Quadruple-point

Examples of solid - liquid systems with two liquid layers are given below the temperature is the temperature at which the two layers separate or the quadruple point. 

Let us first consider the three-phase equilibrium ( -clathrate-gas, for which the values of P and x = 3/( +3) were determined at 25°C. When the temperature is raised the argon content in the clathrate diminishes according to Eq. 27, while the pressure can be calculated from Eq. 38 by taking yA values following from Eq. 27 and the same force constants as used in the calculation of Table III. It is seen that the experimental results at 60°C and 120°C fall on the line so calculated. At a certain temperature and pressure, solid Qa will also be able to coexist with a solution of argon in liquid hydroquinone at this point (R) the three-phase line -clathrate-gas is intersected by the three-phase line -liquid-gas. At the quadruple point R solid a-hydroquinone (Qa), a hydroquinone-rich liquid (L), the clathrate (C), and a gas phase are in equilibrium the composition of the latter lies outside the part of the F-x projection drawn in Fig. 3. The slope of the three-phase line AR must be very steep, because of the low solubility of argon in liquid hydroquinone. 

Along the three-phase line liquid-clathrate-gas the variation of the composition with temperature is considerable (cf. CD in Fig. 3), because when applying Eq. 27 to this equilibrium, the relatively small quantity AH = 0.16 kcal/mole has to be replaced by the much larger difference/ —//ql between the partial molar heat functions of / -hydroquinone and the liquid phase, which amounts to about —6 kcal/mole. The argon content of the solid reaches a minimum at the quadruple point. 

In the P-T projection the difference in slopes of the three-phase lines -clathrate-gas and liquid-clathrate-gas at the quadruple point R is determined by the heat of fusion of the number of moles of hydroquinone associated with one mole of argon in the clathrate under the conditions prevailing at R. If we extrapolate the three-phase line liquid-clathrate-gas to lower pressures (where it is no longer stable), the value of yA decreases until it becomes zero when we are dealing with pure / -hydroquinone. Hence, the metastable part of this three-phase line ends in the triple point B of /1-hydro-... 

Figure 9 represents the system CC14-H2S-H20, where no hydrates occur in the binary system CC14-H20. In the ternary system von Stackelberg and Fruhbuss again determined the lower half of the four-phase line As the binary quadruple point... 

In Fig. 8.8, we see that sulfur can exist in any of four phases two solid phases (rhombic and monoclinic sulfur), one liquid phase, and one vapor phase. There are three triple points in the diagram, where various combinations of these phases, such as monoclinic solid, liquid, and vapor or monoclinic solid, rhombic solid, and liquid, coexist. However, four phases in mutual equilibrium (such as the vapor, liquid, and rhombic and monoclinic solid forms of sulfur, all in mutual equilibrium) in a one-component system has never been observed, and thermodynamics can be used to prove that such a quadruple point cannot exist. 

Figure 6. Effect of palytoxin on the rate of Na influx in Swiss 3T3 cells. Confluent quiescent Swiss 3T3 cells were incubated for 37 C for 7 min in incubation media containing 0.1 pM PTX, 1.1 pM PTX, or 11 pM PTX. Intracellular Na was determined as described in the Experimental section. Data points represent the mean of quadruplicate points.

Is it possible to have a quadruple point in a phase diagram for one component system ... 

Quadruple point is a point where four different phases meet. Thus P = 4, substituting the values in the phase rule equation... 

This is absurd, therefore one component system cannot have a quadruple point in the phase diagram. 

Applying the phase rule, it is found that, in the two component system NaP03 + H20, a maximum of four phases is possible at the quadruple points 199,302). In addition to, at the most, two crystalline substances and water vapor, an amorphous glass-like phase is always present. This phase consists of mixtures of polyphosphates, the chain length of which rises with increasing temperature. Only Na2H2P207, Maddrell s salt (h) and trimetaphosphate occur as stable solid phases in addition to NaH2P04. 

A similar result was obtained with the system Br3+H20, where the hydrate is Br2.10H2O, and the invariant systems occur at the two quadruple points L (6 2° 93 mm.) and B (—0 3° 43 mm.). Iodine forms no known hydrate with water. 

