# Assignment: survey of Analytical chemistry

Assignment: survey of Analytical chemistry ORDER NOW FOR CUSTOMIZED AND ORIGINAL ESSAY PAPERS ON Assignment: survey of Analytical chemistry I would like to help with my homework in Analytical chemistry Ill Attach the homework and the slides of lecture to get the overall idea Assignment: survey of Analytical chemistry thank you homework_1.pdf lecture_1._basic_numerical_analysis_overview.pdf lecture_2._intro_spectrometric_methods.pdf lecture_3._intro_uvvis_molecular_absorption_spectrometry.pdf CHEM 503 Homework #1 (due on Sept. 18, 2018) 1. (10 points) When measured with a 1.00-cm cell, a 8.50?10-5 M solution of species A exhibited absorbances of 0.129 and 0.764 at 475 and 700 nm, respectively. A 4.65 ?10-5 M solution of species B gave absorbances of 0.567 and 0.083 under the same circumstances. Lets assume a solution mixture of A and B, which yielded the following absorbance data in a 1.25-cm cell: 0.675 at 475 nm and 0.696 at 700 nm. What are the concentrations of A and B in the mixture? 2. (10 points) The acid/base indicator HIn undergoes the following reaction in dilute aqueous solution: HIn ? H+ + Icolor 1 color 2 The following absorbance data were obtained for a 5.00 ? 10-4 M solution of HIn in 0.1 M NaOH and 0.1 M HCl. Measurements were made at a wavelength of 485 nm and 625 nm with 1.00-cm cells. 0.1 M NaOH: 0.1 M HCl: A485 = 0.05 A485 = 0.6 A625 = 0.8 A625 = 0.2 In the NaOH solution, essentially all of the indicator is present as In-; in the acidic solution, it is essentially all in the form of HIn. Please calculate the acid dissociation constant for the indicator if a pH 5.00 buffer containing a small amount of the indicator exhibits an absorbance of 0.5 at 485 nm and 0.4 at 625 nm (1.00-cm cells). 3. (10 points) Given the information that Fe3+ + Y4- ? FeYCu2+ + Y4- ? CuY2- Kf = 1.0 ?1025 Kf = 6.3 ?1018 and the further information that, among the several reactants and products, only CuY2absorbs at 750 nm, describe how Cu(II) could be used as indicator for the photometric titration of Fe(III) with H2Y2-. Reaction: Fe3+ + H2Y2- ? FeY- + 2H+ 4. (10 points). Assignment: survey of Analytical chemistry A 5.0-g pesticide sample was decomposed by wet ashing and then diluted to 200.0 mL in a volumetric flask. The analysis was completed by treating aliquots of this solution as indicated. It has known that only the chelate PbL42- will absorb light at wavelength 545 nm and has a linearly calibration curve in a wide range of concentration. Assume the concentration of ligand is far more than that of lead in each measurement so that all the lead will be react with the ligand to form chelate. Volume of Sample Taken, mL Reagent Volumes Used, mL Ligand water 4 ?M Pb Absorbance, A, 545 nm 2+ 20 0 20 10 0.2 50 5 20 5 0.8 Calculate the concentration of lead in the sample. 5. (10 points) A sample of rainwater was collected from four separate locations across the Metroplex. Each sample was measured once by two separate methods for the presence of sulfate. Determine whether the two methods are equivalent with respect to giving the same answer for [SO42-]. Method 1 Method 2 Sample 1 [SO42-] (M) Sample 2 [SO42-] (M) Sample 3 [SO42-] (M) Sample 4 [SO42-] (M) 3.821 x 10-4 4.04 x 10-4 8.93 x 10-5 1.055 x 10-4 9.773 x 10-4 1.233 x 10-3 3.300 x 10-4 3.380 x 10-4 6. (10 points) Use appropriate statistical tests to determine whether the results of replicate measurements (average ± standard deviation given below) by two methods are the same or different at the 95% confidence level. (10 pts) Method A: 624.6 ± 0.8 (n = 10) Method B: 621 ± 3 (n = 5) CHEM 503 Review of Measurement Errors, Statistics, and Calibration Methods What is Chemical Analysis? Identify the unknown (qualitative analysis); Assignment: survey of Analytical chemistry Find the concentration of the analyte present in the sample (quantitative analysis). Classification of Analytical Methods Classical Methods ? Precipitation, extraction, distillation, etc. Instrumental Methods ? Measurements of physical properties of analytes (e.g., conductivity, electrode potential, light absorption or emission, mass-to-charge ratio, fluorescence, and etc. ? Chromatographic and electrophoretic techniques Analysis as a Process (Overview) 1. 2. 3. 4. 