Thermodynamic Data at 1 atm and

Pj), mole fraction (xj), and concentration (Cj). For these units the standard state is defined as unit activity Oj, which is typically Pj = 1 atm and 298 K, or Xj = 1 for pure liquid at 1 atm and 298 K, or C = 1 mole/liter at 298 K, respectively. Students have seen the first two of these for gases and liquids in thermodynamics. We wiU use concentration units wherever possible in this course, and the natural standard state would be a 1 molar solution. However, data are usually not available in this standard state, and therefore to calculate equilibrium composition at any temperature and pressure, one usually does the calculation with Pj or Xj and then converts to Cj ... 

The reverse rate constants for the elementary reactions used in the present work were caJculated from the forward rate constants and the equilibrium constant by assuming microscopic reversibility. Standard states used in tabulations of thermodynamic data are invariably at 1 atm and the temperature of the system. Since concentration units were required for rate constant calculations, a conversion between Kp and Kc was necessary. Values of Kp were taken from the JANAF Thermochemical tables (1984). Kc was calculated from the expression ... 

The thermodynamic quantities listed are for one mole of substance in its standard state, that is at 1 atm pressure. The enthalpies and free energies of formation of substances are the changes in those thermodynamic properties when a substance in its standard state is formed from its elements in their standard states. The standard state of an element is its normal physical state at 1 atm, and for the data given in these tables, 298.15 K. The entropies listed are absolute in the sense that they are based on the assumption that the entropy of a pure substance is zero at the absolute zero of temperature. 

The four-electron reduction of oxygen [reaction (I)] is very irreversible and therefore experimental verification of the thermodynamic reversible potential of this reaction is very difficult. The exchange current densities for reactions (I) and (II) are typically 10" -10" A/cm of real surface area for Pt and other noble metals at room temperatures. Any other side reaction, even if slow and otherwise difficult to detect, may compete with reaction (I) or (II) in establishing the rest potential. Indeed, unless special experimental procedures are used, the thermodynamic potential cannot be obtained at ambient temperature in aqueous electrolytes. Even on the most active platinum electrode in pure acid or alkaline aqueous solution under ordinary conditions, the rest potential in the presence of oxygen at 1 atm and ambient temperature usually does not exceed 1.1 V vs. the NHE and most often has a value close to 1.0 V. In early work on O2 electrochemistry, before reliable thermodynamic data were available, the potential 1.08 V vs. RHE was considered as the reversible value for reactions (I) and (II). 

Given in the literature are vapor pressure data for acetaldehyde and its aqueous solutions (1—3) vapor—liquid equilibria data for acetaldehyde—ethylene oxide [75-21-8] (1), acetaldehyde—methanol [67-56-1] (4), sulfur dioxide [7446-09-5]— acetaldehyde—water (5), acetaldehyde—water—methanol (6) the azeotropes of acetaldehyde—butane [106-97-8] and acetaldehyde—ethyl ether (7) solubility data for acetaldehyde—water—methane [74-82-8] (8), acetaldehyde—methane (9) densities and refractive indexes of acetaldehyde for temperatures 0—20°C (2) compressibility and viscosity at high pressure (10) thermodynamic data (11—13) pressure—enthalpy diagram for acetaldehyde (14) specific gravities of acetaldehyde—paraldehyde and acetaldehyde—acetaldol mixtures at 20/20°C vs composition (7) boiling point vs composition of acetaldehyde—water at 101.3 kPa (1 atm) and integral heat of solution of acetaldehyde in water at 11°C (7). 

Much is known about the surface tensions between surfactant/ water mixtures and air at 1 atm. However (except for thermodynamic equations), hardly anything is known about tensions between aqueous solutions saturated with CO2 at 10 MPa and their conjugate C02 rich phases. Although interfacial tension measurements at such pressures are very uncommon, values of the capillary number and their dependence on surfactant and hydrocarbon structures cannot be determined without such data. 

Table III. Some properties of the divalent cations of elements with atomic numbers twenty to thirty, at 25°C and 1 atm pressure. Radii are in 6 fold coordination (33). EN values are from Allred ( 2 ) Thermodynamic data for Ca, Cu and Zn are from Parker...

Table 2.5 shows the thermodynamic behavior of the water ionization reaction. The variation of log Kjy and AG (molal scale for ions, mole fraction scale for water) with temperature at a fixed pressure of 1 atm and the variation of these quantities with pressure at 25°C are given. These data can be used to obtain the enthalpy change of reaction, AH, and the volume change of reaction, AV. ... 

The gas constant R is frequently encountered in thermodynamics, and so its value will be determined. Use is made of the fact, derived by extrapolating experimental data for a number of gases to zero pressure, that 1 mole of an ideal gas occupies 22.414 liters at 1 atm. pressure and a temperature of 273.16° K. It follows, therefore, that in equation (5.1), P is 1 atm., V is 22.414 liters mole " and T is 273.16° K hence. 

From the principles of thermodynamics and certain thermodynamic data the maximum extent to which a chemical reaction can proceed may be calculated. For example, at 1 atm pressure and a temperature of 680°C, starting with 1 mole of sulfur dioxide and mole of oxygen, 50% of the sulfur dioxide can be converted to sulfur trioxide. Such thermodynamic calculations result in maximum values for the conversion of a chemical reaction, since they are correct only for equilibrium conditions, conditions such that there is no further tendency for change with respect to time. It follows that the net rate of a chemical reaction must be zero at this equilibrium point. Thus a plot of reaction rate [for example, in units of g moles product/(sec) (unit volume reaction mixture)] vs time would always approach zero as the time approached infinity. Such a situation is depicted in curve A of Fig. 1-1, where the rate approaches zero asymptotically. Of course, for some cases equilibrium may be reached more rapidly, so that the rate becomes almost zero at a finite time, as illustrated by curve B. 

A binary stream at the rate of 1000 kmol/h containing 35% mole of component 1 (the lighter component) is to be separated in a distillation column to produce 95% component 1 in the distillate and 90% component 2 in the bottoms. The column will have a partial reboiler and a partial condenser, and will operate at 1 atm. It is proposed to utilize an existing hot process stream in the plant as a heat source for the reboiler, which limits the reboiler duty to 58 x 10 kJ/h. Using either the Y-X diagram or the H-X diagram, determine the number of theoretical trays required, the optimum feed location, the product rates, and the condenser duty. Assume feed thermal conditions that result in a saturated liquid at the feed tray pressure. Use thermodynamic data from Problem 6.1. 

The column will operate at 1 atm with a total condenser at the bubble point and a reflux ratio of 3.0. The thermodynamic data in Problem 6.1 may be used for this mixture. The feeds are assumed to be saturated liquids at feed tray conditions. 

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