Vapor pressure vs. temperature curves

Fig. 139 Vapor pressure vs. temperature curve for isobutyl alcohol. Clausius Clapyron...

When Eq. (4.11) is applied to the vaporization of a pure liquid, dPM/ dT is the slope of the vapor pressure-vs.-temperature curve at the temperature of interest, AV is the diffeVence between molar volumes of saturated vapor and saturated liquid, and AH is the latent heat of vaporization. Thus values of AH may be calculated from vapor-pressure and volumetric data. 

FIG. 1 Vapor pressure vs. temperature curves for water and benzene. 

Figure 1. Vapor pressure vs. temperature curves of important components of orange essential oil (0 0) a-pinene, ( - ) d-limonene, ( A - A ) myrcene, ( o - o ) linalool, ( - ) a-terpineol, ( - ) decanal, ( A - A ) a-citral (Data from (38)).

Referring to Fig. 1, the full line labeled binodal represents the phase boundary, and is the vapor-pressure vs. temperature curve. In raising the temperature, so passing from B to A, the system starts at B with a relatively stable liquid phase, and a relatively unstable vapor phase. As it reaches the binodal, the system is at equilibrium, with equality of chemical potential for... 

A plot of vapor pressure vs. temperature (in °C) for a liquid is an exponentially increasing curve. 

A plot of Hi vs. Tl curves upwards because the vapor pressure vs. temperature also curves upwards. This result is the equilibrium line which we seek. 

The trial-and-error, discussed in detail elsewhere [14], consisted essentially of cross-plotting PV -products vs. temperature and entropy with extrapolation of YendalPs cuiwes until agreement was reached which satisfied the critical values, the vapor pressure and temperature relationships and the PK-products on both plots. The resulting information was then plotted on the T S chart and reexamined for slope and for smoothness. The entropy of the saturated liquid curve resulting from the above procedure was checked by graphical integration. The agreement... 

The plot of pressure vs. temperature for a solid-gas phase change reflects the large effect of tanperature on vapor pressure thus, it resembles the Uquid-gas curve in rising steeply with higher temperatures. 

Fig. 13.1 Reduced vapor pressure and molar density vs. reciprocal reduced temperature for HoO, CH4, H2, and 4He. In each case, were simple corresponding states theory adequate, all data would lie on a single master curve. Using extended CS the curves are fit to acceptable precision, (a) (top) = reduced vapor pressures, (b) (bottom) = reduced liquid molar densities... 

By repeating the experiment at different steady-state temperatures one can determine Zi as a function of T. From this a plot can be made of vs. T for a constant A, which means a constant vapor pressure, p. Changing the temperature in the side tube can establish a new value of p or A in the tube, and another d vs. T curve can be determined. From such a family of 0 vs. T curves one can plot a family of A vs. 9 curves for constant values of T. Since the 0 values were determined for a steady-state condition, the arrival rate. A, must be equal to the evaporation rate, expressed in atoms per square centimeter per second. Hence the A vs. 9 curves are also Fo vs. 6 curves at a constant T. 

Below 500 K heating of the solid salt results primarily in the vaporization of the covalent molecule as a monomer. In this temperature range the only thermal decomposition, into NOz and 02, is exhibited by the solid. The vapor is more stable. The vapor pressure of Cu(N03)2 was determined by Addison and Hathaway48 by extrapolating pressure-time curves to zero time in order to subtract the pressures of N02 and 02. These vapor pressures increased from 0.32 torr at 430 K to 3.59 torr at 405 K. A plot of log P vs. 1/T is linear and yields a sublimation enthalpy of 67.0 kJ. Above 500 K both the solid and the vapor phase decompose to N02 + 02. 

This approximate equation, known as the Clausius/Clapeyron equation, relates the latent heat of vaporization directly to the vapor pressure curve. Specifically, it shows j that ah " is proportional to the slope of a plot of In vs. 1/ T. Experimental data for many substances show that such plots produce lines that are nearly straight. According to the Clausius/Clapeyron equation, this implies that AH " is almost constant, virtually independent of T. This is not true AH " decreases monotonically with increasing temperature from the triple point to the critical point, where it becomes zero. The assumptions on which the Clausius/Clapeyron equation are based have approximate validity only at low pressures. 

A large number of experiments on many substances have shown that a plot of the vapor pressure (p ) of a compound against temperature does not yield a straight line but a curve, as you saw in Fig. 3.9. Many types of correlations have been proposed to transform this curve to a linear form (y = mx + i ) a plot of In (p ) vs. (1/T),... 

The boiling point is the temperature at which the vapor pressure equals the external pressure, so we can also interpret the curves in Figure 12.6 as a plot of external pressure vs. boiling point. For instance, the H2O curve... 

Figure 3 was constructed as mentioned previously from Fig. 2 by cross-plotting isotherms of reduced conductivity vs. A. The thermal conductivity data for carbon monoxide were not used. Then from Fig. 3 the values of k for tritium (A = 1.00) were obtained to predict the temperature dependence of the thermal conductivity of tritium along the vapor pressure curve as shown in Fig, 2. Lastly, it may be pointed out that an extension of the Ne data of Ldchtermann P ] to the critical-temperature locus would appear to give some values of the thermal conductivity which would be very near to those predicted for tritium, and would also require an S-shaped curve, which seems improbable in view of the value of T for neon, i.e, 1.247. A curve for the thermal conductivity of Ne predicated upon behavior similar to argon and tritium is also shown. Derivation of the thermal conductivities of the unsymmetrical isotopic species of hydrogen—HT, HD, and DT— is a triviality and can easily be obtained from Fig. 3. Note that de Boer s theory does not distinguish between the behavior of HT and D2 P ]. For the unsymmetric isotope HT the value of A should be computed after Friedmann [ ] as...

Radiation heat transfer, as used in the simplified time lag method for creating furnace heating curves (temperature vs. time) is really an average condition of the gas blanket temperature, gas blanket thickness, and vapor pressure of triatomic gases. With high excess air, the heat transfer will be less due to lower percentages of the... 

Fig. 2.1-23 Vapor pressure of some substances vs. the temperature. The diagram contains two curves for a constant difference between total pressure and the saturation pressure of water...

Figure 2.1-27 shows the fugacity coefficient vs. the reduced pressure p, each line being parametrized by a value of the reduced temperature. The line for the saturation limit (vapor pressure curve) ends at the critical point. If the critical real gas constant Z deviates from 0.27 then the fugacity coefficient complies with the following empirical law ... 

Thus, the ratio of slopes of the log y vs. xa curves should be in the ratio —xb/xa). When the activity coefficients are determined by means of vapor-pressure data, the restrictions of both constant temperature and constant pressure are impossible ones to fulfill. As will be pointed out... 

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