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EXPERIMENTAL ERRORS & STATISTICS

EXPERIMENTAL ERRORS & STATISTICS. NURUL AUNI BINTI ZAINAL ABIDIN FACULTY OF APPLIED SCIENCE UITM NEGERI SEMBILAN. The number of atoms in 12 g of carbon:. 602,200,000,000,000,000,000,000. The mass of a single carbon atom in grams:. 0.0000000000000000000000199. Scientific Notation.

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EXPERIMENTAL ERRORS & STATISTICS

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  1. EXPERIMENTAL ERRORS & STATISTICS NURUL AUNI BINTI ZAINAL ABIDIN FACULTY OF APPLIED SCIENCE UITM NEGERI SEMBILAN

  2. The number of atoms in 12 g of carbon: 602,200,000,000,000,000,000,000 The mass of a single carbon atom in grams: 0.0000000000000000000000199 Scientific Notation 6.022 x 1023 1.99 x 10-23 N x 10n N is a number between 1 and 10 n is a positive or negative integer Free powerpoint template: www.brainybetty.com

  3. 568.762 0.00000772 move decimal left move decimal right n > 0 n < 0 568.762 = 5.68762 x 102 0.00000772 = 7.72 x 10-6 Addition or Subtraction • Write each quantity with the same exponent n • Combine N1 and N2 • The exponent,n, remains the same 4.31 x 104 + 3.9 x 103 = 4.31 x 104 + 0.39 x 104 = 4.70 x 104 Free powerpoint template: www.brainybetty.com

  4. Multiplication • Multiply N1 and N2 • Add exponents n1and n2 (4.0 x 10-5) x (7.0 x 103) = ? = (4.0 x 7.0) x (10-5+3) = 28 x 10-2 = 2.8 x 10-1 (a x 10m) x (b x 10n) = (a x b) x 10m+n Division • Divide N1 and N2 • Subtract exponents n1and n2 8.5 x 104÷ 5.0 x 109 = ? = (8.5 ÷ 5.0) x 104 - 9 = 1.7 x 10-5 (a x 10m) ÷ (b x 10n) = (a ÷b) x 10m-n Free powerpoint template: www.brainybetty.com

  5. Significant Figures • - The meaningful digits in a measured or calculated quantity. • RULES: • Any digit that is not zero is significant • 1.234 kg 4 significant figures • Zeros between nonzero digits are significant • 606 m 3 significant figures • Zeros to the left of the first nonzero digit are not significant • 0.08 L 1 significant figure • If a number is greater than 1, then all zeros to the right of the decimal point are significant • 2.0 mg 2 significant figures Free powerpoint template: www.brainybetty.com

  6. If a number is less than 1, then only the zeros that are at the end and in the middle of the number are significant • 0.00420 g 3 significant figures • Numbers thatdo not contain decimal points, zeros after the last nonzero digit may or may not be significant. • 400 cm 1or 2 or 3 significant figures • 4 x 102 1 significant figures • 4.0 x 102 2 significant figures Free powerpoint template: www.brainybetty.com

  7. How many significant figures are in each of the following measurements? 24 mL 2 significant figures 4 significant figures 3001 g 0.0320 m3 3 significant figures 6.4 x 104 molecules 2 significant figures 560 kg 2 significant figures Free powerpoint template: www.brainybetty.com

  8. 89.332 + 1.1 one significant figure after decimal point two significant figures after decimal point 90.432 round off to 90.4 round off to 0.79 3.70 -2.9133 0.7867 Significant Figures Addition or Subtraction The answer cannot have more digits to the right of the decimal point than any of the original numbers. Free powerpoint template: www.brainybetty.com

  9. 3 sig figs round to 3 sig figs 2 sig figs round to 2 sig figs Significant Figures Multiplication or Division The number of significant figures in the result is set by the original number that has the smallest number of significant figures 4.51 x 3.6666 = 16.536366 = 16.5 6.8 ÷ 112.04 = 0.0606926 = 0.061 Free powerpoint template: www.brainybetty.com

  10. QUESTION Free powerpoint template: www.brainybetty.com

  11. LOGARITHMS AND ANTILOGARITHMS log 9.57 x 10-4 = -3.019 log 957 = 2.981 Example 3 2 Characteristics Mantissa 0.981 0.019 In converting a number to its logarithm, the number of digits in mantissa of the log of the number (957) should be equal to the number of SF in the number (957). For antilogarithm, 10 0.072 = 1.18 Free powerpoint template: www.brainybetty.com

  12. Types of Errors in Chemical Analysis 1. Absolute Error Definition: The difference between the true value and the measured value E = xi – xt Where xi = measured value xt = true or accepted value Example: If 2.62 g sample of material is analyzed to be 2.52 g, so the absolute error is − 0.10g. Free powerpoint template: www.brainybetty.com

  13. 2. Relative Error Definition: The absolute or mean error expressed as a percentage of the true value. Er = xi – xt x 100% xt The above analysis has a relative error of − 0.10 gx 100% = -3.8% 2.62 g * We are usually dealing with relative errors of less than 1%. A 1% error is equivalent to 1 part in 100. Free powerpoint template: www.brainybetty.com

  14. 2.1 Relative Accuracy Definition: The measured value or mean expressed as a percentage of the true value. Er = xi x 100% xt The above analysis has a relative accuracy of 2.52 gx 100% = 96.2 % 2.62 g Free powerpoint template: www.brainybetty.com

  15. 3. Systematic Error or determinate error • Definition: A constant error that originates from a fixed cause, such as flaw in the design of an equipment or experiment. • It caused the mean of a set data to differ from the accepted value. • This error tends to cause the results to either high every time or low every time compared to the true value. • There are 3 types of systematic error: Oct 2008 Free powerpoint template: www.brainybetty.com

  16. 3.1 Instrumental Errors • All measuring devices contribute to systematic errors. • Glassware such as pipets, burets, and volumetric flasks may hold volume slightly different from those indicated by their graduations. • Occur due to significant difference in temperature from the calibration temperatere. • Sources of uncertainties: Decreased power supply voltage Increases resistance in circuits due to temperature change Free powerpoint template: www.brainybetty.com

  17. 3.2 Method Errors • Non-ideal analytical methods are often sources of systematic errors. • These errors are difficult to detect. • The most serious of the 3 types of systematic errors. Free powerpoint template: www.brainybetty.com

  18. 3.3 Personal Errors • Involve measurements that require personal judgment. • For example : • i) estimation of a pointer between tow scale divisions. • ii) color of solution. • iii) level of liquids with respect to a graduation in a burette. • iv) prejudice. Free powerpoint template: www.brainybetty.com

  19. 3.4 Effect of Systematic Errors Free powerpoint template: www.brainybetty.com

  20. 3.5 Detection and Control of Systematic Errors Free powerpoint template: www.brainybetty.com

  21. 4 Random Error or Indeterminate error • Cause data to be scattered more or less symmetrically around a mean value. • It reflects the precision of the measurement. • This error is caused by the many uncontrollable variables in physical or chemical measurements. Free powerpoint template: www.brainybetty.com

  22. 5 Gross Error • Differ from indeterminate and determinate errors. • They usually occur only occasionally, may cause a result to be either high or low. • For example: • i) part of precipitate is lost before weighing, analytical results will be low. • ii) touching a weighing bottle with your fingers after empty mass will cause a high mass reading for a solid weighed. • Lead to outliers, results in replicate measurements that differs significantly from the rest of the results. Free powerpoint template: www.brainybetty.com

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