Ideal gas equation of state.

I need help for question#3 (as attached). Is the equation of state refers to PV=NRT?

Canonical partition function Q(N,V,T)

I have trouble to answer the question #5, as attached. Since canonical function Q(N,V,T) seems to be a statiscal function, so how do I calculate its energy, entropy, pressure and chemical potential from Q(N,V,T)?

Canonical Distribution

Consider the binomial coefficient...For large values of N and m, show that it has its largest value when m=N/2 (HINT: use Stirling's formula). What is the maximum value? (See attachment for full questions)

Grand canonical partition function

I don't how to do problem 2 (as attached)

Mass of unknown metal, liquid

I need help calculating the density of an unknown metal for an experiment in my Lab class. We were using a pycnometer, water, and an unknown liquid, and an unknown metal. Part one of the experiment deals with getting the density of the unknown liquid, which I think I did okay. I am having trouble with part 2 of the lab in which I need to find the density of the unknown metal and then identify it. Here is the recorded data that I have to work with: Mass of empty flask= 32.722g Mass of flask + unknown liquid= 67.770g Mass of flask + unknown metal = 57.319g Mass of flask + unknown metal + water= 74.650g Mass of flask + water = 59.364g Temp of water = 22 degrees C (at this temp, den... click for more