Solution data, plotting

Most formaldehyde producers recommend a minimum storage temperature for both stabilized and unstabilized solutions. Figure 3 is a plot of data (17,18,122,126) for uiiinhibited (<2.0 wt% methanol) formaldehyde. The minimum temperature to prevent paraformaldehyde formation in unstabilized 37% formaldehyde solutions stored for one to about three months is as follows 35°C with less than 1% methanol 21°C with 7% methanol 7°C with 10% methanol and 6°C with 12% methanol (127). 

This behaviour is thought to be due to the formation of a network structure caused by entanglement of the longchain molecules in solution. Plotting the data of viscosity measurements of pectin solutions of different concentrations reveals the same behaviour, confirming Onogi s observation, with a critical pectin concentration of about 1 % (w/w). 

Figure 3. Typical plot of data output from the rig, showing values of the weight of effluent from the capillary test unit as a function of time, during an experiment. The portion of the curve from B - C shows the efflux of surfactant solution from the foam generator which precedes gas break-through. Portion C -D< shows the efflux of foam of increasing quality. At times larger than D only "dry gas, without liquid phase, emerges.

Figure 12.6 Tafel plots for the exchange of the acetylcholine ion between an aqueous solution and 1,2-DCE the branch on the right-hand side corresponds to transfer from the aqueous to the organic solution. Data taken from Ref. 3.

A series of five standard copper solutions are prepared, and the absorbances are measured as indicated below. Plot the data and determine the concentration of the unknown. 

Fig. 11. Dependences of observed first-order rate constants on nucleophile concentration for thiocyanate susbtitution at dichlorobis(ethylmaltolato)meta-1(IV) complexes M(etmalt)2Cl2, and at a series of tin(IV) complexes SnL2Cl2 with L = the ligands whose formulae are shown against the thin line plots. The data refer to reactions in acetonitrile solution at 298.2 K (data from Refs. (264) and (265)).

Werner (1980) has studied devolatilization in corotating twin-screw extruders when the volatile component was stripped from the polymeric solution by applying a vacuum to the system. Rough estimates of the equilibrium partial pressure of the volatile component in the feedstream for each of the systems studied by Werner indicate that this pressure was less than the applied pressure, which means that bubbles could have been formed. Figure 17 shows the influence of the externally applied pressure on the exit concentration for a methyl methacrylate-poly(methyl methacrylate) system of fixed concentration. Note that the exit concentration decreases as the pressure is decreased, but seems to approach an asymptotic value at the lowest pressures studied. Werner also reported that at a fixed flow rate and feed concentration the exit concentration did not vary with screw speed (over the range 150-300 min" ), which also suggests that ky alay, is independent of screw speed. Figure 18 is a plot of data obtained by Werner on an ethylene-low-density poly(ethylene) system and also shows that decreases in the applied pressure result in decreases in the exit concentration, but here a lower asymptote is not observed. 

A more accurate way to use potentiometric data is to prepare a Gran plot6-7 as we did for acid-base titrations in Section 11-5. The Gran plot uses data from well before the equivalence poinl (Ve) to locate Ve. Potentiometric data taken close to Ve are the least accurate because electrodes are slow to equilibrate with species in solution when one member of a redox couple is nearly used up. 

Figure 3.2 gives a plot of data obtained at various temperatures for a solution of 0.57 wt. per cent of Taps. No. 5 in methyl (4-bromo-phenyl) carbinol. A fair reduction with respect to temperature is observed. When... 

These indicate the limit of our successful numerical BVP integrations near the bifurcation points. In between the x and o marks on the middle branch, the curve is drawn using interpolation of our successful BVP solutions data, while in between two adjacent x or two adjacent o marks, the curve is drawn by extrapolating nearby computed function data. This is done automatically by MATLAB s plot commands. 

Plots of the limiting flux. /mux as a function of solution concentration for latex solution data are shown in Figure 6.9 for a series of latex solutions at various feed solution flow rates. A series of straight line plots is obtained, and these extrapolate to the gel concentration cgel at zero flux. The slopes of the plots in Figure 6.9 are proportional to the term D/S in Equation (6.3). The increase in flux resulting from an increase in the fluid recirculation rate is caused by the decrease in the boundary layer thickness S. 

Figure 7. Variation of Mn2+ emission wavenumber with interatomic distance for the CaO-SrO solid solution and for the calcite - magnesite solid solution. Data for the latter plot were extracted from (14).

Figure 3.55. Plot of cf)es versus AG for the ECL systems involving Ru(phen)3+ (a), Ru(bipy)3+ (b), and Ru(baph)3+ (c) ions in 0.1 M (C2H5)4NPF6 acetonitrile solutions. Data for the ECL systems with nitrocompounds ( ), quinones (o), iV-methylpyridinium cations ( ), and aromatic amines or 2,3,7,8-tetramethoxythianthrene ( ). (From Ref. 193.)...

