Curve Fitting

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9.1 The following data describes the relationship between Celsius and Kelvin
Celsius , Kelvin
200 , -73.15
300 , 26.85
400 , 126.85
450 , 176.85
500 , 226.85
What's the equation for this relationship ?
Solution:
Insert the data set in the Data: (X Y) text field and calculate. The equation visible in the Function field represent the relationship.


9.2 How many Fahrenheit is 100 oCelsius ?
Celsius , Fahrenheit
-73.15 , -99.67
26.85 , 80.33
126.85 , 260.33
176.85 , 350.33
226.85 , 440.33


Solution:
Insert the data set in the Data: (X Y) text field and calculate. The equation visible in the Function field represent the relationship. Use this equation and calculate Y (X = 100).


9.3 Determine the vapor pressure of butadiene at 0oC knowing following temperature/pressure relationship.
0oC , P (mm Hg)
-61.3 , 40
-55.1 , 60
-46.8 , 100
-33.9 , 200
-19.3 , 400
-4.4 , 760
15.3 , 1520
48 , 3700
76.0 , 7600


Solution:
Insert the data set in the Data: (X Y) text field and select Best Fit . The equation visible in the Function field represent the relationship. Use this equation and calculate Y (X = 0).



9.4 Use following experimental data (time and radiation - counts per second) to determine the half life T1/2 for the Pa[234] isotope.
Time(sec) , radiation (cps)
60 , 66.7
150 , 26.9
240 , 11.0
330 , 4.9
420 , 1.7


Solution:
Insert the data set in the Data: (X Y) text field and select Best Fit. The relationship is represented by the equation Y = A * exp(B*X) visible in the Function field. Use the coeff. B in the generated equation and calculate T1/2 knowing that T1/2 = (ln 2)/B .
9.5 The following data where obtained on the rate of hydrolysis of 16% sucrose in 0.1 mol/L HCl aqueous solutions at 34 oC.
t/min , Sucrose remaining %
9.83 , 96.5
59.60 , 80.2
93.18 , 71.0
142.9 , 59.1
294.8 , 32.8
589.4 , 11.1
What is the order of reaction with respect to sucrose ?

Solution:
Insert the data set in the Data: (X Y) text field and select Best Fit. By the curve, an exact exponential decay, we can conclude that the reaction is of first order.


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