Chemistry

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 = 8.314\,\text{J mol}^{-1}\,\text{K}^{-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.

Intuitive explanation

This is a combined gas law problem where you're tracking how a fixed amount of gas responds to simultaneous changes in pressure and temperature. The key insight is that $PV = nRT$ connects all four variables—since $n$ (moles) and $R$ are constant, any change in $P$ or $T$ must be reflected in $V$ . You'll need to find the final pressure first (using the balloon's physical constraint), then calculate the volume change that results from both cooling and pressure drop working together.

Intuitive explanation

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