Spreadsheet curve

Activation energies are found from the Arrhenius equation (Eq. 13). We plot In k against 1/T, with T in kelvins, and multiply the slope of the graph by — R to find the activation energy, with R = 8.3145 J-K 1-mol l. A spreadsheet, curve-fitting program,... 

The approach that we have worked out for the titration of a monoprotic weak acid with a strong base can be extended to reactions involving multiprotic acids or bases and mixtures of acids or bases. As the complexity of the titration increases, however, the necessary calculations become more time-consuming. Not surprisingly, a variety of algebraic and computer spreadsheet approaches have been described to aid in constructing titration curves. 

An Excel spreadsheet (Example8-7.xls) was used to determine the various RTD functions and the computer program PROGS 1 was used to simulate the model response curve with the experimental data. The results show the equivalent number of ideally mixed stages (nCSTRs) for the RTD is 13.2. The Gamma distribution function from Equation 8-143 is ... 

The rate constant for the alkyl bromide reaction is equal to the slope of the line. The best way to determine a slope is by doing a linear curve fit using a spreadsheet or graphing calculator. Somewhat less accurately, any two points on the line determine the slope ... 

Data Table 2 shows values of 0 that are obtained for initial y-position values of 1.5 X 1(T13 m to 7.0 X 10 13 m. (You may like to perform these calculations on a spreadsheet.) Graph the initial y-position versus 0 and draw a smooth curve through the data points. Label this graph Figure C. 

So after having created the math spreadsheets and having improved the efficiency curves, I actually had to do the impossible now. I had to build it. What worried me was not just the fact that I had to obviously parallel over 10 large capacitors to get an effective ESR close to the target, but the fact that I had to ensure that the impedance of the intervening PCB traces also virtually canceled out. 

A from 85VAC input. Its measured efficiency was around 62%, in line with the published datasheet curves, and also the predictions of my Mathcad spreadsheet (that spreadsheet is, incidentally, available on the accompanying CD-ROM of my A to Z book). The output stage of my grizzly creation is shown in Figure 5-3 (try selling this one ). But it works ... 

The width of the cloud is represented by the duration or time to pass, as shown. Develop a spreadsheet to compute the percentage of fatalities expected as a result of this cloud, with this particular shape, passing a fixed location. Set up your spreadsheet to include input parameters of cloud duration and maximum concentration. Use your spreadsheet to draw a plot of the percentage of fatalities vs. duration of exposure. Draw a curve on the plot for each of the maximum concentrations of 40, 50, 60, 70, 80, and 100 ppm. What conclusions can be drawn about the results ... 

ISEs are standardized using standard solutions of the ion dissolved in water or in a solution designed to keep all samples at about the same ionic strength. These solutions can be purchased or prepared in the laboratory and typically cover several orders of magnitude, often between 1 and 10 6 or 10 7 M. Measurements are made at the various concentrations and a standard or calibration curve prepared (see Section 14.9.2). Usually, the meter can be programmed to read the concentration of the ion directly once a suitable curve is obtained. Raw data can also be entered into a spreadsheet, which can be programmed to calculate the amounts of ion present in any units desired. 

Part A Plotting a Standard Curve Using Excel Spreadsheet Software... 

Note Use hypothetical data to practice plotting a standard curve with the Excel spreadsheet software procedure below. Later experiments will refer you back to this procedure to plot standard curves for real experiments. Launch Excel (or click hie then new if already launched) to begin. 

Type in the data for the standard curve in the A and B spreadsheet columns. Use the A column for the concentrations and the B column for the corresponding instrument readout values. For the unknowns and control, type in the instrument readout values in the B column cells, but leave the concentration cells blank. When finished, the A and B columns should appear as in Table 6.1, in which there are four standards with concentrations of 1,2, 3, and 4 ppm, two unknowns, and one control. 

Plot the standard curve using the spreadsheet procedure used in Experiment 18 and obtain the correlation coefficient and the concentrations of the unknowns and control. 

