Physical Chemistry , 1st ed.

nuclei. Many of these aspects are ultimately based on the physical interactions discussed in this chapter. NMR has found some us ...

the appropriate amount of group theory thrown in, would show that magnetic spectroscopic techniques can determine a lot about at ...

16.2 Magnetic Fields and Dipoles, and Electric Charges 16.1.What is the difference between a magnetic field vector and a magneti ...

16.25.Calculate the strength of the magnetic field necessary to observe NMR signals of the NMR-active nuclei from exer- cise 16. ...

17 T HERMODYNAMICS IS ONE OF THE FEW TOPICS that one can ap- proach from two completely different perspectives and arrive at the ...

dynamics must recognize that. It is why we have put off a discussion of statis- tical thermodynamics until after our treatment o ...

n 2 objects in subsystem 2, and niobjects in the ith subsystem, then the num- ber of ways of accomplishing this arrangement, lab ...

But we can also use equation 17.3 if we first determine the probabilities of each score in the grades. Since the score of 0 does ...

function over all possible arrangements. For balls in boxes, summing the prob- abilities is easily done. But for gaseous systems ...

tronic, translational, rotational, vibrational, and other quantum states. We will denote the energy level of the gas particle as ...

each drawing, the occupation numbers N 0 ,N 1 ,N 2 , and N 3 are listed. By ap- plying equation 17.7, we can see that W(1, 0, 1, ...

the system will be represented by each drawing in Figure 17.6. Because there are more ways of making a system with the occupatio ...

If we increase the number of particles as well as the number of possible mi- crostates, an interesting situation develops. As lo ...

In order to maximize ln in terms of the two constraints, we can combine the equations for ln ,N, and Einto a single linear combi ...

where we have used the fact that (^) iNiN. Since e^ is a constant (eis a con- stant and is a constant), we factor that term out ...

The Nand qterms cancel:  N N k i g g k ie e     i k and we can combine the two exponentials algebraically:  N N k i ...

law of thermodynamics says that the change in energy of a system can be partitioned into heat and work. Using the variables from ...

Compare this equation with another equation that can be derived from ther- modynamics:   V E  T 1  (1  / p T)  p ...

q 4  1  4 2.80  10 ^11  4 7.84  10 ^22  4 2.19  10 ^32 q 4 This second example shows how sensitive qis to the val ...

The right side of this equation is most of the right side of equation 17.33. Substituting: ENkT^2   ln T q V (17.34) wher ...