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Devise a temperature scale, abbreviated G, for which the magnitude of the ideal gas constant is \(5.52 \mathrm{JG}^{-1} \mathrm{mol}^{-1}\).

Calculate the pressure exerted by benzene for a molar volume of \(2.00 \mathrm{L}\) at \(595 \mathrm{K}\) using the Redlich-Kwong equation of state: \\[ \begin{aligned} P &=\frac{R T}{V_{m}-b}-\frac{a}{\sqrt{T}} \frac{1}{V_{m}\left(V_{m}+b\right)} \\\ &=\frac{n R T}{V-n b}-\frac{n^{2} a}{\sqrt{T}} \frac{1}{V(V+n b)} \end{aligned} \\] The Redlich-Kwong parameters \(a\) and \(b\) for benzene are \(452.0 \mathrm{bar} \mathrm{dm}^{6} \mathrm{mol}^{-2} \mathrm{K}^{1 / 2}\) and \(0.08271 \mathrm{dm}^{3} \mathrm{mol}^{-1},\) respec- tively. Is the attractive or repulsive portion of the potential dominant under these conditions?

An initial step in the biosynthesis of glucose \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) is the carboxylation of pyruvic acid \(\mathrm{CH}_{3} \mathrm{COCOOH}\) to form oxaloacetic acid HOOCCOCH \(_{2} \mathrm{COOH}\) \\[ \mathrm{CH}_{3} \mathrm{COCOOH}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{HOOCCOCH}_{2} \mathrm{COOH}(s) \\] If you knew nothing else about the intervening reactions involved in glucose biosynthesis other than no further carboxylations occur, what volume of \(\mathrm{CO}_{2}\), is required to produce \(1.10 \mathrm{g}\) of glucose? Assume \(P=1\) atm and \(T=298 \mathrm{K}\).

When Julius Caesar expired, his last exhalation had a volume of \(450 . \mathrm{cm}^{3}\) and contained 1.00 mole percent argon. Assume that \(T=300 . \mathrm{K}\) and \(P=1.00\) atm at the location of his demise. Assume further that \(T\) has the same value throughout Earth's atmosphere. If all of his exhaled Ar atoms are now uniformly distributed throughout the atmosphere, how many inhalations of \(450, \mathrm{cm}^{3}\) must we make to inhale one of the Ar atoms exhaled in Caesar's last breath? Assume the radius of Earth to be \(6.37 \times 10^{6} \mathrm{m}\). [Hint: Calculate the number of Ar atoms in the atmosphere in the simplified geometry of a plane of area equal to that of Earth's surface. See Problem P1.20 for the dependence of the barometric pressure and the composition of air on the height above Earth's surface.

A balloon filled with 11.50 L of Ar at \(18.7^{\circ} \mathrm{C}\) and 1 atm rises to a height in the atmosphere where the pressure is 207 Torr and the temperature is \(-32.4^{\circ} \mathrm{C}\). What is the final volume of the balloon? Assume that the pressure inside and outside the balloon have the same value.

Carbon monoxide competes with oxygen for binding sites on the transport protein hemoglobin. CO can be poisonous if inhaled in large quantities. A safe level of CO in air is \(50 .\) parts per million (ppm). When the CO level increases to \(800 .\) ppm, dizziness, nausea, and unconsciousness occur, followed by death. Assuming the partial pressure of oxygen in air at sea level is 0.20 at \(m\), what proportion of \(\mathrm{CO}\) to \(\mathrm{O}_{2}\) is fatal?

Rewrite the van der Waals equation using the molar volume rather than \(V\) and \(n\).