Chapter 4: Problem 1
Consider the development of the Sackur-Tetrode equation for the translational entropy of an ideal gas. a. Evaluate the constant \(C\) in the expression $$ \frac{Z_{r}}{N}=C \frac{T^{5 / 2} M^{3 / 2}}{P} \text {. } $$ where \(T\) is the temperature in \(\mathrm{K}, M\) the molecular weight, and \(P\) the pressure in bars. b. Hence, show that the translational contribution to the entropy is given by $$ \frac{s_{t}}{R}=\frac{5}{2} \ln T+\frac{3}{2} \ln M-\ln P-1.1516 . $$ c. The experimentally measured value of the entropy for vaporous neon at its boiling point \((27.1 \mathrm{~K})\) and a pressure of one bar is \(96.50 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}\). To verify the theoretical formulation leading to the Sackur-Tetrode equation, compare your predicted value with the given experimental result. Hint: Keep this problem in mind for future calculations
Short Answer
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Key Concepts
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