14BL-Week1Notes.pdf CHEM 14BL
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This 11 page Class Notes was uploaded by Daniel Ochs on Sunday April 3, 2016. The Class Notes belongs to CHEM 14BL at University of California - Los Angeles taught by Casey in Spring 2016. Since its upload, it has received 15 views. For similar materials see General and Organic Chemistry Laboratory I in Chemistry and Biochemistry at University of California - Los Angeles.
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Date Created: 04/03/16
14BL Notes Week 1 Uncertainty in Measurement Experimental measurements are inherently uncertain There can be systematic or random errors: Systematic Error – results from fundamental flaw in design, construction, calibration, operation, or interpretation of experiment Random Error – caused by unpredictable fluctuations in the readings of a measurement apparatus -When Taking measurements, interested in both particular result and also how reliable measurements are. Accuracy and Precision Accuracy – defines the closeness of a measurement to the true value Precision – defines the closeness of a set of results to each other; the reproducibility of a result Precision in Measurement • Choose equipment that has the precision needed for the measurement • Train the experimenter to be able to equipment properly • Focus of upcoming labs: • Next week focus on volumetric pipe • Following week focus on volumetric flask Pipet Calibration Improving reliability of result: 1. Minimizing instrumental errors by calibration 2. Minimizing human errors with practice and being careful -Weight the water delivered by the pipet system several times until the precision of at least half the trials is less than 0.4% Precision in Calculation • Scientific measurements are reported so that any uncertainty in the measurements (error) resides in the last digit • Often times, the manufacturer states the absolute error for the equipment • For Example, the absolute error for the 10-mL pipet is stated as +/- 0.02 mL • For this class in the absence of a specified absolute error, one assumes the error is +/- 1 in the last digit • Examples A. 22.4 L = +/- 0.1 L B. 0.0214 M = +/- 0.0001 M C. 1.00 x 10^3 g = +/- 0.01 x 10^3 g Precision and Signiﬁcant Figures You calibrate two 10 mLpipets: You find that Pipet 1 delivers 10.01 mL of water You find that Pipet 2 delivers 9.98 mL of water Both of your measurements are within the manufacturer’s tolerance (±0.02 mL) Question: Is Pipet 1 more precise than Pipet 2? What exactly is the pipet precision? • Pipets are equally precise • Pipets 1 is more accurate Absolute Error and Relative Error There are two main ways that we report precision in the lab: Absolute error • Same unit as measured value • Same number of decimal places as measured value (Percent) Relative error • Ratio of absolute error to measurement • Unit-less percentage Absolute Error and Relative Error Relative Error = absolute error / measured value 0.02 mL / 10.01 mL = 0.001998 ≈ 0.002 Relative Percent Error = absolute error / measured value ×100% 0.02 mL / 10.01 mL ×100% = 0.1998% ≈ 0.2% [Numbers from previous example, Pipet 1: 10.01 mL ± 0.02] Propagation of Errors When multiple measurements are made to obtain a result, error in the result is affected by the errors in each of the measurements (I) Multiplication or Division C =A×B or C =A/ B (ΔC / C )= (ΔA / A) + (ΔB / B) (II)Addition or Subtraction C =A+B or C =A- B ΔC= ΔA + ΔB Example 2: What is the absolute error and relative percent error for the following calculations? a. 12.014 g − 1.753 g [12.014 g +/- 0.001 g & 1.753 g +/- 0.001 g] ΔC= 0.001 g + 0.001 g Absolute Error = 0.002 g C = 12.014 g 0 1.753 g = 10.261 g ΔC / C = 0.002 g / 10.261 g x 100% Relative Percent Error = 0.02 % b. (0.05024 × 10.00) ÷ 0.2148[0.05024 +/- 0.00001 & 10.00 +/- 0.01 & 0.2148 +/- 0.0001] C = 2.34 ΔC / C = (0.00001 / 0.05024) + (0.01 / 10.00) + (0.0001 / 0.2148) x 100% Relative Percent Error = 0.2 % ΔC / 2.34 = 0.02 ΔC = 0.04 Absolute Error = 0.04 Example 3: What is the absolute error in concentration in g/mL when you dissolve 3.354 g of sugar in 50.00 mL of water? Absolute Error in balance: 0.008 g & Absolute error in 50-mL pipet: 0.04 mL C = 3.354 g / 50.00 mL = 0.06708 g / mL ΔC/ C = (0.008 / 3.354 g) + (0.04 / 50.00 mL) = 0.00348ΔC / 0.06708 = 0.003485 ΔC = 0.002 g / mL Absolute Error = 0.0671 +/- 0.0002 Types of Error There are two main types of errors that you will calculate in this course (these can be reported as absolute errors, relative errors, or relative percent errors): Inherent error Error that comes from the precision of the equipment used (see Example 3) Relative average deviation (RAD) Statistical analysis of your data to determine precision (see page 20-21 in Lab Manual)
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