Figure 5.28 Current response for a 10 pm radius mercury microelectrode immersed in a 5 pM solution of adriamycin, following a potential step from —0.700 to —0.350 V the supporting electrolyte is 1.0 M perchlorate at a pH of 4.5. The inset shows the semi-log plot for data between the marks on the current-time transient, with the time axis being referenced to the leading edge of the potential step. From R. J. Forster, Analyst, 121, 733-741 (1996). Reproduced by permission of The Royal Society of Chemistry...

Linearity. Figure 5 represents linearity plots of data from the vldicon for solutions containing Cr, Cu, Co, Ni, Fe and Mn. 

Average the temperatures at which crystal formation occurs for solutions that contain the same volume of water. Plot these data on graph paper. Set up your graph sideways on the graph paper (landscape orientation). Plot solubility on the vertical axis. (The units are grams of solute per 100 mL of water.) Plot temperature on the horizontal axis. 

Prepare a plot of A4S0 versus the log of the inverse antibody dilution (a 1 10 dilution = 1, a 1 100 dilution = 2, etc.). Plot the data from all five primary antibody samples on a single graph for comparison. If the assay was successful, each antibody solution should produce a sigmoidal curve in this type of plot (see Fig. 17-5). The various primary antibody stock solutions were diluted prior to performing twofold serial dilutions across each row (see step 4). Keep this in mind when you construct your graph. 

However, what if we had more than one variable to consider In other words, we have multivariate data. For example, what if we want to identify trends in the properties of a range of organic molecules The variables we might want to consider could be melting point, boiling point, M, solubility in a solvent and vapour pressure. We can, of course, tabulate the data, as before, but this does not allow us to consider any trends in the data. To do this we need to be able to plot the data. However, once we exceed three variables (which we need to be able to plot in three dimensions) it becomes impossible to produce a straightforward plot. It is in this context that chemometrics offers a solution, reducing the dimensionality to a smaller number of dimensions and hence the ability to display multivariate data. The most important technique in this context is called principal component analysis (PCA). 

Figure 15. Plot of oil recoveries versus process aid addition level from the hot water flotation processing of an oil sand in a continuous pilot plant. Also shown is the correspondence with the zeta potentials, measured on-line, of emulsified bitumen droplets in the extraction solution. (Plotted from data in reference 50.)...

The "family-plot retention data of 5 solutes with a series of poly(methylphenylsiloxane) stationary phases have been examined in terms of the saturation vapor pressure Pa of the solute, the methyl/phenyl ratio of the solvent, and the temperature. Plots of In Vg against In p for a given solute over a range of temperature were found to De linear, as were the "isothermaV, that is, the retention/vapor -pressure plots for an homologous series of solutes at a constant temperature. The family-plot slopes exhibited by the n-alkane probe-solutes were also found to be very sensitive to the aromatic content of the polymers. Thus, it appears that the "family" technique of GC data reduction can be a useful tool for characterizing the physicochemical properties of (polymer) stationary phases. 

In gas absorption operations the equilibrium of interest is that between a relatively nonvolatile absorbing liquid (solvent) and a solute gas (usually the pollutant). As described earlier, the solute is ordinarily removed from a relatively large amount of a carrier gas that does not dissolve in the absorbing liquid. Temperature, pressure, and the concentration of solute in one phase are independently variable. The equilibrium relationship of importance is a plot (or data) of x, the mole fraction of solute in the liquid, against y, the mole fraction in the vapor in equilibrium with x. For cases that follow Henry s law, Henry s law constant m, can be defined by the equation... 

Curve A in Figure 17-6 is a plot of data for the titration in Example 17-4. Curve B is the titration curve for a solution of magnesium ion under identical conditions. The formation constant for the EDTA complex of magnesium is smaller than that of the calcium complex, which results in a smaller change in the p-function in the equivalence-point region. 

Plots of the intracellular pH against if of BCECF in vivo are also shown in Figure 31.6. The correlation function between the intracellular pH and % is different from that in solution, indicating that substantial consideration must be paid to calibration of intracellular pH using solution data [6]. The average fluorescence lifetime is shorter in vivo than in solution, even at the same pH. The correlation function of the intracellular pH in the range from 5.5 to 7.5 is given as follows ... 

Table 7-2 lists the solubility of R/S-ibu-S-lys mixture in an ethanolic solution. Figure 7-23 plots these data on the ternary phase diagram. The data indicate that in the solid phase the tie lines join at the 100%... 

FIG. 4.16 The effect of phosphate on electrophoretic mobility of alumina, plotted as a function of total P concentration in solution (data from Ref. 36). 

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