Ch 3. EXPERIMENTAL ERROR

Transcription

1 Ch 3. EXPERIMENTAL ERROR 3.1 Measurement data how accurate? TRUE VALUE? No way to obtain the only way is approaching toward the true value. (how reliable?) How ACCURATE How REPRODUCIBLE accuracy precision During these process, UNCERTAINTY exists always Significant Figures x x x10 4 * zero significant between numbers after " insignificant before numbers

2 3-2. Sig. Figures in Arithmetic 3.3 1) addition & subtraction x x x increase or decrease in sig. fig. is possible is not significant OK 3.4 2) multiplication & division answer with the least number of sig. fig x ) logarithms & antilogarithms log 339 = : character, 530: mantissa # of sig fig of mantissa = # of sig. figure of antilogarithm (ex. 339 = 3.39x10 2 ) ex) log = log 3.2 = 0.51 antilog 4.37 = 2.3 x 10 4

3 3-3. Types of Error : systematic or random 3.5 1) Systematic error (Determinate Error) : can be eliminated - instrumental & reagent error (incorrectly standardized ph meter) - personal errors : incomplete drying, mechanical loss of materials (during dissolution), : incorrect lab techniques (sample transfer) - method errors (using a wrong method) : background absorption in AAS : faulty detector response in chromatographic & spectroscopic anal. : Matrix effect : Solubility of a precipitate in the solution in which it is precipitated : Failure of a reaction to proceed to quantitative completion : Coprecipitation : Decomposition or volatilization of a precipitate : Induced reactions & side reactions 3-3. Types of Error : systematic or random 3.6 * How to reduce systematic errors? -calibration of apparatus and application of corrections -running a blank determination -running a control determination -using standards: Euronorm CRM, NIST -use of independent methods of analysis -standard addition -internal standards

4 3-3. Types of Error : systematic or random 3.7 2) Random Error (Indeterminate Error) It always exists, and can't be corrected. - Small fluctuations in the successive values Ex) electrical noise. (assumed that it is measured by the same person with great care under nearly the same conditions) Sufficiently large number of observations * Ultimate limitation on the determination of a quantity How to solve this? Best is to reduce How to know random or systematic? Within the statistical limit Beyond the limit By statistical calculations - random error - systematic error 3-3. Types of Error : systematic or random 3.8 3) Precision & Accuracy precision : a measure of reproducibility accuracy : how close a measured value to the true value ex) highly reproducible but a wrong answer? How to get near True Value? by an experienced worker using a well-tested procedures 4) Absolute & Relative Uncertainty For a measurement ml Absolute uncertainty : 0.02 Relative uncertainty: or 0.2%

5 3-4 Propagation of Uncertainty 3.9 uncertainty called as "standard deviation" "confidence interval" HOW does the uncertainty CHANGE during CALCULATION? 1) addition & subtraction e e e e e e e e or percent rel. uncertainty = % Propagation of Uncertainty ) multiplication & division all calculations done with relative uncertainties (% e) % e (% e1) (% e2) (% e3 ) Ex) 1.76( 0.03) 1.89( 002) 0.59( 0.02) ) mixed operations? 1.76( 0.03) 0.59( 0.02) 1.89( 0.02)

6 3-4 Propagation of Uncertainty ) The real rule for Sig figures The first digit of the abs. uncertainty is the last digit in the answer ( ) ( ) ( ) ( ) ( ) ( ) <additional example> Calculate the uncertainty in the number of millimoles of chloride contained in ml of a sample when three equal aliquots of ml are titrated with silver nitrate with the following results: 36.78mL, 36.82mL, 36.75mL. The molarity of the AgNO 3 is M. ( mmol)

7 3-4 Propagation of Uncertainty ) Exponents & Logarithms y y x a x % ey a(% ex ) 1/ 2 x 2% in x --- 1/2(2%) = 1% in y y log x 1 ex e ey ln10 x x x Check with Table

8 Homework 3.15 Ch 3-12, 14, 17, 21