Intensive General Chemistry - Columbia University

Intensive General Chemistry Uncertainty Analysis Wet Techniques Luis Avila Isabelle Vu Trieu [email protected] [email protected] Introduction Measurement and Uncertainty Qualitative Analysis

What is in the unknown? Quantitative Analysis How much of it is in the unknown? Uncertainty in Measurement Measurements always involve a comparison The comparison always involve some uncertainty Length of the beetles 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 Significant Figures Definition: all digits up to and including the first uncertain digit Ex: Beetles 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! 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: Beetles 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 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 Precision versus Accuracy good precision & good accuracy

poor precision but good accuracy good precision but poor accuracy poor precision & poor accuracy 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 Estimating Precision Standard Deviation the ith value

sample mean standard deviation total number of measurements Expressing Experimental Error Absolute error = Magnitude of the random error Ex: Beetles length = 4.00 0.02 cm

Relative error = Ratio of the absolute error to the measurement Ex: 0.02/4.00 = .005 = 5% Beetles length = 4.00 5% cm All your final experimental results must be reported with absolute error. 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 2.00 0.02 cm 4.00 0.02 cm Perimeter? 12.00 0.08 cm Area? cm2

8.00 (1% + 0.5%) 8.0 0.1 cm2 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 Wet Techniques Experiments: Calibrating Glassware

Preparation of standards Titration Qualitative Analysis for Cations Collaborative/Cooperative work necessary! Calibrating Glassware Volumetric glassware: to contain (TC) to deliver (TD) Objectives:

Estimate precision of volumetric glassware Compare with manufacturers uncertainty 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. Qualitative Analysis for Cations Objectives Design a Cation Analysis Scheme Identify and Separate Cations in a mixture Cation Analysis Scheme Volumetry Objectives Prepare solutions of known concentration from primary

and non-primary standards Perform titrations 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.