Straight line solute concentrations

In the colorimetric estimation of p-phenethylbiguanide the plot of readings against concentration is found ipIO) to be a straight line at concentrations less than 10 W. Above this concentration, p-phenethylbi-guanide in solution deviates sharply from Beer s Law. It may be concluded that in the low concentration range over which Beers Law is valid, the compound exists in the monomeric state in aqueous solution. 

The isotherms on an enthalpy-concentration diagram for a system with no heat of dilution are straight lines. Enthalpy-concentration diagrams can be constructed, of course, for solutions having negligible heats of dilution, but they are unnecessary in view of the simplicity of the specific-heat method described in the last section. 

Figure 2.49 Gibbsite solubility vs. pH of water solution (standard conditions). Solid curve is total solubility, straight lines are concentrations of individual A1 forms in solution.

According to Beer s law, a calibration curve of absorbance versus the concentration of analyte in a series of standard solutions should be a straight line with an intercept of 0 and a slope of ab or eb. In many cases, however, calibration curves are found to be nonlinear (Figure 10.22). Deviations from linearity are divided into three categories fundamental, chemical, and instrumental. 

In aqueous solution at room temperature the coefficient B is positive for the majority of electrolytes. For some, however, it is negative in such a case the viscosity at moderate concentrations, where the B term is predominant, is less than that of pure water, while at lower concentrations, where the A s/c term becomes predominant, the value of the viscosity rises above that of pure water. An example of this is shown in Fig. 51, where abcissas are /c. The straight line is a plot of A s/c with A = +0.0052, while the lower curve is a plot of Be with B = —0.033. On adding the ordinates of these two curves the middle curve is obtained, which reproduces, within the experimental error, the values of 17/770 obtained for KC1 in aqueous solution at 18°C. 

Plot the observed e.m.f. values against the concentrations of the standard solutions, using a semi-log graph paper which covers four cycles (i.e. spans four decades on the log scale) use the log axis for the concentrations, which should be in terms of fluoride ion concentration. A straight line plot (calibration curve) will be obtained. With increasing dilution of the solutions there tends to be a departure from the straight line with the electrode combination and measuring system referred to above, this becomes apparent when the fluoride ion concentration is reduced to ca 0.2 mg L-1. 

Hence, by plotting A [or log(l/T)] as ordinate, against concentration as abscissa, a straight line will be obtained and this will pass through the point c = 0, A = 0 (T = 100 per cent). This calibration line may then be used to determine unknown concentrations of solutions of the same material after measurement of absorbances. 

Likewise, record the second derivative spectra of the four standard pseudo-ephedrine hydrochloride solutions and record the peak heights DL at 258-259 nm plot the results against concentration and confirm that a straight line is obtained. 

Solution Plotting E vs. log[Ca2+] gives a straight line with a slope of 29 mV/ decade and an intercept of 245 mV A calcium concentration of 5 x 10 4M thus yields ... 

Solution Plotting E vs. log[Mg2+] gives a straight line the magnesium concentration (2.6 x 10-4m) corresponding to the 125 mV reading can be read directly from the axis. 

Most pectin solutions behave like Newtonian liquids below a pectin concentration of about 1 % (w/w). Onogi (1966) derived the critical concentration of polymer solutions from plotting the double logarithmic curves of viscosity (ii) against concentration at constant shear rates. Each curve consists of two straight lines intersecting at the critical concentration. At higher... 

The accuracy of this method depends on correct extrapolation of the experimental data. The error associated with the extrapolation can be reduced by plotting the experimental data not as a function of concentration but as a function of the square root of concentration. It will be shown below that in this case the experimental data for dilute solutions fall onto a straight line that can be extrapolated more accurately than a curve to zero concentration. 

An alternative graphical solution makes use of the biphasic exponential nature of the plasma concentration function ineq. (39.16). At larger time values, when the effect of absorption has decayed, the function behaves approximately as monoexponential. Under these conditions, and after replotting the concentration data on a (decimal) logarithmic scale, one obtains a straight line for the later part of the curve (Fig. 39.8a). This line represents the P-phase of the plasma concentration and is denoted by C ... 

Fig. 39.13. (a) Semilogarithmic plot of the plasma concentration Cp (pg 1 ) versus time /. The straight line is fitted to the later part of the curve (slow P-phase) with the exception of points that fall below the quantitation limit. The intercept Bp of the extrapolated plasma concentration appears as a coefficient in the solution of the model. The slope is proportional to the hybrid transfer constant p, which is itself a function of the transfer constants of and ifcbpOf the model, (b) Semilogarithmic plot of the... 

Before we introduce the Kalman filter, we reformulate the least-squares algorithm discussed in Chapter 8 in a recursive way. By way of illustration, we consider a simple straight line model which is estimated by recursive regression. Firstly, the measurement model has to be specified, which describes the relationship between the independent variable x, e.g., the concentrations of a series of standard solutions, and the dependent variable, y, the measured response. If we assume a straight line model, any response is described by ... 

The theory has been verified by voltammetric measurements using different hole diameters and by electrochemical simulations [13,15]. The plot of the half-wave potential versus log[(4d/7rr)-I-1] yielded a straight line with a slope of 60 mV (Fig. 3), but the experimental points deviated from the theory for small radii. Equations (3) to (5) show that the half-wave potential depends on the hole radius, the film thickness, the interface position within the hole, and the diffusion coefficient values. When d is rather large or the diffusion coefficient in the organic phase is very low, steady-state diffusion in the organic phase cannot be achieved because of the linear diffusion field within the microcylinder [Fig. 2(c)]. Although no analytical solution has been reported for non-steady-state IT across the microhole, the simulations reported in Ref. 13 showed that the diffusion field is asymmetrical, and concentration profiles are similar to those in micropipettes (see... 

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