Triangle, mass balance

Such a set of axes (or triangle) is known as a mass balance triangle (MBT), or sometimes referred to as a Gibbs Triangle, and is typically used for ternary systems. The region enclosed by the triangle represents all the physically attainable compositions in a ternary system, that is, 0[Pg.18]

FUiURE 23 Schematic showing the compositional change of the residual liquid during batch experimentation. The axes are collectively known as the mass balance triangle. 

CONCEPT Stoichiometric subspace or mass balance triangle ... 

In AR theory (as well as in distillation theory), the region of concentrations that obey mass balance constraints is often referred to as the mass balance triangle— this is because S takes the shape of a scalene or right-angled triangle in and a tetrahedron in We prefer to use the term stoichiometric subspace , however, as S is not always represented by these shapes, particularly for unusual reaction stoichiometry. 

Figure 4. Isotopic mass-balance for measured 6 Fe values of ferric ( ) and ferrous ( ) Fe in solution as a function of Fe(II)/FeT ratios. Although the initial Fe isotope compositions of the fluids have 6 Fe values of 0%o (shown hy dotted mixing line), the lighter Fe isotopes are portioned into the ferrous species following attaimnent of isotopic equilihrium. The triangles (A) represent the calculated isotopic mass balance of the different solutions. Fractionations noted are measured values based on data for equimolar and higher Fe(II)/total Fe ratio experiments. (A) and (D) are for experiments with zero Cl at 22 and 0°C, respectively. (B) and (E) are experiments done with at 11 mM Cl at 22 and 0°C, respectively. (C) and (F) are experiments done with 111 mM Cl at 22 and 0°C, respectively. Modifled from Welch et al. (2003).

A second approach is the triangle method which was developed based on the equilibrium theory model which assumes that the adsorption equilibrium is established everywhere at any time in the column. The equivalent TMB configuration with a four-section emit will be considered here. The model equations consist in four sets of mass balance equations, one for each section j j = 1,- , 4), with the relevant boundary conditions and the integral material balances at the column ends and at the nodes of the unit [16,28]. These equations were given earlier, in Section 17.2 (Eqs. 17.4 to 17.6). 

Figure 3.21 Graphical representation of mass balances for a two-liquid feed stream on a right triangle diagram.

Because plotting data on equilateral triangles has certain inconveniences, sometimes ternary data are presented on a right triangle, as shown by the smaller inset in Figure 8-i. In this graph, the vertical axis represents one component, the horizontal axis the second component and the third component is obtained by mass balance from the two known fractions. 

All these resufts are based on the mass-balance equation. The study shows the influence of the problem parameters on the shape of the evolution path in the composition triangles. On the first hand, the solid solution paranoeters have an influence on the path curvature. Elepending on the parameter values, the path is composed of straight line portions like in the case of Langmuir isotherm or is more or less curved. On the second hand, equilibrium constants influence the path orientation. Orientations themselves are responsible for the value of the intermediate eomposition plateaus. At last the hydrogeological parameters essential modify the front velocity. Evolution paths in... 

Time-dependent mass change of low volumes of DMSO under ambient laboratory conditions. Dry DMSO was pipetted (2 or 5 gL) into the wells in alternating rows of a low-volume 384-well microplate, and the plate was incubated on the laboratory bench under ambient conditions (approximately 21°C and 35% relative humidity) and weighed periodically using an analytical balance. Filled triangles are data from wells initiated with 2-gL DMSO open squares are data from wells initiated with 5-gL DMSO. 

The coordinates of P on AiQ follows from ti, the mass at Ai that balances the triangle on P. Areal coordinates U correspond to the areas t, e.g. ... 

Support a clean porcelain crucible with the cover slightly tilted on a wire triangle, and heat the crucible as hot as possible for 5 minutes (Laboratory Methods D). The bottom of the crucible should glow a dull red (red heat) for the full 5 minutes. Use only tongs to handle the crucible and cover after it has been heated. From this point on in the experiment the crucible and cover must not be touched with your hands. Place the hot crucible and cover in a dessicator, if available, and allow it to cool to room temperature. Then weigh the crucible and cover on an analytical balance (Laboratory Methods C), and record the mass in TABLE 6.1. 

Support a clean crucible and cover on a wire triangle, and heat them for 5 minutes until they are thoroughly dry (Laboratory Methods M). Allow the crucible and cover to cool to room temperature. Then weigh them on an analytical balance (Laboratory Methods C), and record the mass in TABLE 7.1. Use tongs to handle the crucible. 

During the filtration, heat a clean crucible and cover, held by a wire triangle (Laboratory Methods D), as hot as possible for approximately 5 minutes. Permit the crucible to cool to room temperature and then weigh it on an analytical balance. Record the mass in TABLE 14.1. 

Support a clean porcelain crucible without a cover on a wire triangle, and heat for a couple minutes with a Bunsen burner flame until the crucible is thoroughly dry. Allow the crucible to cool, then weigh it on an analytical balance, and record its mass in TABLE 38.2J. Transfer to the crucible about 0.7 g of an unknown metal nitrate hexahydrate, M(N03)x 6H2O, obtained from your instructor. (The metal present is the same as that used in part l.) Weigh the crucible and contents, and record the mass in TABLE 38.2J. 

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