Thank you! The following is all the info I have.

3. (Chandler, 1.13) Suppose an equation of state for a rubber band is = {3) where 1'9 is a constant, L is the length of the rubber band, and the other symbols have their usual meaning. Determine the chemical potential, ,a (T, 15/71), and show that the equation of state satises the analog of the Gibbs-Duhem equation (note that p; = G). 4. Stat Mech requires thinking about probabilities, Let's practice... a) Imagine a box of volume, V, lled with N balls all of diercnt colors (i.e. the balls are distinguishable). What is the probability that all N balls will be in the same half of the box? b} Now imagine that you have 3 balls, one red, one blue, and one green. How many different ways are there of arranging the 3 balls between the two halves of the box? TWhat would be the number of ways if instead the balls were all red, so that you couldn't tell the difference between them? c) Now imagine that you have a number of small boxes that can only t one ball in each box (the boxes are distinguishable, maybe lined in a row...). If you have 5 different boxes and 3 red balls, how many distinguishable ways are there to arrange the balls in the different boxes? Write a general expression for this number of possibilites if there are N boxes and M balls (assuming N > M ). (Aside: Specifying \"distinguishable" vs \"indistinguishable\" balls or particles may at rst glance seem irrelevant to chemistry trust me, it. is very relevant! Suppose you are doing electrolysis of water to create hydrogen gas to power your Toyota Mirai (fuel cell car). No experiment could possibly tell you which particular water molecule ended up being elec- trolyzed to form each H2 molecule. The only possible thing you could do is to isotope label and put in a some fraction of deuterated/heavyr water, but then the D20 and H20 are dis- tinguishable and there would be a very different probability to electrolyze the small amount of D20! get the picture? )