Excel plotting

We recently had the opportunity to examine some enthalpies reported (60) toward isothiocyanic acid (HNCS), isocyanic acid (HNCO) and hydrazoic (HN3) acid. Of the eleven donors with estabhshed Eb and Cb parcimeters, nine gave an excellent plot of Ea vs. Ca leading to Ea and Ca values of 5.30 and 0.227 for isothiocyanic acid. Dioxane and... 

Excluding the intercept term, diere are seven coefficients. A normal probability plot can be obtained as follows. First, rank die seven coefficients in order. Then, for each coefficient of rank p calculate a probability (p — 0.5)/7. Convert diese probabilities into expected proportions of die normal distribution for a reading of appropriate rank using an appropriate function in Excel. Plot the values of each of die seven effects (horizontal axis) against die expected proportion of normal distribution for a reading of given rank. 

Reaction (23) is extremely fast (k 5 X- 10 cm molecule s ), so that HCO is removed solely in (23) and cannot lead to radical branching or secondary initiation. Furthermore [H2O2] is negligible, particularly as initial rates are used. Rearrangement of (1.5) gives (1.6) and from excellent plots of Rco/[HCH0][02] against [HCHO], kif was obtained directly from the intercept. 

For comparison the author has generated an Excel plot (Figure 3) using the data from Figure 2. This is for those readers who work with this popular spreadsheet. 

Prepare the Calibration Curve. It is preferable to measure each standard three times and plot the average the standard deviation of each point can be calculated, and the range of one standard deviation or the range of data for each point can be marked on the calibration curve. Using Excel, plot the trendline, with the regression line equation (slope and intercept). 

Linearity. Calculate and the y intercept as a percentage of the midrange response. Calculate the response factor (RF) for each experimental point on the line, and using Excel, plot the RF vs. concentration. From the slope (RF/unit concentration), calculate the RF change over the range of experimental points and calculate this as a percentage of the average RF value. 

Using Excel, plot the deflection of a beam whose letgfo is 5 m with die modulus of elasticity of = 200 GPa and / = 99.1 X 10 mm. The beam is designed to carry a load of 10,000 N/m. What is the maximum deflection of the beam ... 

Fig. 2.8 Assumed function E t) = cos(2otI,/0.32) (64 points) and its FT in Excel plotted versus u and versus frequency...

Figure 6.27 shows that we crushed a fly with a steam-roller processed variable Cost in Excel using a special format of electronic worksheet which inserts thousands spacer, white space between three numbers, into numbers and thus, simplifying its reading. However, one can crush earnestly, for example, to access those Excel functions that Mathcad does not have (calendar functions) or to make Excel plot in Mathcad (pie chart). Besides, to enter data in Excel table is more convenient and quicker one can use special Excel features - AutoFit and others. 

Let us consider synthetic data for Enzyme-X which is similar to the actual data for pancreafic carboxypeptidase [13,14] (note the name of an enzyme ends in -ase ). We use synthetic data, so we can insert key points into an Excel plot. It should be clear that at low substrate concentrafion, the rate increases rapidly as more substrate is added. However, in spite of the efficiency of an enzyme, there is only a small amount in solution. Thus, the rate approaches a limit as more and more substrate saturates the active sites of the enzymes in solution and eventually reaches a limit, V , as shown in Figure 8.7. Special points have been inserted into the data so that you can see the limiting rate of0.090 mM/s and see that at half that rate, 0.045 mM/s, the substrate concentrafion is 0.0065 mM which is the value of Km- The value of Km is not easily seen on the first plot but when we show the double reciprocal plot in Figure 8.8 we get a more precise value of Km value in two ways. There are really two intercepts in the double-reciprocal plot, which apparently was the innovation of Lineweaver and Burk [15] in 1934. We can use the third and fourth columns of Table 8.1 to make such aplotforour Enzyme-X data in Figure 8.8. 

In MS Excel, plot PCI vs. PC2 from the PCA sheet/tab by selecting the columns and clicking on the Chart Wizard icon in the Standard Toolbar (View>Toolbars>Standard). 

The intensities are plotted vs. v, the final vibrational quantum number of the transition. The CSP results (which for this property are almost identical with CI-CSP) are compared with experimental results for h in a low-temperature Ar matrix. The agreement is excellent. Also shown is the comparison with gas-phase, isolated I. The solvent effect on the Raman intensities is clearly very large and qualitative. These show that CSP calculations for short timescales can be extremely useful, although for later times the method breaks down, and CTCSP should be used. 

Good to excellent Hammett plots were obtained using substituent constants (see Figure 2.6). Surprisingly, literature examples of good Hammett correlations of stability constants are rare The p-values are shown in Table 2.7. 

Striking confirmation of the conclusion that the BET area derived from a Type IV isotherm is indeed equal to the specific surface is afforded by a recent study of a mesoporous silica, Gasil I, undertaken by Havard and Wilson. This material, having been extensively characterized, had already been adopted as a standard adsorbent for surface area determination (cf. Section 2.12). The nitrogen isotherm was of Type IV with a well defined hysteresis loop, which closed at a point below saturation (cf. F, in Fig. 3.1). The BET area calculated from it was 290 5 0 9 m g , in excellent agreement with the value 291 m g obtained from the slope of the initial region of the plot (based on silica TK800 as reference cf. p. 93). 

A tabulation of the partial pressures of sulfuric acid, water, and sulfur trioxide for sulfuric acid solutions can be found in Reference 80 from data reported in Reference 81. Figure 13 is a plot of total vapor pressure for 0—100% H2SO4 vs temperature. References 81 and 82 present thermodynamic modeling studies for vapor-phase chemical equilibrium and liquid-phase enthalpy concentration behavior for the sulfuric acid—water system. Vapor pressure, enthalpy, and dew poiat data are iacluded. An excellent study of vapor—liquid equilibrium data are available (79). 

In fig. 26 the Arrhenius plot ln[k(r)/coo] versus TojT = Pl2n is shown for V /(Oo = 3, co = 0.1, C = 0.0357. The disconnected points are the data from Hontscha et al. [1990]. The solid line was obtained with the two-dimensional instanton method. One sees that the agreement between the instanton result and the exact quantal calculations is perfect. The low-temperature limit found with the use of the periodic-orbit theory expression for kio (dashed line) also excellently agrees with the exact result. Figure 27 presents the dependence ln(/Cc/( o) on the coupling strength defined as C fQ. The dashed line corresponds to the exact result from Hontscha et al. [1990], and the disconnected points are obtained with the instanton method. For most practical purposes the instanton results may be considered exact. 

There is an excellent correlation between these data and the gas-phase data, in terms both of the stability order and the energy differences between carbocations. A plot of the gas-phase hydride affinity versus the ionization enthalpy gives a line of slope 1.63 with a correlation coefficient of 0.973. This result is in agreement with the expectation that the gas-phase stability would be somewhat more sensitive to structure than the solution-phase stability. The energy gap between tertiary and secondary ions is about 17kcal/mol in the gas phase and about 9.5 kcal/mole in the SO2CIF solution. 

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