Versus molality

Figure 8.3 Schematic plot of mean ionic activity coefficient y versus molality (m) for typical strong electrolytes [1 1 (e.g., HC1), light dashed line 2 1 (e.g., H2S04), heavy dashed line], showing the extreme deviations from ideality (dotted line) even in dilute solutions.

Figure 6 Viscosity of [bmim][BF4] versus molal concentration of chloride added as [bmim]Cl at 20 °C (where [bmim] is the l-butyl-3-methylimidazolium cation).

Standard electrode potentials are based on electrolytes of unit activity, with a hypothetical ideal molality of one . Raw laboratory data arrive as simple e.m.f. values versus molality. How do we find ° ... 

Figure 9.7-3 Solute fugacity in real and ideal Henry s law solutions, (ri) Solute fugacity versus mole fraction. (b) Solute fugacity versus molality.

Figure V-25 Plot of log,Qy+ versus molality of aqueous NiBr2 solutions at 298.15 K. Solid line SIT, e(Ni, Br ) = 0.268 Experimental data from [78LIB/MAC],...

Figure V-26 Plot of osmotic coefficient versus molality of aqueous NiBr2 solutions at...

Figure V-28 Plot of logjo 7+ versus molality of aqueous Ni(C104)2...

Fig. 17.4. Stoichiometric mean ionic activity of HCl (a ,Hci) versus molality of HCl. Crosses are data points from Table 17.2 dotted line is Henry s Law, having an activity of 1.0 at 1.0 molal HCl. The stoichiometric mean ionic activity coefficient at muci =0J sxy/xz = 0.772.

The importance of activity coefficients is evident in Figure 17.6, which shows measured y versus molal concentration for selected salts in 350°C hydrothermal solutions. Activity coefficient corrections (that is, correction to the concentration to get the activity) of one to two orders of magnitude such as these are not at all uncommon in aqueous systems. 

Example 4.1. Thermodynamic properties of isobutane were measured at subcritical temperatures from 70°F (294.29°K) to 250°F (394.26°K) over a pressure range of 10 psia (68.95 kPa) to 3000 psia (20.68 MPa) by Sage and Lacey. Figure 4.1 is a log-log graph of pressure (psia) versus molal volume (fP/lbmole) of the experimental two-phase envelope (saturated liquid and saturated vapor) using the tabulated critical conditions from Appendix I to close the curve. Shown also is an experimental isotherm for 190°F (360.93°K). Calculate and plot 190°F isotherms for the R-K equation of state and for the ideal gas law and compare them to the experimental data. 

Figure 7. Log (Sq/S) for acetone (upper curves) and HCN (lower curves) versus molality of added salt in aqueous solutions. (After Reference 1, p. 271).

FIGURE 12.3 Activity coefficient and osmotic coefficient versus molality for urea in water (From J. Rosgen, B. M. Pettitt, and D. W. Bolen, 2004, Uncovering the Basis for Nonideal Behavior of Biological Molecules, Biochemistry, 43, 14472 J. Rosgen, B. M. Pettitt, J. Perkyns, and D. W. Bolen, 2004, Statistical Thermodynamic Approach to the Chemical Activities in Two-Component Solutions, Journal of Physical Chemistry B, 108, 2048.)... 

Figure 15.5 B versus molality for several salts. Data from Pitzer and Brewer (1961).

The prediction from the theoretical argument above, that a solute activity coefficient in a dilute solution is a linear function of the composition variable, is borne out experimentally as illustrated in Fig. 9.10 on page 264. This prediction applies only to a nonelectrolyte solute for an electrolyte, the slope of activity coefficient versus molality approaches —oo at low molality (page 290). 

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