For an inert calibration gas X

CHEMISTRY · Multi-part · AP · Chemistry · Properties of Substances and Mixtures · Properties of Substances and Mixtures

Problem

For an inert calibration gas X, the temperature dependence of the second virial coefficient is approximated by

B(T)=b_0-\frac{b_1}{T}

where

b_0=0.020\,\text{L}\,\text{mol}^{-1}

and

b_1=150\,\text{K}\,\text{L}\,\text{mol}^{-1}

. A research team will measure the universal gas constant

R

by collecting the gas in a reservoir kept at a fixed pressure of

0.800\,\text{atm}

. The apparatus permits bath temperatures between

280\,\text{K}

and

350\,\text{K}

. (a) Using the virial equation truncated after the second term, calculate the compressibility factor

Z

for gas X at

T=300\,\text{K}

and at

T=340\,\text{K}

. Show all working and express each

Z

value to four significant figures. (b) For each temperature, compute the percent error that would result from assuming ideal-gas behavior when determining

R

. (c) Based on your quantitative results, recommend which temperature within the allowed range should be selected to minimize the error in

R

. Explain how further increases or decreases in temperature would affect

Z

and the associated error.

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