Linear passing through the origin

The order n may be calculated with the help of above equation. Again a plot of logarithms of ratio of half-life periods versus ratio of initial concentrations will be linear passing through the origin with a slope equal to (n - 1) and thus the order can be determined from its slope. 

In figure 4.19 an example Is given of a result meeting all the imposed requirements E3(j.(A p) is linear, passes through the origin and reverses perfectly... 

This equation, known as the Randles-Sevcik equation, predicts that the peak current is proportional to the square root of the sweep rate. This is analogous to the inverse sqnare root of time dependence found with potential steps (equation (11.2.7)). Therefore, a plot of tp vs. should be linear, pass through the origin and have a gradient from which the diffusion coefficient may be estimated. Below is a list of the diagnostic criteria used to characterise a reversible voltammogram ... 

If the first term on the right-hand side of the above equation is called Q, then a plot of (1 - 0 - Q) versus should be linear, pass through the origin and have a slope oi n 10)v V2Eij. 2C)l+ 2) ... 

We shall begin with the simplest case of a linear function passing through the origin to intr oduce the method and set up the ground rules. The more complicated... 

Using a hand calculator, find the slope of the linear regression line that passes through the origin and best satisfies the points... 

Expand the three detemiinants D, Dt, and for the least squares fit to a linear function not passing through the origin so as to obtain explicit algebraic expressions for b and m, the y-intercept and the slope of the best straight line representing the experimental data. 

The t and a.-methods, the nature of which was explained in Chapter 2, may be used to arrive at a value of the micropore volume. If the surface of the solid has standard properties, the t-plot (or a,-plot) corresponding to the isotherm of the nonporous powder in Fig. 4.11(a) will be a straight line passing through the origin (cf. curve (i) of Fig. 4.11(6)) and having a slope proportional to the specific surface of the powder. For the microporous powder which yields the isotherm (iii).of Fig. 4.11(a), the t-plot (or Oj-plot) will have the form of curve (iii) of Fig. 4.11(6) the linear branch of this curve will be parallel to curve (i), since it corresponds to the area of the outside of the particles which is identical with that of the nonporous parent particles. 

Prepare a plot of reaction rate (-dC /dt) versus f(C ). If the plot is linear and passes through the origin, the rate equation is consistent with the data, otherwise another equation should be tested. Figure 3-17 shows a schematic of the differential method. 

The intensity of the emitted fluorescence In is, therefore, directly proportional to the amount of substance applied a This relationship is much simpler than the Kubelka-Munk function and always leads to a linear calibration curve passing through the origin If this is not true then interference is occurring [5]... 

Plots of the left-hand side of this equation versus corresponding ratios of [Fe(II)]/ [V(in)] are linear. Such plots appear to pass through the origin so that k2 must be large. The gradients of the plots yield a value for k since k 2l i... 

This means that id (diffusion-controlled) is proportional to the square root of he(f and its linear plot passes through the origin, which property is often used as a check on the diffusion-controlled electron-transfer reaction14. 

Hence the picture of the cathodic and anodic waves obtainable for a completely reversible redox couple by means of the RDE corresponds fully with that in Fig. 3.9 the value of i, i.e., the height of the sigmoidal waves, is linearly proportional to to1/2 and to C (see eqn. 3.89 and the Levich constant). If for a well chosen combination of C and E a plot of i against co1/2 deviates from a straight line passing through the origin, then in the kinetics of the electrode reaction we have to deal only with a rapid electron transfer (cf., Fig. 3.10) or even with a slow electron transfer (cf., Fig. 3.11), in which latter instance the transfer coefficient a plays an appreciable role (cf., eqns. 3.17 and 3.18). 

Mn and Mw/Mn values calculated from these data were plotted against Wjgvg (e.g., Figure 2). At both -70 and -90°C Mn increases with Wjbve Importantly, Mjj versus WibVE plots are linear over a wide range of WibVE s and pass through the origin. At higher Wjbve s> however, the plots tend to deviate from linearity. 

The effect of the initial initiator concentration (Ij>-DCC]0) on Mn was studied at -90°C (Figure 3). Mjj increased at all [ -DCC]0 s and the Mjj versus WjbVE plots passed through the origin. The slopes of the linear portions of these plots were inversely proportional to [ -DCC]0. Similar results were obtained with samples prepared at -70°C. 

Figure 6 shows plots of Mjj ol poly(MVE) versus the cumulative weight of added MVE, Wmve M s increase linearly with increasing Wmve and the lines pass through the origin. Mn is higher at a lower initiator concentration, [p-DCC]Q the slope of the plots is nearly proportional to the reciprocal of [p-DCC]0. 

Linear M versus W plots passing through the origin, indicating quasiliving polymerizations 2) (X) M independent of... 

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