221FinalEquations

221FinalEquations - Constants R = 8.314 J-K-1-mol-1 N0 = 6.022 1023 mol-1 Related Information Quadratic Equation if ax bx c = 0 2 kB = 1.381 10-23

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Constants R =8 . 314 J-K - 1 -mol - 1 k B =1 . 381 × 10 - 23 J-K - 1 e . 1602 × 10 - 19 C m e =9 . 11 × 10 - 31 kg N 0 =6 . 022 × 10 23 mol - 1 h . 626 × 10 - 34 J-s c =2 . 998 × 10 8 m-s - 1 & 0 . 854 × 10 - 12 C 2 N - 1 m - 2 Related Information Quadratic Equation: if ax 2 + bx + c =0 , then x = - b ± b 2 - 4 ac 2 a Standard Deviation: s = ± ( x i - x ) 2 N - 1 Error Propagation Equation: σ 2 y ( u, v,. .. )= σ 2 u ² dy du ³ 2 + σ 2 v ² dy dv ³ 2 + ··· t-tests: True Mean Comparison: x 1 - x 2 = ± ts/ N Measured Means Comparison (when σ 2 1 = σ 2 2 ): x 1 - x 2 = ± ts pooled ± N 1 + N 2 N 1 N 2 s pooled = ´ s 2 1 ( N 1 - 1) + s 2 2 ( N 2 - 1) N 1 + N 2 - 2 Measured Means Comparison (when σ 2 1 ² = σ 2 2 ): | x 1 - x 2 | = ± t µ s 2 1 /N 1 + s 2 2 2 ν = ( s 2 1 1 + s 2 2 2 ) 2 ( s 2 1 1 ) 2 N 1 +1 + ( s 2 2 2 ) 2 N 2 - 2 Degrees of Freedom, ν t(90%) t(95%) t(99%) 1 6.314 12.706 63.657 2 2.920 4.303 9.925 3 2.353 3.182 5.841 4 2.132 2.776 4.604 5 2.015 2.571 4.032 6 1.943 2.447 3.707 7 1.895 2.365 3.500 8 1.860 2.306 3.355 9 1.833 2.262 3.250 10 1.812 2.228 3.169 1.64 1.96 2.576 Table 1: Values of t for ν degrees of freedom for 95% conFdence levels. ν = N - 1 = degrees of freedom, and conFdence limit = x ± ts N . 12
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F Distribution F = s 2 A s 2 B . (1) Note that critical F values in the two-tailed F -test table with probability p/ 2 can be found in the one-tailed table F -test with probability p . ν 1 =1 2 3 4 5 6 7 8 9 10 12 15 20 ν 2 1 161.4 199.5 215.7 224.6 230.2 234.0 236.8 238.9 240.5 241.9 243.9 245.9 248.0 254.3 2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 19.41 19.43 19.45 19.50 3 10.13 9.552 9.277 9.117 9.013 8.941 8.887 8.845 8.812 8.786 8.745 8.703 8.660 8.53 4 7.709 6.944 6.591 6.388 6.256 6.163 6.094 6.041 5.999 5.964 5.912 5.858 5.803 5.63 5 6.608 5.786 5.409 5.192 5.050 4.950 4.876 4.818 4.772 4.735 4.678 4.619 4.558 4.36 6 5.987 5.143 4.757 4.535 4.387 4.284 4.207 4.147 4.099 4.060 4.000 3.938 3.874 3.67 7 5.591 4.737 4.347 4.120 3.972 3.866 3.787 3.726 3.677 3.637 3.575 3.511 3.445 3.23 8 5.318 4.459 4.066 3.838 3.687 3.581 3.500 3.438 3.388 3.347 3.284 3.218 3.150 2.93 9 5.117 4.256 3.863 3.633 3.482 3.374 3.293 3.230 3.179 3.137 3.073 3.006 2.936 2.71 10 4.965 4.103 3.708 3.478 3.326 3.217 3.135 3.072 3.020 2.978 2.913 2.845 2.774 2.54 12 4.747 3.885 3.490 3.259 3.106 2.996 2.913 2.849 2.796 2.753 2.687 2.617 2.544 2.30 15 4.543 3.682 3.287 3.056 2.901 2.790 2.707 2.641 2.588 2.544 2.475 2.403 2.328 2.07 20 4.351 3.493 3.098 2.866 2.711 2.599 2.514 2.447 2.393 2.348 2.278 2.203 2.124 1.84 Table 2: Critical values of F
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This note was uploaded on 07/17/2008 for the course CHEM 221 taught by Professor Grandinetti during the Spring '08 term at Ohio State.

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221FinalEquations - Constants R = 8.314 J-K-1-mol-1 N0 = 6.022 1023 mol-1 Related Information Quadratic Equation if ax bx c = 0 2 kB = 1.381 10-23

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