(I) How does the number of atoms in a 27.5-gram gold ringcompare to the number in a silver ring of the same mass?

I) We consider atoms of rubidium in the gaseous state. The molar mass of rubidium is M-87 g/mol. 1) At T=900 K, the rubidium acts like and ideal gas. At this temperature the free energy F is given by h2 F = -kgT ln Z where Z = with z N! V and A = (; 1/2 N being the number of 2TmkBT particles of the gas and m the mass of one particle. a) Explain the presence of the N! in the equation. b) Derive the expression of F as a function of T and the number of particles per unit volume, n=N/V. c) Show that u = T In(nA) where 7 is a quantity that you will express as a function of T.

7) Assuming a typical nitrogen or oxygen molecule is about 0.3 nm in diameter, what percent of the room you are sitting in is taken up by the volume of the molecules themselves? Assume the room is at 1 atm and 23°C and that the molecule can be approximated as a cube.