A sealed rigid metal sphere contains a sample of oxygen gas

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

Problem

A sealed rigid metal sphere contains a sample of oxygen gas. During a calibration run, the pressure inside the sphere is measured at several temperatures, producing a set of data that lie on a straight line when pressure

P

(in kPa) is plotted versus temperature

T

(in

^{\circ}\!\text{C}

). The line passes through the points

(20^{\circ}\!\text{C},\,101\,\text{kPa})

and

(-273^{\circ}\!\text{C},\,0\,\text{kPa})

. The internal volume of the sphere is

2.00\,\text{L}

and the amount of gas is later determined by chemical analysis to be

0.0800\,\text{mol}

. (a) Identify the physical significance of the temperature at which the line intersects the horizontal axis. (b) Using the assumptions that characterize an ideal gas, explain why the pressure–temperature data are expected to fall on a straight line for this experiment. (c) Calculate the theoretical numerical value of the slope

\displaystyle \frac{\Delta P}{\Delta T}

of the pressure–temperature graph (expressed in \text{kPa}/^{\circ}\!\text{C}) for the given amount of gas and volume. Compare the sign and magnitude of your calculated value with the trend shown by the experimental data, commenting briefly on any agreement or discrepancy.

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