High-concentration effects equilibrium approximation

From experimental data for the ethanol-water system without salt, obtained at 700 and 760 mmHg, it can be seen that within this pressure range the effects of pressure on the equilibrium data are small enough to be within the experimental scatter. In fact, in previous works (8,11,12,13,18,19,23,24,27) there seems to be no clear difference between the equilibrium data at 700 and at 760 mmHg. Errors obtained in the determination of liquid and vapor compositions are approximately 0.05 wt % for the systems without salt. For salt-saturated systems, the same error prevails for the vapor phase, while the error is between 0.1 and 0.2 wt % for liquid phase compositions. The error for the boiling temperature is less than 0.1 °C for the systems without salt, but for saturated solutions the error is much greater from 0.2°C for nonconcentrated solutions to 3°C or more for highly concentrated solutions. 

Neretnieks [5] studied the effects of temperature and concentration on surface diffusion, using a pseudo lineeir technique to approximate the slope of isotherm as depicted in Figure 1. An equilibrium point (c=ce2 and q=q 2) was connected to an origin (c=0 and q=0) by a straight line in order to approximate actual slope of the isotherm at Ce2. It is obvious that his pseudo-linear technique offers poor approximation for highly nonhneeu isotherms, which 6ure often found in industrial applications. 

The importance of linear chromatography comes from the fact that almost all analytical applications of chromatography are carried out xmder such experimental conditions that the sample size is small, the mobile phase concentrations low, and thus, the equilibrixim isotherm linear. The development in the late 1960s and early 1970s of highly sensitive, on-line detectors, with detection limits in the low ppb range or lower, permits the use of very small samples in most analyses. In such cases the concentrations of the sample components are very low, the equilibrium isotherms are practically linear, the band profiles are symmetrical (phenomena other than nonlinear equilibrium behavior may take place see Section 6.6), and the bands of the different sample components are independent of each other. Qualitative and quantitative analyses are based on this linear model. We must note, however, that the assumption of a linear isotherm is nearly always approximate. It may often be a reasonable approximation, but the cases in which the isotherm is truly linear remain exceptional. Most often, when the sample size is small, the effects of a nonlinear isotherm (e.g., the dependence of the retention time on the sample size, the peak asymmetry) are only smaller than what the precision of the experiments permits us to detect, or simply smaller than what we are ready to tolerate in order to benefit from entertaining a simple model. 

In problems that involve the common ion effect, we are usually given the starting concentrations of a weak acid HA and its salt, such as NaA. As long as the concentrations of these species are reasonably high (> 0.1 M), we can neglect the ionization of the acid and the hydrolysis of the salt. This is a valid approximation because HA is a weak acid and the extent of the hydrolysis of the A ion is generally very small. Moreover, the presence of A (from NaA) further suppresses the ionization of HA and the presence of HA further suppresses the hydrolysis of A. Thus we can use the starting concentrations as the equilibrium concentrations in Equation (16.1) or Equation (16.4). 

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