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

A steel cylinder of volume 40.0 L holds oxygen at 150 bar and 27 °C…

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A steel cylinder of volume $40.0\ \text{L}$ holds oxygen at $150\ \text{bar}$ and $27\ ^\circ\text{C}$ . A hospital uses some of the gas. The pressure falls to $100\ \text{bar}$ , and the temperature is still $27\ ^\circ\text{C}$ . Treat oxygen as an ideal gas. (a) Find the amount of oxygen at the start. (b) Find the mass of oxygen that was used, with $M = 32.00\ \text{g/mol}$ . (c) At $1.00\ \text{bar}$ and $27\ ^\circ\text{C}$ , what volume would the used gas fill?

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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