Page 173 - Physical Chemistry

lev38627_ch05.qxd 3/3/08 9:33 AM Page 154

154
Chapter 5 A B C D E F
Standard Thermodynamic 1 CO Cp polynomial fit a b c d
Functions of Reaction
2 T/K Cp Cpfit 28.74 -0.00179 1.05E-05 -4.29E-09
Figure 5.7 3 298.15 29.143 29.022
4 400 29.342 29.422 3 2
Cubic polynomial fit to C° of y = -4.2883E-09x + 1.0462E-05x -
P,m 5 500 29.794 29.923 1.7917E-03x + 2.8740E+01
CO(g). CO C P, m
6 600 30.443 30.504
7 700 31.171 31.14 36
8 800 31.899 31.805
34
9 900 32.577 32.474
10 1000 33.183 33.12 32
11 1100 33.71 33.718
30
12 1200 34.175 34.242
13 1300 34.572 34.667 28
14 1400 34.92 34.967 0 500 1000 1500
15 1500 35.217 35.115

After the plot appears, click on a data point on the chart, thereby highlighting all
the data points. From the Chart menu, choose Add Trendline. In the Trendline dialog
box, click on the polynomial picture and change the Order of the polynomial to 3.
Click the Options tab of the Trendline dialog box and click in the box Display equa-
tion on chart. Then click OK. You will see the cubic-fit equation displayed on the
chart, with coefficients equal to the values given in Example 5.6. (The coefficients are
chosen so as to minimize the sum of the squares of the deviations of the experimental
C° values from the values calculated with the polynomial.) You can adjust the num-
P,m
ber of significant figures visible in the coefficients by double-clicking on the trendline
equation on the chart and clicking on the Number tab of the Format Data Labels box;
then choose the Scientific category and change the number of decimal places.
(For Excel 2007, the chart is created as follows. After selecting all the data, click
on the Insert tab, then click on Scatter; then click on the graph subtype that has only
points with no lines. You will see the chart. Click the Layout tab. Click on Trendline;
then click More Trendline Options. In the Format Trendline box, click the polynomial
button and change the order to 3; click on Display Equation on chart; click Close. You
will see the polynomial curve and its equation. To get more significant figures in the
coefficients, right click on the displayed equation and click on Format Trendline
Label. In the Format Trendline Label box, click on Number at the left, click on
Scientific and increase the number of decimal places; click Close.)
To see how well values calculated from the polynomial equation fit the data, enter
the labels a, b, c, d in cells D1, E1, F1, G1; enter the values of the coefficients in cells
D2, E2, F2, G2; enter the label Cpfit in cell C2; and enter the formula
=$D$2+$E$2*A3+$F$2*A3^2+$G$2*A3^3
into cell C3. The equals sign tells the Excel spreadsheet that this is a formula, mean-
ing that what is displayed in cell C3 will be the result of a calculation rather than the
text of what is typed in C3. The * denotes multiplication and the ^ denotes exponen-
tiation. The $ signs are explained below. When this formula is entered into C3, the
number 29.022 appears in C3. This is the value of the polynomial (5.20) at 298.15 K,
the value in A3. (To see the formula that lies behind a number in a cell, we can select
the cell and look in the formula bar that lies above the spreadsheet.) Then click on cell
C3 to highlight it and choose Copy from the Edit menu. (In Excel 2007, click on
Copy on the Home tab.) Then click on cell C4 and drag the mouse from C4 to C15 to
highlight these cells. Then choose Paste from the Edit menu. (In Excel 2007, click on
Paste on the Home tab, and then click Paste in the drop-down menu.) This will paste