3) / (8.314 J/mol ∙ K * (120 + 273) K) = 76.3 molmass = 76.3 mol * 28.8 g/mol = 2.20 × 10^3 g = 2.20 kgTherefore, the mass of hot air inside the balloon is 2.20 kg, which is closest to choice A, 1780 kg.

Ideal Gas Law: a Hot Air Balloon Has a Volume