Page 190 - Physical Chemistry

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2CO1g2 O 2 1g2 S 2CO 2 1g2 135 35.988, 36.277, and 36.544. Use a spreadsheet to fit a cubic
polynomial [Eq. (5.20)] to these data.
C1gr2 O 2 1g2 S CO 2 1g2 94
5.28 Instead of inserting a trendline, another Excel procedure
find H° of FeO(s) and of Fe O (s). to fit a cubic function to C data is as follows. Enter the C data
298
3
f
2
P
P
in cells A3 to A15; enter the T values in B3 to B15; enter the T 2
5.19 Given the following H° /(kJ/mol) values,
298
values in C3 to C15 by entering the formula =B3^2 in C3 and
3
4NH 3 1g2 5O 2 1g2 S 4NO1g2 6H 2 O1l2 1170 copying and pasting this formula to C4 to C15; enter the T val-
ues in D3 to D15. From the Tools menu, choose Data Analysis.
2NO1g2 O 2 1g2 S 2NO 2 1g2 114 (In Excel 2007, click the Data tab and then click Data Analysis.)
(If Data Analysis is not visible on the Tools menu, choose
3NO 2 1g2 H 2 O1l2 S 2HNO 3 1l2 NO1g2 72
Add-Ins on the Tools menu, check Analysis ToolPak and click
find H° for NH (g) 2O (g) → HNO (l) H O(l) without OK.) In the Data Analysis box choose Regression and click OK.
3
2
3
298
2
using Appendix data. In Input Y Range enter A3:A15 (the colon indicates a range);
in Input X Range enter B3:D15; click in the Residuals Box, the
5.20 Apply H° n H°to Eq. (1) preceding Eq. (5.11) Line Fit Plots box, and the Residual Plots box; then click OK.
f
i
i
i
and use data in Eqs. (1), (2), and (3) to find H° of C H (g). On a new sheet in the workbook, you will get output that in-
298
2
f
6
5.21 (a) A gas obeys the equation of state P(V b) RT, cludes the desired coefficients in a column labeled Coefficients.
m
where b is a constant. Show that, for this gas, H m,id (T, P) The predicted C values and their errors (the residuals) will also
P
3
H m,re (T, P) bP. (b) If b 45 cm /mol, calculate H m,id be listed. (You can go from one sheet of a workbook to another
H m,re at 25°C and 1 bar. by clicking on the tab for the desired sheet at the bottom of the
screen.) Carry out this procedure for the CO C data and verify
P
5.22 Use Appendix data to find the conventional H° of that the same results are found as in Sec. 5.6. The Regression
m
(a) H (g) at 25°C; (b) H (g) at 35°C; (c) H O(l) at 25°C; procedure allows one to find the coefficients A, B, C, D, ... in
2
2
2
(d) H O(l) at 35°C. Neglect the temperature dependence of C . the fit g(x) A Bf (x) Cf (x) Df (x) , where f , f ,
2
P
3
2
1
2
1
f , . . . are functions that do not contain unknown constants. In
3
Section 5.5 this example, the f’s are T, T , and T .
3
2
5.23 True or false? (a) The rate of change of H° with respect
P
to temperature is equal to C°. (b) The rate of change of H° 5.29 Another form besides (5.20) used to fit C data is A
P
2
2
with respect to pressure is zero. (c) For a reaction involv- BT CT D/T . Use the Regression procedure of Prob. 5.28
ing only ideal gases, C° is independent of temperature. to find the coefficients A, B, C, and D that fit the CO data. You
P
2
TdT (T T ) .
T 2 1 2 will need a column containing 1/T values. Use the spreadsheet
(d) T 1 2 2 1
to calculate the sum of the squares of the residuals for this fit
5.24 Use data in the Appendix and the approximation of ne- and compare with the fit given by (5.20). Entering the Excel
glecting the temperature dependence of C° P,m to estimate H° 370 formula =SUM(K3:K15) into a cell will put the sum of the
for the reactions of Prob. 5.10. numbers in cells K3 to K15 into that cell.
5.25 Compute H° 1000 of HCl(g) from Appendix data and Section 5.7
f
these C° /[J/(mol K)] expressions, which hold from 298 K to
P,m
1500 K. 5.30 True or false? For the combustion of glucose, S° equals
T
H°/T.
T
2
2
27.14 0.0092741T>K2 1.381110 5 T >K 2
5.31 For solid 1,2,3-trimethylbenzene, C° P,m 0.62 J mol 1
3
9
3
7.645110 T >K 2 K 1 at 10.0 K. Find S° at 10.0 K for this substance. Find C° P,m
m
and S° at 6.0 K for this substance.
m
2
2
26.93 0.033841T>K2 3.896110 5 T >K 2
5.32 Substance Y melts at 200 K and 1 atm with H
m
fus
3
3
9
15.47110 T >K 2 1450 J/mol. For solid Y, C° cT dT for 10 K T
3
4
P,m 2 3
2
2
30.67 0.0072011T>K2 1.246110 5 T >K 2 20 K and C° P,m e fT gT hT for 20 K T 200 K.
2
3
For liquid Y, C° i jT kT lT for 200 K T 300
P,m
3
3
9
3.898110 T >K 2 K. (a) Express S° m,300 of liquid Y in terms of the constants c, d,
e, ..., l. (b) Express H° m,300 H° of liquid Y in terms of these
m,0
for H (g), Cl (g), and HCl(g), in that order. constants. Neglect the difference between 1-atm and 1-bar prop-
2
2
erties of the solid and liquid.
Section 5.6
5.26 Set up a spreadsheet and verify the CO C fit given in 5.33 C P,m values at 1 atm for SO [mainly from Giauque and
2
P
Sec. 5.6. Stephenson, J. Am. Chem. Soc., 60, 1389 (1938)] are as fol-
lows, where the first number in each pair is T/K and the second
5.27 Values of C° /(J/mol-K) for O (g) at T/K values of number (in boldface type) is C P,m in cal/(mol K). Solid: 15,
2
P,m
298.15, 400, 500, ..., 1500 are 29.376, 30.106, 31.091, 0.83; 20, 1.66; 25, 2.74; 30, 3.79; 35, 4.85; 40, 5.78; 45, 6.61;
32.090, 32.981, 33.733, 34.355, 34.870, 35.300, 35.667, 50, 7.36; 55, 8.02; 60, 8.62; 70, 9.57; 80, 10.32; 90, 10.93; 100,