Saturation curves

Two additional illustrations are given in Figures 6 and 7 which show fugacity coefficients for two binary systems along the vapor-liquid saturation curve at a total pressure of 1 atm. These results are based on the chemical theory of vapor-phase imperfection and on experimental vapor-liquid equilibrium data for the binary systems. In the system formic acid (1) - acetic acid (2), <() (for y = 1) is lower than formic acid at 100.5°C has a stronger tendency to dimerize than does acetic acid at 118.2°C. Since strong dimerization occurs between all three possible pairs, (fij and not... 

Direct quantitation of receptor concentrations and dmg—receptor interactions is possible by a variety of techniques, including fluorescence, nmr, and radioligand binding. The last is particularly versatile and has been appHed both to sophisticated receptor quantitation and to dmg screening and discovery protocols (50,51). The use of high specific activity, frequendy pH]- or p lj-labeled, dmgs bound to cmde or purified cellular materials, to whole cells, or to tissue shces, permits the determination not only of dmg—receptor saturation curves, but also of the receptor number, dmg affinity, and association and dissociation kinetics either direcdy or by competition. Complete theoretical and experimental details are available (50,51). 

For temperatures below the vapor—Hquid critical temperature, isotherms to the left of the Hquid saturation curve (see Fig. 3) represent states of... 

This equation follows from equation 66, because vaporization occurs at the constant pressure Moreover, the heat of vaporization is related to the slope of the vapor—Hquid saturation curve through the Clapeyron equation ... 

Values of andt, are given by the saturation curve of the psychrometric chart, such as Fig. 12-2. By trial and error, = 72.1 F, or the adiabatic-saturation temperature is 0.1 F higher than the wet-bulb temperature. 

The coordinates refer directly to the temperature and enthalpy of any point on the water operating hne but refer directly only to the enthalpy of a point on the air operating line. The corresponding wet-bulb temperature of any point on CD is found by projecting the point horizontally to the saturation curve, then vertically to the temperature coordinate. The integral [Eq. (12-8)] is represented by the area ABCD in the diagram. This value is known as the tower characteristic, vaiying with the L/G ratio. 

When the saturation curve (

relative humidity (Mollier diagram is complete (Fig. 4.9). 

Next we draw the saturation curve in the hj -x coordinate system. Vapor pressures can be calculated with Eqs. (4.106) and (4.108) or taken directly from the tables. The humidity x corresponding to the saturation pressure pi,(t) is calculated with Eq. (4.83) noting that p = 0.875 bar. The enthalpy of humid saturated air is calculated with Eq. (4.94) ... 

The saturation curve is drawn through points (x, ), calculated for different... 

With high temperatures the x values will not fit into the diagram. Then the hj values have to be calculated with smaller x values in order to draw the isotherms. In Table 4.6 these values are calculated with values x = x q% at various temperatures. Drawing the fundamental axes and isotherms with the instructions given above and the saturation curve with the help of Table 4.6 leads to the Mollier diagram in Fig 4,10u. 

The total pressure thus has no importance. If this result is. sought from a Mollier diagram by finding the intersection of the humidity line (jr = humidity of air = constant) and the saturation curve, which gives the dewpoint temperature, a diagram constructed for a pressure of 9.S0 mbar should be used. A decent ap-proximation can be found from a diagram constructed for pressure p 1 bar. 

If, instead, the air is damped adiabatically with the wet cloth, so that the state of the air varies, the cloth will settle to a slightly different temperature. Each state of air (0, x) is represented by a certain wet bulb temperature 6, which can be calculated from Eq. (4.116) or its approximation (4.123), when the partial pressures of water vapor are low compared with the total pressure. When the state of air reaches the saturation curve, we have an interesting special case. Now the temperatures of the airflow and the cloth are identical. This equilibrium temperature is called the adiabatic cooling border or the thermodynamic wet bulb temperature (6 ). 

Eable 4.7)Draw in the Mollier diagram at the 14 °C point of the saturation curve (a) the state change line of the adiabatic humidification and (b) an auxiliary line, associated with the wet bulb temperature measurement, by means of which the state can be defined. The pressure of air is p = 1 bar. 

The enthalpy of humid air responding to the point 14 C on the saturation curve is... 

