The table below lists measured pressures for a 0.250 mol sample of an ideal gas…
CHEMISTRY · Multi-part · A Level · Chemistry · Amount of substance · Amount of substance
Problem
The table below lists measured pressures for a 0.250 mol sample of an ideal gas confined in a rigid 5.00 L vessel at various temperatures.
Temperature (K)
Measured Pressure (atm)
250
1.02
300
1.23
350
1.43
400
1.63
The same gas sample is now subjected to the following experimental cycle:
1. It is cooled at constant volume from 400 K to 200 K.
2. At 200 K the vessel is fitted with a movable piston and the gas is compressed isothermally until its pressure equals the original 1.23 atm measured at 300 K.
3. Finally, the gas is heated at the new constant volume back to 400 K.
Assume ideal behavior throughout.
(a) Using the data in the table, determine the proportionality constant that relates pressure and temperature for this gas in the rigid vessel. Include the appropriate units.
(b) For the cooling step (400 K → 200 K at constant volume), calculate the factor by which collision frequency with the vessel walls changes, and state whether this factor represents an increase or decrease.
(c) For the isothermal compression at 200 K, derive an expression for the new vessel volume in terms of the initial 5.00 L volume and the pressures involved. Then calculate its numerical value.
(d) Combining all three steps, compute the overall factor by which the average spacing between gas particles has changed after the complete cycle compared to the original state at 400 K and 5.00 L. Provide reasoning that clearly distinguishes the effects of temperature change from those of volume change.