Page 239 - Physical Chemistry

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Chapter 7 Figure 7.8
One-Component Phase Equilibrium
and Surfaces Spreadsheet for finding H . The lower view shows the formulas.
m
vap
A B C D E F G
1 vapor pressure H2O CC eqn lst sqs
2 t 90/C T/K P/torr ln P/torr 1/T P(exp fit) res-sqs
3 39.99 313.14 55.364 4.01393 0.003193 55.58574 0.04917
4 49.987 323.137 92.592 4.5282 0.003095 92.37595 0.046677
5 59.984 333.134 149.51 5.00736 0.003002 148.9069 0.363762
6 69.982 343.132 233.847 5.45467 0.002914 233.4571 0.152036
7 79.979 353.129 355.343 5.87308 0.002832 356.7985 2.118484
8 sumsqres 2.73013
9 b m
10 20.43627 -5141.24

A B C D E F G
1 vapor press
2 t 90/C T/K P/torr ln P/torr 1/T P(exp fit) res-sqs
3 =40-0.01 =A3+273.15 55.364 =LN(C3) =1/B3 =EXP($F$10+$G$10/B3) =(F3-C3)^2
4 =50-0.013 =A4+273.15 92.592 =LN(C4) =1/B4 =EXP($F$10+$G$10/B4) =(F4-C4)^2
5 =60-0.016 =A5+273.15 149.51 =LN(C5) =1/B5 =EXP($F$10+$G$10/B5) =(F5-C5)^2
6 =70-0.018 =A6+273.15 233.847 =LN(C6) =1/B6 =EXP($F$10+$G$10/B6) =(F6-C6)^2
7 =80-0.021 =A7+273.15 355.343 =LN(C7) =1/B7 =EXP($F$10+$G$10/B7) =(F7-C7)^2
8 sumsqres =SUM(G3:G7)
9 b m
10 20.43627 -5141.24

chosen, enter D3:D7 as the Input Y range and E3:E7 as the Input X range. Click
the Output range button and enter a cell such as A14 as the upper left cell of the
least-squares-fit output data. Click the Residuals box and the Residual Plots box,
and click on OK. You get a host of statistical data as output. The desired constants
b and m are the two numbers listed under the heading Coefficients. One finds
20.4363 as the intercept b and 5141.24 as the slope m (the coefficient of the X
Variable). (You are also told that there is a 95% probability that the slope lies in the
range 5093 to 5190.) Although the residuals [the deviations of the experimen-
tal ln (P/torr) values from the values calculated using the straight-line fit] are small,
note that the graph of the residuals is roughly parabolic with positive residuals for
the middle three points and negative residuals for the first and last points. This in-
dicates that the data fit a curved line a bit better than a straight line. (We know that
H is not really constant, and two other approximations have been made.) For
m
data that have random errors on top of a straight-line fit, the residuals are randomly
positive and negative. [Another way in Excel to get the coefficients of a straight-
line fit is to enter the formulas =SLOPE(D3:D7,E3:E7) and =INTERCEPT
(D3:D7,E3:E7) into two empty cells. A third way is to graph the data using an
XY (Scatter) plot that plots only the data points. Then add a trendline to the chart,
as discussed in Sec. 5.6.]
1
Since we plotted ln (P/torr) versus 1/T, the slope has units K . Thus
5141.2 K 1 H /R, and
m
1
1
1
¢H 15141.2 K 218.3145 J mol K 2 42.75 kJ>mol
m