Sackur- Tetrode

On applying Stirling s approximation, replacing V/N by kT/P, and using Eq. XVII-20 and setting P = 1 atm, the final result, known as the Sackur-Tetrode equation, is... 

The standard entropies of monatomic gases are largely determined by the translational partition function, and since dris involves the logarithm of the molecular weight of the gas, it is not surprising that the entropy, which is related to tire translational partition function by the Sackur-Tetrode equation,... 

The Sackur-Tetrode equation was derived for the molar entropy for a monatomic gas to be... 

The standard (298.15 K and 10" kPa pressure) entropies of monatomic ions in the gas phase may be estimated by using the Sackur-Tetrode equation ... 

Term (2) calculated by the high-accuracy multistep CBS-APNO method (Section 5.5.2.2b) was 341.2 kcal mol-1 or 1426 kJ mol-1. The Sackur-Tetrode equation for the gas-phase entropy of the proton was mentioned in this regard, but in fact the algorithm automatically handles this. 

Equation 2.8-2 is referred to as the Sackur-Tetrode equation. Since we have expressions for these three properties, we can calculate the properties U, H, A, and CP ... 

Use the Sackur-Tetrode equation [Eq. (76)] to calculate the standard molar entropy of neon considered an ideal gas at 298 K. 

We will illustrate the method by outlining the calculation of the (differential) entropy of adsorption. For S, we use the Sackur-Tetrode expression, Eq. (76) of Chapter 5, with a term added for the internal degrees of freedom ... 

The first term, called the (differential) configurational entropy, results from the different possible ways the adsorbed molecules can occupy the surface sites. The last two terms, which are negative, are the Sackur-Tetrode entropy due to the lost translational degrees of freedom of the gaseous molecules. 

The self diffusion of particles and the entropy of the system are both a result of random particle motions. With the Sackur-Tetrode equation the molar entropy, S of the above system can be calculated at temperature Tand pressure p ... 

Upper values data from most extensive calculations lower values best experimental data available, thermodynamic functions calculated from partition functions by means of the Sackur-Tetrode equation... 

Sjg. One uses the Sackur-Tetrode equation for the translational entropy of a monatomic ion in the gas phase and it gives... 

MG° = AGJh+ -AGbh+)- It has been usually assumed that these free energies differ from enthalpies for proton transfer by a TAS° term approximately equal to that calculable from the symmetry changes in the reaction. Thus the AG and PA values differ by the entropy term calculated for a free proton by the Sackur-Tetrode equation (7.75 kcal mol" ) and by the entropy term because of symmetry changes expressed in Eq. (9). 

A proton contains no electrons and its free energy cannot be calculated quantum mechanically. Calculation of this energy using the standard equations of thermodynamics and the Sackur-Tetrode equation [15] yields the same value as can be deduced experimentally from the NIST database. The translational energy of 1.5RT combined with PV = RT and H= E PV yields a value of H° (H+) equal to 5/2(RT) or 1.48 kcal/mol. Use of the Sackur-Tetrode equation yields the entropy, TS(H+) = 7.76 kcal/mol at 298 K and latm pressure. Finally, since G = H-TS, G°(H+) = -6.28 kcal/mol. 

The Ggas H+ value also cannot be determined quantum mechanically. Its value, however, has less uncertainty, and is the same whether determined from experimental values available in the NIST website or from the Sackur-Tetrode equation [15], and is consistently accepted as -6.28 kcal/mol for a standard state of 1 atm [1,2]. 

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