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06-10_AB_significant_5_web - 9 22,27,29 Analysis of...

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9/ 22,27,29 Analysis of experimental error 10/4 EXAMINATION # 1
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Uncertainty (practical): how well we can read an instrument! what is our experience with a particular method? standard deviation confidence interval
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However: pK a = 4.76; K a = 1.75 x 10 -5 Using 1.00 mole of CH 3 COONa, per liter: M = (15 + 12 + 32 + 23)g = 82g M = molecular mass (the sum of atomic masses in a molecule = c CH3COONa = C Na+ = 1.00 M) (K b is the base hydrolysis constant) K a K b K w = K b = × - × - = × - 100 10 14 175 10 5 57 10 10 . . . CH COO H O K b CH COOH OH 3 2 3 - + + - 
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CH COO H O K b CH COOH OH 3 2 3 - + + -  ] 3 [ ] ][ 3 [ - - = COO CH OH COOH CH b K K b = × - × - = × - 100 10 14 175 10 5 57 10 10 . . . b K M c COO CH = - 00 . 1 3 - = COO 3 CH c 2 x b K M c b K x COO CH 5 10 4 . 2 00 . 1 10 10 7 . 5 3 - × = - × = = - pH = = 9.40
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M x COOH CH OH 5 10 4 . 2 ] 3 [ ] [ - = = - M x COO CH ) 5 10 4 . 2 00 . 1 ( ] 3 [ - - = -
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DATA HANDLING  SIGNIFICANT FIGURES PROPAGATION OF ERROR Harris, pages: 51 – 54
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A result of chemical analysis consists of two elements: the value (x) and the error e (or s ). x ± e Even if the error is not given explicitly, one can assume that the error is accounted for by presenting the value of the result with an adequate number of significant figures .
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SIGNIFICANT FIGURES The number of significant figures is the minimum number of digits necessary to write a value without a loss in accuracy. Scientific notation should be used in order to avoid ambiguity created by end zeros ( trailing zeros ) of a number. The number of figures is very often higher than the number of significant figures. The figures have to be used to express the order of magnitude. (Below, the # of sign. figures = 4) 124 000 vs. 1.240 × 10 5 As 4 significant figures only, the last significant figure is uncertain to at least ± 1.
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Correct (e.g., given) is: V = 37.5 ± 0.5 mL (any value between 37.0 and 38.0 is possible) Incorrect : V = 37.50 mL The best we can do is to write: V = 37.5 mL This overestimates the accuracy, we only show the minimum uncertainty which is ±1 in the last digit: V = 37.5 ± 0.1 mL The explicitly given error is by far a better method to express the uncertainty .
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What is the number of significant figures in arithmetic operations? The result should be rounded off to keep the same decimal place as in the least accurate of the numbers to be operated on.
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