5. Sampling Choice of Analytical Method Sample Preparation Quantitation (measurement) Data Anaysis Analysis as a Process (Overview) 1. Sampling Representative Sample Collection Constituent Concentration Remains Stable Contamination Problems Type of Storage Container (material, freezing needed?) Inorganic constituents plastics and Teflon Organic constituents glass, metal, Teflon Analysis as a Process (Overview) 2. Choice of Analytical Method Theoretical Basis sound method Accuracy and Precision defines suitability of technique Sensitivity can the method detect the analyte? Selectivity ability to discriminate analyte of interest from complex background Speed and Cost important to consulting laboratories Simplicity Instrument Availability Analysis as a Process (Overview) 3. Sample Preparation Separation and/or concentration of analyte from a complex matrix Dissolution of solids 4. Quantitation (measurement) Performing the instrumental analysis Preparation of a calibration or working curve Determination of the concentration of an unknown (raw data) Analysis as a Process (Overview) 5. Data Analysis Determine the concentration of the unknown and other statistical values: Mean (average) value Error (or % error) Standard Deviation Detection limit Dynamic range Sensitivity Confidence intervals Significant Figures (Review) Assignment: survey of Analytical chemistry The number of significant figures is the minimum number of digits needed to write a given value in scientific notation without loss of accuracy. In other words, a number contains some certain digits plus only one uncertain (estimate) digit. How many significant figures? Significant Figures (continue) Remember: Use scientific notation as possible as you can to avoid error. Zero are significant when they occur in the middle of a number or at the end of a number on the right-hand side of a decimal point. Rounding-off When rounding-off, look at all the digits beyond the last place desired. < 5 round down > 5 round up = 5 round to the nearest even Data Analysis ? A statistical/mathematical process, which transforms the raw data into a format that can be easily understood. Error ? Always present in each experimental measurement. (To minimize the error need s to have some basic statistics !!) Two types of error Systematic errors Random errors Systematic Errors Cause: due to flaws in equipment or experimental design. Characteristics Have a known cause and thus a definite value; Reproducible. Examples: Instrument not calibrated correctly (e.g., pH meter, buret); Careless mistakes in making standards; Blank (chemical reagents used contains analyte of interest.) Systematic errors can usually be corrected !!! Detection of Systematic Errors Analyze samples with known values (e.g., Standard Reference material); Analyze blank samples to verify the instrument will produce a result with a 0 value; Use different instruments and/or methods to test a same sample, and compare the results obtained. Random Errors Cause: an unknown source that cant be controlled. Features: always present ? cant be always corrected (but can be minimized!). Examples: Noise due to instrument; Difference in the readings obtained between different individuals. Illustration of the Frequency Distribution Replicate Weight Measurements Frequency Distribution of Penny Weights Number of Pennies in Range Frequency Table Range (g) Number Assignment: survey of Analytical chemistry 2.4654 2.5097 5 2.5097 2.5539 5 2.5539 2.5982 0 2.5982 2.6425 0 2.6425 2.6867 0 2.6867 2.7310 0 2.7310 2.7753 0 2.7753 2.8195 0 2.8195 2.8638 0 2.8638 2.9081 0 2.9081 2.9523 0 2.9523 2.9966 0 2.9966 3.0409 0 3.0409 3.0851 2 3.0851 3.1294 8 9 8 7 6 5 4 3 2 1 0 8 5 5 2 0 0 0 0 0 0 0 0 0 0 0 3.1294 3.0409 2.9523 2.8638 2.7753 2.6867 2.5982 2.5097 3.0851 2.9966 2.9081 2.8195 2.7310 2.6425 2.5539 2.4654 Mass Range (g) Frequency Distribution for Replicate Absorbance Measurements Random Distributions If a continuous random variable is normally distributed or has a normal probability distribution, then a relative frequency histogram of the random variable has the shape of a normal or Gaussian curve (bell-shaped and symmetric). Characterization of Random Distributions The Normal Distribution A normal distribution is bell-shaped and symmetric. The distribution is characterized by the mean, (x- or m, mu) and the standard deviation (s or s, sigma). The mean defines the center value and standard deviation defines the spread. Characterization of Random Distributions The Standard Deviation The standard deviation is the distance from the mean to the inflection point of the normal curve; the place where the curve changes from concave down to concave up. A smaller standard deviation means that your results are more reproducible (they dont vary as much from measurement to measurement). Standard Deviations and Areas Under the Normal Curve For any normal curve with mean mu (m) and standard deviation sigma (s): 68 percent of the observations fall within ±1 standard deviation of the mean. 95 percent of observation fall within ± 2 standard deviations. 