As an example of using a Mollier diagram in defining the state of air, we can take a typical measurement from the local exhaust hood of a paper machine. Tbe temperature of the exhaust air is 82 C and its wet bulb temperature 60 "C. In Fig. 4AQd we move from the saturation curve at the point 60 °C straight up along the constant enthalpy line ( = 460 kj/kg d.a.) until we reach the isotherm... 

FIGURE 14.7 Substrate saturation curve for au euzyme-catalyzed reaction. The amount of enzyme is constant, and the velocity of the reaction is determined at various substrate concentrations. The reaction rate, v, as a function of [S] is described by a rectangular hyperbola. At very high [S], v= Fnax- That is, the velocity is limited only by conditions (temperature, pH, ionic strength) and by the amount of enzyme present becomes independent of [S]. Such a condition is termed zero-order kinetics. Under zero-order conditions, velocity is directly dependent on [enzyme]. The H9O molecule provides a rough guide to scale. The substrate is bound at the active site of the enzyme. 

FIGURE 15.11 Heterotropic allosteric effects A and I binding to R and T, respectively. The linked equilibria lead to changes in the relative amounts of R and T and, therefore, shifts in the substrate saturation curve. This behavior, depicted by the graph, defines an allosteric K system. The parameters of such a system are (1) S and A (or I) have different affinities for R and T and (2) A (or I) modifies the apparent for S by shifting the relative R versus T population. 

The converse situation applies in the presence of I, which binds only to T. T binding will lead to an increase in the population of T conformers, at the expense of Rq (Figure 15.11). The decline in [Rq] means that it is less likely for S (or A) to bind. Consequently, the presence of I increases the cooperativity (that is, the sigmoidicity) of the substrate saturation curve, as evidenced by the shift of this curve to the right (Figure 15.11). The presence of I raises the apparent value of L. 

In addition to COg, Cl and BPG also bind better to deoxyhemoglobin than to oxyhemoglobin, causing a shift in equilibrium in favor of Og release. These various effects are demonstrated by the shift in the oxygen saturation curves for Hb in the presence of one or more of these substances (Figure 15.35). Note that the Og-binding curve for Hb + BPG + COg fits that of whole blood very well. 

The importance of the BPG effect is evident in Figure 15.35. Hemoglobin stripped of BPG is virtually saturated with Og at a pO of only 20 torr, and it cannot release its oxygen within tissues, where the jbOg is typically 40 torr. BPG shifts the oxygen saturation curve of Hb to the right, making the Hb an Og... 

In this form, Alhas the units of torr.) The relationship defined by Equation (A15.4) plots as a hyperbola. That is, the MbOg saturation curve resembles an enzyme substrate saturation curve. For myoglobin, a partial pressure of 1 torr for jbOg is sufficient for half-saturation (Figure A15.1). We can define as the partial pressure of Og at which 50% of the myoglobin molecules have a molecule of Og bound (that is, F= 0.5), then... 

FIGURE A15.3 Oxygen saturation curve for Hb in the form of Fversus pO, assuming n =... 

Prepare a plot of the saturation curve for air-water. Establish the operating line by starting at the point set by the oudet cold water temperature and the enthalpy of air at the wet bulb temperature, and with a slope L /Ga assumed between 0.9 and 2.7. See Figure 9-109. 

No load saturation curve measuring starting torque, current and power. 

The process line meets the saturation curve at - 1°C, giving the ADP (which means that condensate will collect on the fins as frost). 

Figure 1 shows the pH-rate profiles of some active complexes. Both Ni2 + and Zn2 + ion complexes of 8 afford saturation curves with inflection at around pH s 6 and 8, respectively, which represent, most likely, the ionization of the hydroxyl group complexed with a Ni2+ or a Zn2+ ion. The pKa = 8.6 was assigned for the ionization of the hydroxyl group of the latter complex 12). The lower pH for the ionization of the Ni2+ ion complex in respect to that of the Zn2+ ion complex indicates that the ligand 8 coordinates to Ni2+ ion more tightly than to Zn2+ ion, which is in conformity with a larger K value (1120 M) for the Ni2 + ion than for the Zn2 + ion complex (559 M) at pH 7.05 (Table 2). 

For any given value of T, equation (1) gives on solution at least one value of p. If we put x — T, y = p, the assemblage of points representing the various possible solutions of (1) constitute a curve which is called the saturation curve. 

If an isotherm T = Ti is drawn to cut the saturation curve, the point (or points) of intersection must satisfy (1), i.e., in this... 

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