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Slope of graph

Since these reaction products exhibit considerable absorbance at the wave lengths utilized in the rate measurements, the calculation of rate constants required a technique incorporating this factor. Two methods of calculation were employed successfully. In some cases, limiting absorbances (A00) were determined and the rates were obtained from the slopes of graphs of log (A0—A00)/(A—A0o) vs. time. These served to demonstrate the pseudo-first-order nature of the rate constant however, the more general calculation procedure was that due to Guggenheim (11). The first-order dependence of the rate on the concentration of alkyl halide was shown by varying initial concentrations. [Pg.139]

Physical properties for calculation of X Slopes of graphs are X values Slopes of graphs are X values... [Pg.109]

Table I shows self-diffusion coefficients (T = 300 K) for the three interlayer cations in low-order hydrates of montmorillonite, as calculated conventionally from the slopes of graphs of the (three-dimensional) mean-square cation displacement versus time (8, 16-18). Experimental values of the cation self-diffusion coefficients in aqueous solution also are listed (32). It is apparent that monovalent cation mobility in the one-layer hydrate is at best a few percent of that in bulk aqueous solution, and that the mobility increases significantly with increasing water content, to approach about 25% of the bulk-solution value in the three-layer hydrate. The constrained geometry and the charge sites on the clay mineral surface thus act to retard significantly the diffusive motions of interlayer cations through adsorbed water. Table I shows self-diffusion coefficients (T = 300 K) for the three interlayer cations in low-order hydrates of montmorillonite, as calculated conventionally from the slopes of graphs of the (three-dimensional) mean-square cation displacement versus time (8, 16-18). Experimental values of the cation self-diffusion coefficients in aqueous solution also are listed (32). It is apparent that monovalent cation mobility in the one-layer hydrate is at best a few percent of that in bulk aqueous solution, and that the mobility increases significantly with increasing water content, to approach about 25% of the bulk-solution value in the three-layer hydrate. The constrained geometry and the charge sites on the clay mineral surface thus act to retard significantly the diffusive motions of interlayer cations through adsorbed water.
From the slope of the linear graphs 1 and 2, the viscosity t] of the solution was calculated using the Washburn equation [Eq. (2)]. The viscosity value t] = 0.96 cPs caleulated from graph 2 coincides with known values for bulk solution. However, the slope of graph 1 is higher and corresponds formally to t] = 1.7 ePs. This discrepancy may be eaused by additional viscous... [Pg.357]

Fig. 2 The Pr-h loading graph. The slope of graph represented Young s modulus in the loaded state... Fig. 2 The Pr-h loading graph. The slope of graph represented Young s modulus in the loaded state...
These last equations take account of the salt effect observed for reactions between ions, the slopes of graphs of log A/Ao versus Vju being very close to those predicted by Equation (2.49) at low concentrations (Fig. 2.4). At higher... [Pg.20]

These values are in agreement with the values obtained from the slopes of the two linear portions of the appropriate graph which includes many more points. [Pg.641]

Crystallizers with Fines Removal In Example 3, the product was from a forced-circulation crystallizer of the MSMPR type. In many cases, the product produced by such machines is too small for commercial use therefore, a separation baffle is added within the crystallizer to permit the removal of unwanted fine crystalline material from the magma, thereby controlling the population density in the machine so as to produce a coarser ciystal product. When this is done, the product sample plots on a graph of In n versus L as shown in hne P, Fig. 18-62. The line of steepest ope, line F, represents the particle-size distribution of the fine material, and samples which show this distribution can be taken from the liquid leaving the fines-separation baffle. The product crystals have a slope of lower value, and typically there should be little or no material present smaller than Lj, the size which the baffle is designed to separate. The effective nucleation rate for the product material is the intersection of the extension of line P to zero size. [Pg.1661]

In this equation, all of the terms except y +i and x but including x, are constant. Hence the relationship between and x is linear with a slope of L j(L + D) and a line representing the relationship on a graph of y vs jc must pass tlrrough y = jcd when x — jcd, since tire vapour and the liquid have the same composition in the product. This is called the rectifying operating line in a graphical representation of tire distillation process. [Pg.358]

The q-line starts on the x-axis at Xp. The value of q is the same as for conventional McCabe-Thiele. The slope of the q-line in the Ryan graph is the McCabe-Thiele slope minus 1. Therefore for bubble point feed the q-line is vertical for the conventional McCabe-Thiele and Ryan. For dew point feed the slope is 0 for the conventional McCabe-Thiele and -1 for Ryan. [Pg.55]

It is clear that a graph of ln(V j-) or In(k ) against 1/T will give straight line. This line will provide actual values for the standard enthalpy (AH ), which can be calculated from the slope of the graph and the standard entropy (AS ), which can be calculated from the intercept of the graph. These types of curves are called van t Hoff curves and their important characteristic is that they will always give a linear relationship between In(V r) and (1/T). However, it is crucial to understand that the distribution... [Pg.49]

Figure 3-24 shows the relationship between 1/C as a function of time t. The graph is a straight line, therefore, the assumed order of the reaction is correct. The slope of the line from the regression analysis is the rate constant k. [Pg.195]

Quite often isochronous data is presented on log-log scales. One of the reasons for this is that on linear scales any slight, but possibly important, non-linearity between stress and strain may go unnoticed whereas the use of log-log scales will usually give a straight-line graph, the slope of which is an indication of the linearity of the material. If it is perfectly linear the slope will be 45°. If the material is non-linear the slope will be less than this. [Pg.52]

It is apparent from equation (2.123) that a graph of BD0 against fracture energy Uc (using different crack depths to vary 0) will be a straight line, the slope of which is the material toughness, Gc. [Pg.155]

The clothing insulation necessary for comfort or a neutral thermal sensation (TS = 0) in a thermally uniform 50% RH still-air environment is graphed in Fig. 5.5. The slope of the graph is such that comfort temperature is decreased about 0.6 °C for each 0.1 do increase in clothing insulation. The... [Pg.181]

In these calculations T is taken in the middle of the experimental range k is the Boltzmann constant and h is Planck s constant. From Eq. (5-48) it can be seen that a plot of ln(A /7 ) against 1/7" has a slope of — A7/ /7 such a graph is called an Eyring plot. [Pg.246]


See other pages where Slope of graph is mentioned: [Pg.966]    [Pg.1038]    [Pg.772]    [Pg.1047]    [Pg.221]    [Pg.250]    [Pg.305]    [Pg.201]    [Pg.49]    [Pg.41]    [Pg.202]    [Pg.338]    [Pg.66]    [Pg.942]    [Pg.966]    [Pg.1038]    [Pg.772]    [Pg.1047]    [Pg.221]    [Pg.250]    [Pg.305]    [Pg.201]    [Pg.49]    [Pg.41]    [Pg.202]    [Pg.338]    [Pg.66]    [Pg.942]    [Pg.1426]    [Pg.81]    [Pg.272]    [Pg.124]    [Pg.157]    [Pg.486]    [Pg.274]    [Pg.275]    [Pg.496]    [Pg.676]    [Pg.36]    [Pg.1137]    [Pg.104]    [Pg.113]    [Pg.240]    [Pg.240]    [Pg.576]    [Pg.601]   
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