At sunrise a high-altitude weather balloon is filled with of an unknown diatomic gas

CHEMISTRY · Multi-part · A Level · Chemistry · Amount of substance · Amount of substance

Problem

At sunrise a high-altitude weather balloon is filled with

1.2\,\text{kg}

of an unknown diatomic gas. The balloon is spherical with an initial radius of

0.75\,\text{m}

. Inside the balloon the gas temperature is

270\,\text{K}

, and the internal pressure equals the ambient atmospheric pressure of

0.61\,\text{atm}

. As the balloon ascends during the day, solar heating raises the gas temperature to

300\,\text{K}

, and the balloon expands to a new radius of

0.85\,\text{m}

. During the ascent no gas enters or escapes, the temperature remains uniform, and the gas behaves ideally. The external atmospheric pressure at the higher altitude is

0.50\,\text{atm}

. Take

R=0.0821\,\text{L\,atm\,mol}^{-1}\text{K}^{-1}

. (a) Using the morning conditions, compute the molar mass of the unknown diatomic gas. (b) Identify the most plausible gas from the following list and justify your choice: nitrogen (

\text{N}_2

), oxygen (

\text{O}_2

), hydrogen (

\text{H}_2

), or carbon monoxide (

\text{CO}

). (c) After the balloon has expanded and reached the higher altitude, determine the gauge pressure (internal minus external) of the gas inside the balloon.

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