Henry straight line

The straight lines in Fig. 8.21 show that the solubility of a gas is directly proportional to its partial pressure, P. This observation was first made in 1801 by the English chemist William Henry and is now known as Henry s law. The law is normally written... 

The result of the described methodical solution to monitor gas-consuming reactions at reduced partial pressure under isobaric conditions is shown in Figure 10.8 for the catalytic hydrogenation of COD with a cationic Rh-complex. The slope of the measured straight lines corresponds to the maximally obtainable rate (Vsat = k2 [E]0 = k 2 [H2] [E]0) [42 b], which is directly proportional to the hydrogen concentration in solution and at validity of Henry s law to the hydrogen partial pressure above the reaction solution. The experiments prove that the dilution factor of the gas phase can adequately be found in the rate constant (Further examples can be found in [47].)... 

Figure 20.12 Air-water exchange of an aldehyde A converting to a diol D by a hydration/dehydration reaction. Since the diol D cannot leave the water, the slope of its concentration at the air/water interface is zero. For simplicity, the scales of A and D are chosen such that the equilibrium constant of hydration, K and the Henry s law constant of the aldehyde, KAa/vl, are 1. The dashed straight line marked [A] onre>ct,ve he>Ps t0 picture the modification due to the reactivity of A.

Where me is the amount of gas absorbed in the volume V of the polymer at equilibrium and pc is the corresponding partial pressure of the gas being studied. In order to check if S stays constant, one measures the me value for several pressures pe at the same temperature. S comes then from the slope of the straight line me = f(pe). Deviations from linearity of the line means deviations from Henry s law. 

Figure 12.21 Plot of/, vs. x, showing extrapolation to x, = 1. The straight lines represent ideal-solution models based on Henry s law and the Lewis/Randall rule.

To calculate activities in the present scheme one determines the vapor pressures of solutions for various xif with special emphasis on the range where Henry s Law holds. Extrapolation of the straight line to xA — 1 yields Pf. Then XjPf corresponds to the vector DE and Pi, to the vector DF in Fig. 3.11.1. A measurement of PA corresponding to xA then yields aA and 7i. For more precise work, Eq. (3.11.6) must be employed. 

Note further that as xx - 1, all curves in Fig. 3.13.3 merge with the one for which B - 0 this agrees with the experimental fact that Raoult s Law always holds in this range. Similarly, as xx - 0 one obtains a straight line region consistent with Henry s Law here the slope as xx - 0 varies with each solution. For B < 0 negative deviations from Raoult s Law are encountered, but for B > 0 one finds positive... 

Figure 2. Simulated isotherms for methane-in carbon slit pores of varying widths are shown here. The number of adsorbed molecules per unit area of pore wall is plotted as a function of the pressure times the Henry s constant, which gives the single straight line shown for the limiting low pressme parts of the isotherms. Pore widths in A are shown on the Figure. From Ref. [22], Sep. Sci. and Tech. 27 (1992), 1837-1856.

As mentioned in Section 3.3, experimental investigations have shown that at very great dilution the vapor pressure of the solute obeys Henry s Law, Pi = Ky Xi, in the limit x,- -> 0. The straight line OP of Fig. 3.11.1 shows the vapor... 

To use this result one must execute detailed measurements of the vapor pressures of the actual solutions at great dilution, where Henry s Law is obeyed. Extrapolation of the resulting straight line to the composition of pure solvent then establishes pf. Now the vectors and in Fig. 3.11.1 correspond to XiPf and P, respectively. A measurement of P, at the particular composition x, then yields the activity or activity coefficient in this regime. For more precise work Eq. (3.11.6) must be used, in the manner discussed earlier. 

Finally, the activity coefficient with respect to molality may be determined in precisely the same manner as sketched above. One equates (3.5.21c) with (3.1.4a) to obtain the analogue of (3.11.8), with c replaced by m. One then chooses as a reference solution the hypothetical Henry s Law case in which the straight line region of the P versus m, curve at low mi is extrapolated to m,- = 1. Let the corresponding hypothetical vapor pressure be P . This leads to an equation of the form (3.11.10), (3.11.11) and to the relation... 