Six new triple points are seen to appear in Fig. 7.3, and still others are found at higher P and lower 7. However, no quadruple points (or coexistence features of higher order) are found, as predicted by the Gibbs phase rule. 

In Figure 2.2-8 the critical endpoint temperatures for the family 0f CO2 + n-alkanes systems are plotted as a function of the carbon number n. If in a particular binary system the three-phase curve hhg is followed to low temperature then at a certain temperature a solid phase is formed (solid n-alkane or solid C02 at low carbon numbers). This occurs at one unique temperature because we now have four phases in equilibrium in a binary system, so according to the phase rule F= 0. Below this so-called quadruple point temperature the hhg curve is metastable. 

In Figure 2.2-8 also the quadruple point temperatures of the different systems is plotted and the curve through this points intersects the curve through the critical endpoints at a carbon number 23< <24. This means that for carbon numbers larger than 23 no stable hhg and h+h... 

Figure 2.2-8. The family of carbon dioxide with n-alkanes. Critical endpoint temperatures and quadruple point temperatures as a function of carbon number n. quadruple point hhgscoi, quadruple point 5n-aikaneW/g A UCEP l2=lig LCEP /2=//g A UCEP hh=g-...

As discussed for CO2 + n-alkane systems at carbon numbers n<24 the three-phase curve hhg ends a low temperature in a quadruple point s2l2lig. This is shown schematically in Figure 2.2-9a and b. In the quadrupel point three other three-phase curves terminate. The s2hh curve runs steeply to high pressure and ends in a critical endpoint where this curve intersects the critical curve. The s2l2g curve runs to the triple point of pure component B and the s/l/g curve runs to lower temperature and ends at low temperature in a second quadruple point s2silig (not shown). 

With increasing carbon number of the n-alkane the melting curve of the n-alkane shifts to higher temperature. As a result also the quadruple point s2lil2g shifts to higher temperature (Figure 2.2-9b) and eventually coincides with the critical endpoint l2+(li=g) of the l2l/g curve... 

Point Q2 is a quadruple point. At Q2, four phases are in equilibrium liquid water, hydrocarbon liquid, hydrocarbon gas, and solid hydrate. The almost vertical line extending from point Q2 separates the area of liquid water and hydrocarbon liquid from the area of liquid water and hydrate. 

Qi, which occurs at approximately 32°F, is also a quadruple point representing the point at which ice, hydrate, liquid water, and hydrocarbon gas exist in equilibrium. The vertical line extending from point Qj separates the area for hydrate and liquid water from the area for hydrate... 

QUADRUPLE POINT. The temperature at which four phases are in equilibrium, such as ice, saturated salt solution, water vapor, and salt. 

Roozeboom postulated upper/lower hydrate quadruple points using SO2 as evidence ... 

Villard measured hydrates of CH4, Crip. C2H4, C2H2, N2O Villard measured hydrates of (pip and suggested that the temperature of the lower quadruple point is decreased by increasing the molecular mass of a guest Villard suggested hydrates were regular crystals... 

FIGU RE 1.2 Phase diagrams for some simple natural gas hydrocarbons that form hydrates. Ql lower quadruple point Q2 upper quadruple point. (Modified from Katz, D.L., Cornell, D., Kobayashi, R., Poettmann, F.H., Vary, J.A., Elenbaas, J.R., Weinaug, C.F., The Handbook of Natural Gas Engineering, McGraw Hill Bk. Co. (1959). With permission.)... 

In Figure 1.2, the intersection of the above three phase lines defines both a lower hydrate quadruple point Qi (I-Lw-H-V) and an upper quadruple point Q2 (Lw-H-V-Lhc)- These quadruple points are unique for each hydrate former, providing a quantitative classification for hydrate components of natural gas. 

Each quadruple point occurs at the intersection of four three-phase lines (Figure 1.2). The lower quadruple point is marked by the transition of Lw to I, so that with decreasing temperature, Qi denotes where hydrate formation ceases from vapor and liquid water, and where hydrate formation occurs from vapor and ice. Early researchers took Q2 (approximately the point of intersection of line Lw-H-V with the vapor pressure of the hydrate guest) to represent an upper temperature limit for hydrate formation from that component. Since the vapor pressure at the critical temperature can be too low to allow such an intersection, some natural gas components such as methane and nitrogen have no upper quadruple point, Q2, and... 

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