Analytical Chemistry. Course Philosophy

Transcription

1 Analytical Chemistry Definition: the science of extraction, identification, and quantitation of an unknown sample. Example Applications: Human Genome Project Lab-on-a-Chip (microfluidics) and anotechnology Environmental Analysis Forensic Science Course Philosophy develop good lab habits and technique background in classical wet chemical methods (titrations, gravimetric analysis, electrochemical techniques) Quantitation using instrumentation (UV-Vis, AAS, GC) 1

2 Analyses you will perform Basic statistical exercises %purity of an acidic sample %purity of iron ore titrations %Cl in seawater Water hardness determination UV-Vis: Amount of caffeine and sodium benzoate in a soft drink AAS: %Cu in pre- and post-198 pennies GC: Gas phase quantitation using an internal standard Chapter 1: Chemical Measurements

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4 Example, p. 15: convert 0.7 pc to electrons Chemical Concentrations Molarity (M) moles liter -3 1gram 10 grams mg ppm 3 10 grams 10 grams 1000 grams 6 mg L 4

5 Example, p. 19: Molarity of Salts in the Sea (a) Calculate molarity of.7 g acl/dl (b) [MgCl ] = M. How many grams in 5 ml? Dilution Equation Concentrated HCl is 1.1 M. How many milliliters should be diluted to 500 ml to make M HCl? M 1 V 1 = M V (1.1 M)(x ml) = (0.100 M)(500 ml) x = 4.13 M 5

6 Chapter 3: Math Toolkit accuracy = closeness to the true or accepted value (given by the AVERAGE) precision = reproducibility of the measurement (given by the STADARD DEVIATIO) Significant Figures Digits in a measurement which are known with certainty, plus a last digit which is estimated beaker graduated cylinder buret 6

7 Rules for Determining How Many Significant Figures There are in a umber All nonzero digits are significant (4.006, 1.01, ) Interior zeros are significant (4.006, 1.01, ) Trailing zeros FOLLOWIG a decimal point are significant (10.070) Trailing zeros PRECEEDIG an assumed decimal point may or may not be significant Leading zeros are not significant. They simply locate the decimal point (0.0000) Reporting the Correct # of Sig Fig s Multiplication/Division Rule: Round off to the fewest number of sig figs originally present ans =

8 Reporting the Correct # of Sig Fig s Addition/Subtraction , Rule: Round off to the least certain decimal place Reporting the Correct # of Sig Fig s Addition/Subtraction in Scientific otation Express all of the numbers with the same exponent first: 1.63 x x x

9 Reporting the Correct # of Sig Fig s Logs and anti-logs Rounding Off Rules digit to be dropped > 5, round UP = 159 digit to be dropped < 5, round DOW = 158 digit to be dropped = 5, make answer EVE = = BUT =

10 Wait until the ED of a calculation in order to avoid a rounding error ( ) x = = ? sig figs 5 sig figs 3 sig figs 0.15 = 0. Propagation of Errors A way to keep track of the error in a calculation based on the errors of the variables used in the calculation error in variable x 1 = e 1 = "standard deviation" (see Ch 4) e.g ml percent relative error = %e 1 = e 1 *100 x 1 e.g. 0.1*100/43.7 = 0.8% 10

11 Addition & Subtraction Suppose you're adding three volumes together and you want to know what the total error (e t ) is: e t e t e 1 e e 3... e t e 1 e e 3... Multplication & Division %e %e t t % e % e % e... 1 %e % e % e ( 0.03) x 1.89 ( 0.0) 0.59 ( 0.0) %e t * (1.1) (3.4) 0.0 * * % 11

12 Combined Example 1.10 ( 0.10) 0.5 ( 0.00).57 ( 0.35) Chapter 4: Statistics 1

13 Gaussian Distribution: 1 P( x i ; ; ) exp ( xi ) / Fig 4. Mean measure of the central tendency or average of the data (accuracy) lim 1 x i i 1 _ 1 x i 1 x i Infinite population Finite population Standard Deviation measure of the spread of the data (reproducibility) i 1 ( x ) i s i1 ( x i x) 1 _ Infinite population Finite population 13

14 Standard Deviation and Probability Confidence Intervals 14

15 Confidence Interval of the Mean The range that the true mean lies within at a given confidence interval True mean lies within this range ts ts μ x _ ts x 15

16 Example - Calculating Confidence Intervals In replicate analyses, the carbohydrate content of a glycoprotein is found to be 1.6, 11.9, 13.0, 1.7, and 1.5 g of carbohydrate per 100 g of protein. Find the 95% confidence interval of the mean. ave = 1.55, std dev = = 5, t =.776 (-1) = 1.55 ± (0.465)(.776)/sqrt(5) = 1.55 ±

17 Rejection of Data - the Grubbs Test A way to statistically reject an outlier G crit outlier X s Compare to G crit from a table at a given confidence interval. Reject if G exp > G crit Sidney: 10., 10.8, 11.6 Cheryl: 9.9, 9.4, 7.8 Tien: 10.0, 9., 11.3 Dick: 9.5, 10.6,

18 Linear Least Squares (Excel s Trendline ) - finding the best fit to a straight line 18