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Unformatted text preview: the place were the approximation was made, viz: 3 2 2 4 10 14 . 5 03 . 10 8 . 8×= × x where, note, we have now written x 2 as the second iteration and substituted the value of x 1 only in the place where we approximated it to be negligible – in the denominator. Solving yields x 2 = 4.68 × 10 –3 . Cycle 3 : We now repeat the process to obtain: 3 2 3 4 10 68 . 4 03 . 10 8 . 8×= × x yielding x 3 = 4.72 × 10 –3 . Note that the difference between x3 and x2 is smaller than that between x2 and x1. Cycle 4 : Repeat and get x 4 = 4.72 × 10 –3 . To the number of significant digits, the value of x is now constant and said to be “selfconsistent” or to have “converged.” The exact value obtained from solving the quadratic formula is x = 4.717 × 10 –3 ....
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 Fall '07
 Warren
 Chemistry, Bases, pH, arbitrary specific case

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