While exploring the planet Ardana, the USS Enterprise collected a sample of Zienite, 118Zi318, and gave it to Sally Samarium and Erbie Terbium, members of the science staff, for analysis. Sally collected data on how the volume of the gas responded to pressure, while Erbie measured the response of Zienite's volume to changes in temperature. The data collected is summarized in the following graphs:
Assuming that Zienite is representative of all gases on Ardana answer the following questions.
1. What mathematical relationship would the Ardanians be using for their "Boyle's Law"?
2. What mathematical formula would the Ardanians be using for their "Charles' Law"?
3. Would there still be an absolute zero on Ardana? Explain
4. What limitations, if any, would be placed on pressure?
5. What would be the mathematical relationship for the "Ideal Gas Law" on Ardana?
6. One of the assumptions made in the derivation of the Ideal Gas Law, is that the kinetic energy of gas particles is directly proportional to the temperature, KE=kT. Would this relationship still be true on Ardana? If not, what would be the new relationship?
7. Sketch the plot of P vs T.
8. What would be the new units on R?
I use this exercise to challenge my second year chemistry students. It is assigned as an exercise after we discuss the assumptions of an Ideal Gas and derive the Ideal Gas Law. This exercise helps students see the effect of the assumptions made for the derivation of the Ideal Gas Law.
1. Direct relationship: V=kP or V1/P1=V2 /P2
2. Inverse relationship: VT=k or V1T1=V2T2
3. Probably not because zero volume would be reached only at infinite temperature.
4. Pressure could never reach zero for a real gas, because the volume would be zero.
5. VT=nRP. Note: With this change R would no longer have the same units.
6. Possibly, but there is the possibility that it could be: KE=k/T. This is because if temperature and pressure are inversly proportional to each other and if pressure is due to the collisions of gas particles with the walls of the container then as temperature rises these collisions and the energy associated with them need to decrease.
7. It would be a linear relationship (P=kT).