1. Suppose that a list contains the values 20 44 48 55 62 66 74 88 93 99 at index positions 0 through 9. Trace the values of the variables….

## calculate the a values using the expressions below:

2-D Regression. Using the Power vs. Speed and Throttle setting data in problem 13-6, find the coefficients for the polynomial fitting equation

Proble 13-6

NMR Titration. The protonation constants K1 and K2 of a diprotic acid H2A were determined by NMR titration. (Protonation constants, for example,

are used in this example because they simplify the equilibrium expressions The chemical shift S of a hydrogen near the acidic sites was measured at a number of pH values over the range pH 1 to pH 11. The data are shown in the following Figure (data table and figure are on the CD that accompanies this book).

At any pH value there are three acid-base species in solution: H2A, HAand A2-; the observed chemical shift is given by the expression

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:

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