Head Space Analysis. A plot of peak area as a function of concentration for aqueous solutions of MMA was found to be a straight line as shown in Figure 4. This plot provides a Henry s Law relationship between the concentration of MMA in solution and its corresponding vapor pressure. In addition to these standard systems, the vapor pressure over samples from the Lj and microemulsion phases was also determined for the 14.7 wt% SLS aqueous solution. At low concentrations, the peak area is again linearly related to MMA concentration. As the saturation point is approached, however, the peak area increases more slowly. For any of the surfactant systems, the concentration of MMA in the continuous aqueous phase can be determined by constructing a horizontal line from the surfactant curve to the standard curve and then dropping a vertical line down to the concentration axis. The intercept is the concentration in the continuous phase and the amount of MMA in the micellar phase then follows from mass balance. Figure 4 shows that the concentration of MMA in the aqueous phase at the L j phase boundary and in the microemulsions is approximately 0.15 M. This is also the solubility limit of MMA in water. 

For dilute solutions, which might be found in most air pollution control conditions. Eq. (25) reduces to Eq. (24)—a general equation that can be used along with a general equilibrium relationship such as Eqs. (13) and (15). For this case of a dilute solution, Eq. (24) will be used along with Eq. (9), Henry s law. Then, both the equilibrium line and the operating line will plot as a straight line on an x-y plot. 

Fig. 1.12 Vapor pressure of methanol for dilute solutions of methanol in water plotted against the mole fraction of methanol. The straight line shows the vapor pressure according to Henry s law, and the broken line, that according to Raoult s law.

For dilute solutions and when Henry s law applies, the equilibrium curve and the operating lines are straight lines. Overall mass-transfer coefficients are convenient in this case. The expression for the height of packing can be written as... 

Recognition of the fact that elements always displayed the same chemical behavior - regardless of their isotopic composition - led to a reformulation of the periodic law. The idea that each element was characterized by a unique number had already been demonstrated experimentally by Henry Moseley (1887-1915). By studying the X-ray diffraction patterns produced by a variety of elements, he discovered that the frequencies of the K lines differed from element to element in a predictable and consistent fashion. He went on to show that the frequency of any line in the X-ray spectrum is approximately proportional to A(N-b) where A and b are constants and N is an integer that he termed the atomic number of the element. Moseley was able to identify the number N with the number of protons in the atomic nucleus. Plots of the square root of the frequency for the K and L lines in the X-ray spectra of the elements versus their atomic number, reproduced in Figure 5, show almost straight lines. From this work, it became clear why the order in which certain element pairs appeared in the periodic table needed to be reversed. The pairs in question are argon (39.95) and potassium (39.10) cobalt (58.93) and nickel (58.69) and tellurium (127.60) and iodine (126.91), the... 

Similar results were found by Henry and Gilbert [33], who studied sulfur removal, nitrogen removal, and hydrocracking in small reactors. Most of the first-order plots were curved upward when LHSV was used, but straight lines were obtained with LHSV. The explanation proposed was that the reaction rate was directly proportional to the dynamic holdup, which was predicted to increase with following... 

Moseley s law Lines in the x-ray spectra of elements have frequencies that depend on the proton number of the element. For a set of elements, a graph of the square root of the frequency of x-ray emission against proton number is a straight line (for spectral lines corresponding to the same transition). The law is named for the British physicist Henry Gwyn Jeffreys Moseley (1887-1915). 

For binary mixtures we can use a simple plot, as in Figure 10.5, to compare the Henry s law ideal solution to the Lewis-Randall ideality. The plot shows the real fugacity for component 1, as well as the Lewis-Randall and Heruy s law straight lines. The Lewis-Randall fugacity coincides with the real value at Xj = 0 and at Xj = 1, but the Henry s law fugacity coincides only at Xj = 0. Also, since x lies on [0,1], the intercept of the Henry s law curve at Xj = 1 is the Heruy s constant at the given T and P. 

The data are plotted in Figure 5.3. The regions where the vapor pressure curves show approximate straight lines are denoted R for Raoult and H for Henry. A and B denote acetic acid and benzene respectively. 

Moseley s law The frequencies of the lines in the X-ray spectra of the elements are related to the atomic numbers of the elements. If the square roots of the frequencies of corresponding lines of a set of elements are plotted against the atomic numbers a straight line is obtained. The law was discovered by Henry Moseley (1887-1915). 

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