A high-altitude weather balloon is filled at ground level (1.00 atm) with 5.00 mol of…
CHEMISTRY · Multi-part · AP · Chemistry · Properties of Substances and Mixtures · Properties of Substances and Mixtures
Problem
A high-altitude weather balloon is filled at ground level (1.00 atm) with 5.00 mol of helium gas at 270 K. As the balloon ascends, the external pressure drops, and the gas cools to 220 K. Assume the helium behaves ideally and that no gas escapes from the balloon.
(a) Calculate the root-mean-square speed of the helium atoms at the initial ground-level temperature of 270 K. (Molar mass of He = 4.00 g mol−1; R=8.314J mol−1K−1.)
(b) Determine the root-mean-square speed of the helium atoms after the temperature has dropped to 220 K.
(c) Using the ideal-gas law and your results from parts (a) and (b), discuss qualitatively how the pressure of the helium inside the balloon changes as it rises, assuming the balloon’s volume does not change appreciably in the short interval considered.
(d) In reality the balloon’s envelope expands significantly during ascent. Explain, in terms of molecular motion and average kinetic energy, why the balloon expands even though the average molecular speed decreases with altitude.