A rigid 10.0 L vessel contains 2.00 mol of an unknown gas X
CHEMISTRY · Multi-part · AP · Chemistry · Properties of Substances and Mixtures · Properties of Substances and Mixtures
Problem
A rigid 10.0 L vessel contains 2.00 mol of an unknown gas X. The measured pressures at several temperatures are shown in the table below.
Temperature T (K) | Measured Pressure P_meas (atm)
140 | 1.85
160 | 2.05
180 | 2.25
200 | 2.40
220 | 2.55
For each temperature, the pressure Pideal that would be predicted for an ideal gas can be calculated from the amount of gas present, the temperature, and the volume of the vessel.
(a) For each temperature in the table, calculate Pideal and the fractional deviation φ=PidealPmeas−1. Present your results in a clearly labeled table.
(b) Plot (conceptually, no actual graph required) the fractional deviation φ versus 1/T. Describe the qualitative shape of the plot and state whether the relationship appears approximately linear over the temperature range provided.
(c) Using the two extreme data points (140 K and 220 K), determine the slope of the best‐fit line that relates φ to 1/T. Express the line in the form φ=m(T1)+b, identifying m and b.
(d) Employ your linear model to predict (i) the fractional deviation φ and (ii) the corresponding measured pressure of gas X at 130 K.
(e) Discuss at least one limitation of using the linear model from parts (b)–(d) to extrapolate the behavior of gas X at temperatures significantly below 140 K.