Physical Chemistry , 1st ed.

difference between the dissociation limit and the very bottom of the electronic potential well is labeled De. However, in realit ...

Now, calculating the electronic partition function: qelect 1 exp qelect2.03 1080 Let us check to see if we need to include ...

nonzero minimum energy of vibration (the “zero-point energy”). Because vi- brational motions of molecules represent another form ...

a 2 in the denominator of the exponent) and assume that each vibrational level is singly degenerate so that giequals 1: qvibeh ...

Example 18.4 For I 2 (g),vis 310 K. Calculate qvibfor I 2 at the following temperatures: a.30 K b.1000 K Solution a.At 30 K, we ...

up to 3N6 terms. One way of writing this is to use the symbol;qvibcan be written as qvib 3 N 6 j 1   i 1 gieE^ j/kT (18 ...

Similarly, the other two vibrational temperatures are 5163 K and 2287 K. All three vvalues are larger than the stated temperatu ...

In Chapter 14, we found that the rotational energy of a diatomic molecule is Erot J(J 2 I 1)^2  (18.27) where Jis the rotati ...

(Note that the limits on the integral stay the same.) The integral in equation 18.30 has a known solution; it has the form 0 e ...

that affects the number of possible wavefunctions (that is, the degeneracies), and thus the partition function. Ultimately, we w ...

Scenario 2: fermion nuclei (that is, half-integer spin nuclei) tottrans vib elect nuc rot antisym sym sym sym* sym sym,J ...

symmetric nuclear wavefunctions and 2I^2 I2(^12 )^2 ^12 1 antisymmet- ric nuclear wavefunction. Since all rotational state ...

over all of the Jvalues, so we can substitute ^12 times the summation over all J’s: qrot,nuc(2I 1)^2 ^12   all J’s (2J 1 ...

won’t go into). The symmetry number is ultimately equal to the number of pure rotational symmetry operations in the point group ...

Example 18.8 Calculate the rotational partition function of gaseous NH 3 at 1000 K. The ro- tational temperatures are 13.6 K, 13 ...

(Nfactorial).N, recall, is the number of molecules in the system. For indistin- guishable particles, then, the overall partition ...

SkT   ln T Q  V ln Q (^1)  (18.48) AkT(ln Q 1) (18.49) GkTln Q (18.50) Notice that each expression involves the nat ...

ofEwith respect to temperature and come up with a simple expression for the heat capacity: CVNk  ^3 2  ^3 2  (^)  3 N* 6 ...

Example 18.9 Calculate the constant-volume heat capacity of 1 mole of gaseous water at 727°C and 1 bar pressure. Compare this to ...

Algebraically, we can bring the reactants to the other side of the “equation” and rewrite equation 18.55 as (^) CC (^) DD AA  ...