1. Luis Avila avila@chem.columbia.edu Isabelle Vu Trieu ilv2@columbia.edu Intensive General Chemistry Uncertainty Analysis Wet Techniques

2. Introduction Measurement and Uncertainty Qualitative Analysis What is in the unknown? Quantitative Analysis How much of it is in the unknown?

3. Uncertainty in Measurement Measurements always involve a comparison The comparison always involve some uncertainty Length of the beetle’s body? -between 0 and 2 in -between 1 and 2 in -between 1.5 and 1.6 in -between 1.54 and 1.56 in -between 1.543 and 1.548 in Convention: Read 1/10 of the distance between the smallest scale division

4. Significant Figures Definition: –all digits up to and including the first uncertain digit Ex: Beetle’s length is 1.55 in (3 sig fig) 4.0 cm (2 sig fig) 0.04 m (1 sig fig) –The more significant figures, the more reproducible a measurement is (ex: ∏) –Counts and defines numbers are exact - They have no uncertain digits!

5. Counting significant figures in a series of measurements Compute the average Identify the first uncertain digit Round the average so that the last digit is the first uncertain digit Ex: Beetle’s length »Measurement 1: 3.98 cm »Measurement 2: 4.01 cm »Measurement 3: 4.00 cm AVERAGE = 4.00 cm or 4.00 x 10 -2 m

6. Precision of Calculated Results calculated results are never more reliable than the measurements they are built from multistep calculation: never round intermediate results! Sums and differences: round result to the same number of fraction digits as the poorest measurement Ex: 4.01+ 22.2222 = 26.23 Products and quotients: round result to the same number of significant figures as the poorest measurement Ex: 4.01 x 22.2222 = 89.1

7. Precision versus Accuracy good precision & good accuracy good precision but poor accuracy poor precision & poor accuracy poor precision but good accuracy

8. Precision versus Accuracy Random Errors versus Systematic Errors Precision –Reproducibility –Check by repeating measurements –Poor precision results from poor technique Random Errors –Random sign –Varying magnitude Accuracy –Correctness –Check by using a different method –Poor accuracy results from procedurial or equipment defects Systematic Errors –Reproducible sign –Reproducible magnitude

9. Estimating Precision Standard Deviation standard deviation sample mean total number of measurements the ith value

10. Expressing Experimental Error Absolute error = Magnitude of the random error Ex: Beetle’s length = 4.00 ± 0.02 cm Relative error = Ratio of the absolute error to the measurement Ex: 0.02/4.00 =.005 = 5% Beetle’s length = 4.00 ± 5% cm All your final experimental results must be reported with absolute error.

11. Propagation of Errors Result obtained by adding or subtracting experimental quantities absolute error = sum of the absolute errors in the exp quantities Result obtained by multiplying or dividing exp quantities relative error = sum of the relative errors in the exp quantities Absolute error = Relative error x Measurement 4.00 ± 0.02 cm 2.00 ± 0.02 cm Perimeter? 12.00 ± 0.08 cm Area? 8.00 ± (1% + 0.5%) cm 2 8.0 ± 0.1 cm 2

12. Propagation of Errors Result obtained by multiplying or dividing an exp qty by a constant Absolute error = same constant x absolute error in the exp quantity Logarithmic expression Relative error = 0.434 x relative error in the exp quantity Average Absolute error = greatest absolute error in exp quantities being averaged Only absolute errors can be used for final results

13. Wet Techniques Experiments: –Calibrating Glassware –Preparation of standards –Titration –Qualitative Analysis for Cations Collaborative/Cooperative work necessary!

14. Calibrating Glassware Volumetric glassware: –“to contain” (TC) –“to deliver” (TD) Objectives: –Estimate precision of volumetric glassware –Compare with manufacturer’s uncertainty

15. Gravimetric Calibration Determine: –Mass of water in the Measured volume –Temperature of water Calculate: –Volume of water (using the density of water) Compare: – Calculated and Measured Vwater.

16. Qualitative Analysis for Cations Objectives –Design a Cation Analysis Scheme –Identify and Separate Cations in a mixture

17. Cation Analysis Scheme

18. Volumetry Objectives –Prepare solutions of known concentration from primary and non-primary standards –Perform titrations

19. Pre-lab questions E2 - 6: Retrieve the MSDS of KHP and NaOH. Calculate the mass of NaOH and KHP needed in order to prepare the solutions. E2 - 12: Sketch an alternative analysis scheme starting with precipitation with NaOH instead of HCl.