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Analytical Chemistry Midterm Review

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McMaster University
Engineering Technology
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Equations//Symbols//Calculations Absolute error(E) = x xi - t Relative error (E r) 100% = 10 ppt = 1000ppm Sample mean ( )x= If N is large then the mean (x) is called the population mean, (μ) and if it is in the absence of errors then μ or the population mean is called the true result Spread = (highest – lowest) Mean deviation (d) = average value of result mean result x x x x x Standard deviation (σ or s) Detailed results show that when we calculate the standard deviation, we can predict the following if the result is repeated many times; - 68% of results will be within 1 σ of the mean - 96% of results will be within 2σ of the mean - 99.7 of results will be within 3σ of the mean Population standard deviation (σ): If N > 20 x x x x Sample standard deviation (s): If N < 20 x x x x The mean ( X ) and the standard deviation (σ or s) values apply to the numerical value of the result Coefficient of variation (CV): x x Relative error (Relative.Standard.Deviation%): x x 6 1L = 1000mL = 1000g = 1000000 mg - (mass of solute(mg) / 10 mg solution = ppm Buoyancy error Temperature correction Error caused by buoyancy is < 0.1% for objects with density > 2g/cm 2 Volume, mL Volume, mL Temperature, T, ºC At T Corrected to 20ºC 20 ºC 1.0028 1.0028 //other temperatures // // 25 ºC 1.0040 1.0037 Ex. A 25mL pipet delivers 24.976 g of water weighed against steel mass at 25 ºC - @ 25 ºC: V = 24.976 g 1.0040 mL/g o V = 25.076 mL - @20 ºC: V = 24.976 g 1.0037 mL/g o V = 25.068 mL Rounding Going from infinite set of #’s to a finite set of #’s When rounding calculations, carry at least one extra digit beyond significant digits through calculations to avoid rounding error Significant digits - Magnitude - Units - Error Rules for “Sig figs” - All non-zero digits are significant - Zeros are significant if: o Between significant figures o Right of decimal and right of significant figures - For logarithms anything before decimal is not significant and anything after the decimal. Rules for significant figures in calculations - Addition and/or subtraction o Round answer to the “least reliable” decimal place - Multiplication and/or division o Round answer to match the factor with the fewest number of significant figures - Mixed calculations o Determine the number of significant digits in the same order for which you perform the calculation B.E.D.M.A.S - Multiple calculations o Save any round until the end of the problem - Mean ( X ) o Decimal places for the mean should match the decimal places of the measurements used to calculate the mean - Standard deviation (σ or s) o Decimal places for the standard deviation should match the decimal places of the measurements used to calculate the standard deviation Error propagation (σ propagation) - Addition/subtraction - Multiplication/division Then multiply by y Rounding error propagation - Round the S ty appropriate significant figures - Round answer y to the same # of decimal places as the error term Practice Quiz 1: Four solutions prepared by dissolving appropriate amounts to make 250mL solution in flask 1 2 3 4 5 6 7 8 9 Solution Compound g mg g/mol # of # of concentration ppm # moles mL [mol/L] 1 A 200.0 39.99 2 B 1.260 0.0210 3 C 18.00 2000.0 4 C 3.600 100.0 Gravimetric analysis (Weighing) Sample variance (s ):
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