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CHEMISTRY

Precision, Accuracy and Uncertainty. CHEMISTRY. Definitions. Precision : the degree of agreement among several measurements of the same quantity; the reproducibility of a measurement. Accuracy : the ability to be precise and avoid errors.

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CHEMISTRY

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  1. Precision, Accuracy and Uncertainty CHEMISTRY

  2. Definitions • Precision: the degree of agreement among several measurements of the same quantity; the reproducibility of a measurement. • Accuracy: the ability to be precise and avoid errors. • Uncertainty of measurement: the characteristic reflecting the fact that any measurement involves estimates and cannot be exactly reproduced.

  3. Laboratory Experiments • Precision involves the type of instrument used; where as Accuracy is dependant upon the student using it. • Uncertaintyis used to check to see if the use of instruments is reliable within reasonable standards.

  4. When In Rome • 1. In the laboratory all numbers that can be read are recorded. • 2. Do not estimate between numbers. • 3. Record the accuracy of the instrument as +/- the smallest unit on the instrument.

  5. Examples • A Decigram balance is accurate to the nearest 0.1 g. When recording a mass measured on this instrument the numbers are: 125.2 +/- 0.1 g • A Centigram balance is accurate to the nearest 0.01g. When recording a mass measured on this instrument the numbers are: 15.24 +/- 0.01 g

  6. More Examples • A digital thermometer is accurate to the nearest 0.1 0C. So a temperature is recorded as 23.4 +/- 0.1 0C.

  7. What about the Math? • How do we handle the calculations when the uncertainty is recorded? • ADDITION: 12.3 +/- 0.1 g • + 22.3+/- 0.1 g • Use the maximum – minimum method • MAX: To get the largest possible value then add the largest value to the largest value.

  8. Solve • Problem: 12.3 +/- 0.1 g • + 22.3+/- 0.1 g • 34.6 +/- 0.2 g Add Unc. • MaxMin • 12.4 12.2 +22.4 +22.2 34.8 34.4 34.8 +34.4 69.2/2=34.6 34.8 Large 34.6 Ave 34.4 small } 0.2 =34.6 +/- 0.2g } 0.2

  9. And • When adding or subtracting numbers with an uncertainty the uncertainties are added. • What about multiplying and dividing?

  10. Be Fruitful and Multiply • Multiply the following: • (123.4 +/- 0.1)( 12.33 +/- 0.02) • MaxMin Largest Value is obtained by multiplying Large x Large and the smallest is determined by small x small 123.5 x 12.35 = 1525.225 123.3 x 12.31 = 1517.823 1525.225 Large 1521.524 Ave 1517.823 Small 1525.225 +1517.823 AVE 3043.048/2 = 1521.524 } 3.701 } 3.702 1521.524 +/- 3.702 1522 +/- 4 4 sig figures

  11. Divided? • 234.3 +/- .2 • 12.56 +/- .02 • MaxMin • 234.5234.1 • 12.54 12.58 The Max value for division is L/S and the Min value is S/L =18.70016 =18.60890 18.70016 18.60890 37.30906/2 = 18.6543 18.70016 large 18.65430 ave 18.60890 small { 0.045 { 0.045 18.65 +/-0.05

  12. Another Way • 234.3 +/- .2 • 12.56 +/- .02 • 234.3 +/- 0.2/234.3 = 234.3 +/- 8.54 x 10-4 % • 12.56 +/- 0.02/12.56 = 12.56 +/- 1.59 x 10-3 % • (234.3) / (12.56) +/- ( 8.54 x 10-4 + 1.59 x 10-3) • 18.65 +/- 2.444 x 10-3 % • 18.65 +/- (2.444 x 10-3 x 18.65) • 18.65 +/- 0.05

  13. On the Calculator-TI Language • 234.3 ±.2 • 12.56 ±.02 • .2 234.3 = STO 1 • .02 12.56 = 2nd SUM 1 • Now the % unc is in the memory. • Do the operation • 234.3 12.56 = 18.65 (ans) x RCL 1 = .05 (unc) • 18.65 ± 0.05 ● ● ● ● ● ●

  14. The Other TI • 234.3 ±.2 • 12.56 ±.02 • .2 234.3 =, STO = (This puts the ans in Mem A) • +.02 12.56 =,STO = (adds to the memory) • Now the % unc is in the memory. • Do the operation • 234.3 12.56 = 18.65 (ans) x 2nd RCL =,= .05 (unc) • 18.65 ± 0.05 ● ● ● ● ● ●

  15. Heat of Combustion • The following is the directions to perform the first Laboratory Experiment. Thermometer 400 ml Beaker with water Ring Stand Candle 1000 ml Beaker

  16. Procedure • 1. Determine the mass of the 400 ml beaker on the decigram balance. • 2. Using a graduated cylinder pour 100 ml of water in the beaker and determine its mass with water. • 3. Stick the candle to a piece of paper. • 4. Determine the mass of the candle before burning using the centigram balance. • 5. Set up the apparatus. • 6. Determine the initial temperature of the water. • 7. Light the candle under the 400 ml beaker and allow to burn for 5 minutes. Take the final temperature of the water. • 8. After blowing out the candle and waiting 1 minute determine the mass of the candle after burn.