Create the standard curves (one for caffeine and one for benzoate) by plotting peak size vs. concentration. Use the spreadsheet procedure in Experiment 18. Obtain the concentrations of the unknowns and the control. Plot the results for the control sample on the control chart for this instrument posted in the laboratory. 

Both new and experienced users can take advantage of software to lead them through instrument set-up and data acquisition. Automated quantitation routines are available to calculate compound amounts in samples. These routines offer complete flexihihty to generate custom report formats. By integrating retention time information and internal or external cahhration curves can he calculated. Quantitation data can he exported to popular spreadsheet programs. 

If you already use a spreadsheet, you can skip this section. The computer spreadsheet is an essential tool for manipulating quantitative information. In analytical chemistry, spreadsheets can help us with calibration curves, statistical analysis, titration curves, and equilibrium problems. Spreadsheets allow us to conduct what if experiments such as investigating the effect of a stronger acid or a different ionic strength on a titration curve. We use Microsoft Excel in this book as a tool for solving problems in analytical chemistry. Although you can skip over spreadsheets with no loss of continuity, spreadsheets will enrich your understanding of chemistry and provide a valuable tool for use outside this course. 

To make a graph from the spreadsheet in Figure 2-19d, go to the INSERT menu and select CHART. A window appears with a variety of options. The one you will almost always want is XY (Scatter). Highlight XY (Scatter) and several options appear. Select the one that shows data points connected by a smooth curve. Click Next to move to the next window. 

Example EH Using a Spreadsheet to Find Area Beneath a Gaussian Curve... 

In a spreadsheet, enter the mean in cell A2 and the standard deviation in cell B2. To find the area under the Gaussian curve from — oo to 900 h in cell C4, we select cell C4 and go to the INSERT menu and choose FUNCTION. In the window that appears, select the Statistical functions and find NORMDIST from the list of possibilities. Double click on NORMDIST and another window appears asking for four values that will be used by NORMDIST. (If you click on help, you will find a cryptic explanation of how to use NORMDIST.)... 

The method of least squares is used to determine the equation of the best straight line through experimental data points. Equations 4-16 to 4-18 and 4-20 to 4-22 provide the least-squares slope and intercept and their standard deviations. Equation 4-27 estimates the uncertainty in x from a measured value of y with a calibration curve. A spreadsheet greatly simplifies least-squares calculations. 

G. G3 Calibration curve. (You can do this exercise with your calculator, but it is more easily done by the spreadsheet in Figure 4-13). In the Bradford protein determination, the color of a dye changes from brown to blue when it binds to protein. Absorbance of light is measured. 

Eventually, we will derive a single, unified equation for a spreadsheet that treats all regions of the titration curve. To understand the chemistry of the titration, it is sensible to break the curve into three regions described by approximate equations that are easy to use with a calculator. 

By now you should understand the chemistry that occurs at different stages of a precipitation titration, and you should know how to calculate the shape of a titration curve. We now introduce spreadsheet calculations that are more powerful than hand calculations and less prone to error. If a spreadsheet is not available, you can skip this section with no loss in continuity. Consider the addition of liters of cation M+ (whose initial concentration is C ) to liters of solution containing anion X- with a concentration C%. 

Equation 7-18 relates the volume of added M+ to [M+], [X-], and the constants V7, C, and CjJ,. To use Equation 7-18 in a spreadsheet, enter values of pM and compute corresponding values ofVM, as shown in Figure 7-10 for the iodide titration of Figure 7-7. This is backward from the way you normally calculate a titration curve in which VM would be input and pM would be output. Column C of Figure 7-10 is calculated with the formula [M+l = 10 pm, and column D is given by [X-] = k sp/[M+]. Column E is calculated from Equation 7-18. The first input value of pM (15.08) was selected by trial and error to produce a small V You can start wherever you like. If your initial value of pM is before the true starting point, then VM in column E will be negative. In practice, you will want more points than we have shown so that you can plot an accurate titration curve. 

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