Draw a graph of P(ε) vs. ε for 4 identical molecules that have 3 energy packets (ε) that are randomly distributed over the 4 molecules. Label your axes.
||| _ _ _
|| | _ _
| | | _
For the graph, calculate the probability of each happenstance (ex. ||| vs. _) and graph.
There should be points at (0,⁶/₁₂) (1,⁴/₁₂) (2,¹/₁₂) (3, ¹/₁₂).
If, for a given reaction, E†=0.5ε, then what fraction of the molecules have enough energy to react? Information from previous flashcard.
P(ε) for all ε above 0.5; i.e., |||, ||, and |.
Which of the folllowing are state functions?
Temperature and Volume are state functions; the system does not "care" how it attained its values of temperature or volume.
Consider a system where a weight is suspended from a plunger that sits on an ideal, monoatomic gas. There is one mole of gas and the initial volume is 1.00 L at 298 K. What is the initial external pressure?
Answer: 24.47 atm.
Consider a system where a weight is suspended from a plunger that sits on an ideal, monoatomic gas. There is one mole of gas and the initial volume is 1.00 L at 298 K. The weight is removed isothermally in two separate pieces. After the first piece is removed, the volume is 3.00 L. After the second piece is removed, the volume is 3.50 L. What is the work done by this expansion in Joules?
Work done by the gas has a negative value, 101.3 J = 1 L•atm
No work is done for the second part because there is no opoosing force, and hence no work (all the weight has been removed, the gas is expanding against a vacuum).
w=P₂(V₂-V₁), with Pext=P₂.
Consider a graph of V vs. Pext; infinitesimal change is the integral, a piecewise change is under the curve. The height of a block is given by the right-hand endpoint (i.e. P₂) and the width by the change in volume.
If a gas was expanded in an isolated cylinder, there would be no heat transfer between the environment and the gas. In this case, would the temperature of the gas increase, decrease, or change the same? Why?
The temperature of the gas would decrease because the gas molecules would be more spread out, and thus the energy would be more spread out.