A bicycle-tire manufacturer wishes to verify the consistency of laboratory…

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

Problem

A bicycle-tire manufacturer wishes to verify the consistency of laboratory instruments by determining the universal gas constant

R

from routine quality-control measurements. A technician fills a test tire with pure nitrogen gas, records a pressure of

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

at a temperature of

302\;\text{K}

, and later removes the gas to obtain its mass, measured as

5.18\;\text{g}

. The internal volume of the inflated tire is known from geometric measurements to be

3.40\times10^{-3}\;\text{m}^{3}

. The molar mass of nitrogen is

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

. Nitrogen behaves ideally under the stated conditions. (1) Determine the number of moles of nitrogen originally contained in the tire. (2) Using the measured values, calculate the universal gas constant

R

. (3) Compare your calculated value to the accepted value of

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

by computing the percent error. State whether the instruments appear properly calibrated, justifying your conclusion in terms of the percent error magnitude.

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