Thermodynamic Properties of Molecules from

Equation 18.42 is certainly complicated. However, we note two things. First, virtually all of the information required to evaluate equation 18.42 for a molecule is available experimentally, mostly using various spectroscopic techniques. Second, because equation 18.42 is independent of the identity of the molecule, it is a relatively simple task to write a computer program to evaluate Qsys for a given system. As we will see in the next section, once we have an expression for Qjyj, we will be able to derive expressions for various thermodynamic properties. These expressions can also be evaluated by calculator or computer program. In fact, an important use of these equations of statistical thermodynamics is not to verify that they yield numbers that agree with experiment, but to predict the thermodynamic properties at different conditions or for new substances whose thermodynamic properties have not been measured. 

Recall that the major aim of statistical thermodynamics is to be able to calculate the thermodynamic properties of systems using the mathematics of statistics. It has taken us some time and effort to get to this point, because we first had to determine the forms of the partition functions for a molecule. Having done that now, we can turn our attention to thermodynamic properties. 

we will state that even though the exact expression for the partition function Q is somewhat expanded from the partition function q for a monatomic gas, the basic relationships between Q and various thermodynamic functions are the same. That is. 

Unless otherwise noted, all art on this page is Cengage Learning 2014. 

Notice that each expression involves the natural logarithm of Q (or a derivative of the natural logarithm of Q). Recall also that Q for a molecule is defined as the product of five independent q s. Logarithms of products can be rewritten as the sum of logarithms of the individual terms in the product that is, 

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Statistical mechanics is often thought of as a way to predict the thermodynamic properties of molecules from their microscopic properties, but statistical mechnics is more than that because it provides a complementary way of looking at thermodynamics. The transformed Gibbs energy G for a biochemical reaction system at specified pH is given by... 

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