For a diatomic gas near room temperature, the internal partition function is simply the rotational partition function multiplied by the degeneracy Ze of the electronic ground state.

Calculate the entropy of a mole of oxygen (Ze = 3) at room temperature and atmospheric pressure, and compare to the measured value.

(b) Calculate the chemical potential of oxygen in earth's atmosphere near sea level, at room temperature. Express the answer in electron-volts.

Solution Preview

We can calculate the entropy from the partition function as follows. The partition function for an ideal gas is:

Z = Z1^(N)/N!

where Z1 is the partition function for a single molecule. Z1 factorizes:

Z1 = Z_{trans}*Z_{rot}*Z_{vib}*Z_{elec}*etc.

The translational part of the partition function is:

Z_{trans} = V*(2 pi m kT/h^2)^(3/2)

Since a partition function must be dimensionless the factor

(2 pi m kT/h^2)^(3/2)

must have the dimensions of an inverse volume. You can easily check this. This is the volume at which quantum effects become important. We define the quantity:

Vq = (2 pi m kT/h^2)^(-3/2)

to simplify expressions, but note that Vq depends on the temperature.

We ignore the vibrational part of the partition function and the electronic part is given by the degeneracy of the ground state, which ...

... this directly in the formula for the entropy. ... The chemical potential for the gas as a function ... In case of diffusive equilibrium, chemical potentials are equal ...

... Similarly chemical potential can be determined as the rate of change of entropy with respect to N while the temperature can be expressed as rate of change of ...

... in many forms, such as heat, light, chemical energy, and ...Chemicals may also be considered from a potential energy ... This is also commonly referred to as entropy. ...

... of the component and solubility.For example, some chemicals do not ... covalent bonds of a solute affect the entropy of an ... is a type of a strong chemical bond that ...

... together with the fact that the total entropy can only ... systems that have the same number of chemicals of each ... As the battery is used, the chemical reactions in ...

... and atmospheric pressure, compute the internal energy, the enthalpy, the Helmholtz free energy, the Gibbs free energy, the entropy, and the chemical potential. ...

... of free energy, enthalpy and entropy, the calculated ...Chemical and Engineering News, 38, 46, August, (1960 ... Commutator for Resistance and Potential M easurements ...