MediumChemistryHigh School (11–12)States of MatterNumericalBoard Exam AP A-Level IB

A weather balloon is filled with helium at 27 °C…

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A weather balloon is filled with helium at $27\ ^\circ\text{C}$ . It holds $1250\ \text{L}$ at $1.00\ \text{atm}$ . It rises to a height where the pressure is $0.40\ \text{atm}$ and the temperature is $-33\ ^\circ\text{C}$ . The helium does not leak. Treat it as an ideal gas. (a) Find the volume of the balloon at that height. (b) Find the amount of helium. (c) Find the mass of helium, with $M = 4.003\ \text{g/mol}$ .

Need a reminder? The key ideaShow

$PV = nRT$ with $T$ in kelvin and $R$ chosen to match the units of $P$ and $V$ : $8.314\ \text{kPa L K}^{-1}\ \text{mol}^{-1}$ , $0.08314\ \text{L bar K}^{-1}\ \text{mol}^{-1}$ or $0.08206\ \text{L atm K}^{-1}\ \text{mol}^{-1}$ . For a fixed amount of gas, $P_1V_1/T_1 = P_2V_2/T_2$ . The molar mass is $M = dRT/P = mRT/(PV)$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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