Page 359 - Excel for Scientists and Engineers: Numerical Methods

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PH

Figure 14-12. NMR titration.
At any pH value there are three acid-base species in solution: H2A, HA-
and A2-; the observed chemical shift is given by the expression
6cdc = a060 + a14 + a262
where a, is the fraction of the species in the form containing j acidic
hydrogens and q is the chemical shift of the species. The a values can be
calculated using the expressions below:
PJ LH' 1'
a, =
W,[H+IJ
P, =K,K ,... K, (Po =1)
KIK2 [H' l2
a2 =
1 + K, [H'] + K,K2 [H'I2

Use the Solver to determine KI, K2, &, 61 and 6;.

7. 2-D Regression. Using the Power vs. Speed and Throttle setting data in
problem 13-6, find the coefficients for the polynomial fitting equation
P=(a~++bT+c)SS+(dT+e)S+f