F , molality

The latest weather report includes the following statement The temperature is 78°F, barometric pressure is 29.9 inches, and the relative humidity is 87%." From this information, estimate the mole fraction of water in the air and the dew point ( F), molal humidity, absolute humidity, and percentage humidity of the air. 

A == absorption factor OnIKVn D — molal distillate rate F molal feed rate K = equilibrium constant = y/x m = ratio, see page 352 Ml = mols of liquid in feed My mols of vapor in feed... 

The following data (for 25°C) were obtained at the pzc for the Hg-aqueous NaF interface. Estimate and plot it as a function of the mole fraction of salt in solution. In the table,/ is mean activity coefficient such that a = f m , where m is mean molality. 

FIG. 2-29 Enthalpy-concentration diagram for aqueous sodium hydroxide at 1 atm. Reference states enthalpy of liquid water at 32 F and vapor pressure is zero partial molal enthalpy of infinitely dilute NaOH solution at 64 F and 1 atm is zero. [McCahe, Trans. Am. Inst. Chem. Eng., 31, 129(1935).]... 

Heat of Precipitation. Entropy of Solution and Partial Molal Entropy. The Unitary Part of the Entropy. Equilibrium in Proton Transfers. Equilibrium in Any Process. The Unitary Part of a Free Energy Change. The Conventional Standard Free Energy Change. Proton Transfers Involving a Solvent Molecule. The Conventional Standard Free Energy of Solution. The Disparity of a Solution. The E.M.F. of Galvanic Cells. 

The symbol used is dependent upon the method of expressing the concentration of the solution. The recommendations of the IUPAC Commision on Symbols, Terminology and Units (1969) are as follows concentration in moles per litre (molarity), activity coefficient represented by y, concentration in mols per kilogram (molality), activity coefficient represented by y, concentration expressed as mole fraction, activity coefficient represented by f... 

Values taken from S. Glasstone. Thermodynamics for Chemists. D. Van Nostrand Company Inc., Toronto, p. 443 (1947). The values tabulated in this reference were taken from D. N. Craig and G. W. Vinal, J. Res. Natl. Bur. Stand.. Thermodynamic Properties of Sulfuric Acid Solutions and Their Relation to the Electromotive Force and Heat of Reaction of the Lead Storage Battery", 24, 475-490 (1940). More recent values at the higher molality can be found in W. F. Giauque. E. W. Hornung. J. E. Kunzler and T. R. Rubin, The Thermodynamic Properties of Aqueous Sulfuric Acid Solutions and Hydrates from 15 to 300° K", J. Am. Chem. Soc.. 82, 62-70 (1960). 

Sei f-Test 8.9B Calculate the molality of methanol in aqueous solution, given that the mole fraction of methanol is 0.250. 

Step 1 Convert the observed freezing-point depression into solute molality by writing F.q. 5b in the form... 

The concentration of substances added e.g. to maintain a certain pH is sometimes not stated exactly in the original report this is indicated by an x. Concentrations are given in units as reported if not stated otherwise (M = molarity m = molality, F equal to M). 

Figure 1.86. Variation in chemical compositions (in molal unit) of hydrothermal solution with temperature. Thermochemical data used for the calculations are from Helgeson (1969). Calculation method is given in Shikazono (1978a). Chloride concentration in hydrothermal solution is assumed to be 1 mol/kg H2O. A-B Na concentration in solution in equilibrium with low albite and adularia, C-D K concentration in solution in equilibrium with low albite and adularia, E-F HaSiOa concentration in equilibrium with quartz, G-H Ca + concentration in equilibrium with albite and anorthite (Shikazono, 1978a, 1988b).

At 900 °F the equilibrium constant for this reaction is 5.62 when the standard states for all species are taken as unit fugacity. If the reaction is carried out at 75 atm, what molal ratio of steam to carbon monoxide is required to produce a product mixture in which 90% of the inlet CO is converted to C02 ... 

The second approach involves simultaneous variation of the weight of catalyst and the molal flow rate so as to maintain W/F constant. One then plots the conversion achieved versus linear velocity, as shown in Figures 6.4c and 6Ad. If the results are as indicated in Figure 6Ad, mass transfer limitations exist in the low-velocity regime. If the conversion is independent of velocity, there probably are no mass transfer limitations on the conversion rate. However, this test is also subject to the sensitivity limitations noted above. 

Species Effluent molal flow rate F iCpi... 

Equations (d) and (e) contain two unknowns D and B, which can be determined once F, XF, XB, and XD are specified. In addition, if the assumption of constant molal overflow is made, then the liquid L and vapor flows V are... 

C-t, which means, of course, that the ideal solution model is adopted, no matter the nature or the concentrations of the solutes and the nature of the solvent. There is no way of assessing the validity of this assumption besides chemical intuition. Even if the activity coefficients could be determined for the reactants, we would still have to estimate the activity coefficient for the activated complex, which is impossible at present. Another, less serious problem is that the appropriate quantity to be related with the activation parameters should be the equilibrium constant defined in terms of the molalities of A, B, and C. As discussed after equation 2.67, A will be affected by this correction more than A f//" (see also the following discussion). 

The effect of concentration of free (molecular) ammonia on the activity of the electrolyte was derived mainly from two 80 C data points of Miles and Wilson having 16 to 17 molal free ammonia concentration. Data points below 0.2 ionic strength were fitted by application of Kielland s estimation of ionic activity coefficients(6 2). Details are presented elsewhere(45), together with graphs giving partial pressures of ammonia and hydrogen sulfide for temperatures from 80 to 260 F over a range of liquid concentration. 

The standard state for the mean ionic activity coefficient is Henry s constant H., f is the standard-state fugacity for the activity coefficient f- and x. is the mole fraction of electrolyte i calculated as though thi electrolytes did not dissociate in solution. The activity coefficient f is normalized such that it becomes unity at some mole fraction xt. For NaCl, xi is conveniently taken as the saturation point. Thus r is unity at 25°C for the saturation molality of 6.05. The activity coefficient of HC1 is normalized to be unity at an HC1 molality of 10.0 for all temperatures. These standard states have been chosen to be close to conditions of interest in phase equilibria. 

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