A student injects a measured quantity of dry air into a rigid container and seals it

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

Problem

A student injects a measured quantity of dry air into a

6.20\;\text{L}

rigid container and seals it. Immediately afterward, a pressure gauge reads

1.52\times10^{5}\;\text{Pa}

and a temperature probe inserted through a rubber septum shows

298\;\text{K}

. The mass of air added is determined to be

7.22\;\text{g}

. The average molar mass of dry air may be taken as

28.9\;\text{g}\,\text{mol}^{-1}

. Use these data to estimate the universal gas constant

R

and to evaluate the quality of the result. Assume the air behaves ideally. (1) Determine the number of moles of air in the container. (2) Calculate a numerical value for the universal gas constant

R

using the measured quantities. (3) Using the accepted value

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

, compute the percent error of your experimental value. (4) The laboratory instruments have the following absolute uncertainties: volume

\pm 0.05\;\text{L}

, pressure

\pm 2\;\text{kPa}

, temperature

\pm 1\;\text{K}

, and mass

\pm 0.05\;\text{g}

. Estimate the absolute uncertainty in your calculated value of

R

by appropriate propagation of uncertainties. State clearly whether the accepted value lies within the uncertainty range of your result and comment on the reliability of the experiment.

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