  17. Data • Measurement Student Value Class Average • Mass of empty beaker • Mass of beaker + water • *Mass of water Mass of candle before burn • Mass of candle after burn • *Mass of candle burned • Initial temperature • Final temperature • *Change in temperature • specific heat of water • *Total heat • *Heat of combustion • *% uncertainty • *% Error 112.3 ± 0.1 g 211.5 ± 0.1 g ___________ 12.65 ± 0.01 g 12.03 ± 0.01 g ____________ 24.3 ± 0.1 0C 36.2 ± 0.1 0C ____________ 4.18 j/g 0C ____________ ____________ ____________ ____________

  18. The Lab • SYMBOLS • q = heat • m = mass • C = specific heat: the amount of heat a substance can hold per gram, per degree Celsius. • Δt = change in temperature • Heat=mass x specific heat x change temperature. • q = m C Δt

  19. Calculations • C. Mass of Water • 211.5 ± 0.1g • -112.3 ± 0.1g • 99.2 ± 0.2g When adding or subtracting – add the uncertainties • F. Mass of candle burned • 12.65 ± 0.01g • -12.03 ± 0.01g • 0.62 ± 0.02g When adding or subtracting – add the uncertainties

  20. Continue • I. Change in Temperature • 36.2 ± 0.1 0C • - 24.3 ± 0.1 0C • 11.9 ± 0.2 0C When adding or subtracting – add the uncertainties • J. Total Heat • q = m x c x Δt • q – The letter used for heat comes from a Latin word that started with a “q”.

  21. Formula, Substitution, Answer • q = m x c x Δt • = ( 99.2 ± 0.2g )( 4.18 j/g0C )( 11.9 ± 0.20C) • = 4,930 ± 90 j • The place of the uncertainty is the same as the number. • Most heat quantities are expressed in kilojoules. • = 4,930 j 1.00 kj • 1.00 x 103 j • = 4.93 ± 0.09 kj • The place of the uncertainty is the same as the number

  22. Use the Calculator-My TI • ( 99.2 ± 0.2g )( 4.18 j/g0C )( 11.9 ± 0.20C) • .2 99.2 = STO 1 • .2 11.9 = 2nd SUM 1 • Now the % unc is in the memory. • Do the operation • 99.2 x 4.18 x 11.9 = 4,930(ans) x RCL 1 = 90 (unc) • 4,930 ± 90 j ● ● ● ●

  23. Use the Calculator-Other TI • ( 99.2 ± 0.2g )( 4.18 j/g0C )( 11.9 ± 0.20C) • .2 99.2 = STO = • + .2 11.9 = STO = • Now the % unc is in the memory. • Do the operation • 99.2 x 4.18 x 11.9 = 4,930(ans) x 2nd RCL = = 90 (unc) • 4,930 ± 90 j ● ● ● ●

  24. Heat of Combustion • Heat of Combustion • Hc = Total Heat (q ) • Mass of candle burned (mc) • Hc = 4.93 ± 0.09 kj • 0.62 ± 0.02g • Hc = 8.0 ± 0.4 kj/g

  25. Use the Calculator-My TI • Hc = 4.93 ± 0.09 kj • 0.62 ± 0.02g • .09 4.93 = STO 1 • .02 0.62 = 2nd SUM 1 • Now the % unc is in the memory. • Do the operation • 4.93 0.62 = 8.0(ans) x RCL 1 = 0.4 (unc) • 8.0 ± 0.4 kj/g ● ● ● ● ● ●

  26. Use the Calculator-Other TI • Hc = 4.93 ± 0.09 kj • 0.62 ± 0.02g • .09 4.93 = STO = • +.02 0.62 = STO = • Now the % unc is in the memory. • Do the operation • 4.93 0.62 = 8.0(ans) x 2nd RCL= = 0.4 (unc) • 8.0 ± 0.4 kj/g ● ● ● ● ● ●

  27. Check The Instruments • Percent Uncertainty • % Unc. = Unc x 100% • Ans • = 0.4 x 100% • 8.0 • = 5.0 % • When the % Unc is less than 10% the experiment is considered reliable.

  28. Check the Student • Percent Error • The % Error is comparing a student value to a standard value. • In this lab the standard value will be the class average. ( Assume for this lab that is 8.16 kj/g ) • % Error = High Value (H) – Low Value (L) x 100% • High Value (H) • = 8.16 – 8.0 x 100% • 8.16 • = 2.0% • % Error is acceptable when below 10%

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