99.7 percent of observations fall within ± 3 standard deviations of the mean. Standard Deviation Standard Deviation measures how closely the data are clustered about the mean. The smaller the deviation, the more precise the measurements Assignment: survey of Analytical chemistry We distinguish two types of standard deviations based on the number of samples involved Population Standard Deviation (?) (N > 20) Sample Standard Deviation (s) (N < 20) Calculating a Standard Deviation Based on the difference between each _ value (xi) and the mean ( x or µ). Also based on the degrees of freedom For a sample std. dev. the degrees of freedom = N 1 For a population std. dev. The degrees of freedom = N 2 ( x ? x ) ?i?0 i N s? N ?1 ? ( x ? m ) i i ?0 N s? N 2 Analytical Figures of Merit Analytical Figures of Merit refers to statistical information about an analytical technique or analysis. They are used to quantitatively compare methods and provide information about the quality of a data set. Analytical Figures of Merit 1. Sample Concentration. Best estimate of the concentration of an unknown Determined from mean value Corrections made for Blank value Sample dilution Analytical Figures of Merit 2. Precision Estimate. Reported as s x Coefficient of Variation (CV) = Relative Standard Deviation (RSD) Requires s or ?. Confidence Limits ? Make sure the calibration curve is good. (Linear regression) Analytical Figures of Merit 3. Accuracy Estimate Reported as % Error 4. Sensitivity (of Method) Based on slope of calibration curve and reproducibility Analytical Figures of Merit 5. Detection Limit. (3 x Std. Dev. of a blank signal; reported as concentration units) 6. Dynamic Range DL > LOL (Detection Limit to Limit of Linearity) Sample Mean Mean (or average) sum of the measured values divided by the number of measured values Two types based on sample size Population Mean (m) N > 20 Sample mean ( x ) N < 20 N x or µ ? ?x i?0 N i Accuracy and Precision Precision Describes the reproducibility of results Describes how well a series of measurements agree with each other Related to random error Accuracy How close a result is to the true or accepted value Related to systematic error Propagation of Uncertainty y = x1 ? x2, ey ? e ? e y = x1 ? x2, y = x1 / x2, %e y ? %ex21 ? %ex22 2 x1 2 x2 Assignment: survey of Analytical chemistry An Illustration of the difference between accuracy and precision Low accuracy, low precision Low accuracy, high precision High accuracy, high precision High accuracy, low precision Comparison of Random and Systematic Errors Random Error: results in a scatter of results centered on the true value for repeated measurements on a single sample. Systematic Error: results in all measurements exhibiting a definite difference from the true value Random Error Systematic Error plot of the number of occurrences or population of each measurement (Gaussian curve) How to Describe Accuracy Accuracy is determined from the measurement of a certified reference material (CRM) Accuracy is described in terms of Error Absolute Error = (X µ) Relative Error (%) = 100(X µ)/µ where: X = The experimental result µ = The true result (i.e. CRM value) How to Describe Precision Range: the high to low values measured in a repeat series of experiments. Standard Deviation: describes the distribution of the measured results about the mean or average value. Absolute SD SD ? n ?(X ? X ) i 2 /( n ? 1) i ?1 Relative Standard Deviation (or Coefficient of Variation) RSD(%) ? (SD / X )100 where: n = total number of measurements Xi = measurement made for the ith trial = mean result for the data sample Confidence Intervals Allow us to calculate a range of values in which we can be confident, at some level, that the true value lies; The limits depend on the degree of certainty desired. Confidence Intervals (CI) Have two basic forms depending on whether s ? ? (or simply interpreted as the number of data). 1. When s ? ?, the CI is given by: x ? zs (Single Measurement) zs x? N (Multiple Measurements) 2. When ? is unknown, the CI is given by: ts x? N Calculating a Confidence Interval t?s m ?x? n where n is the number of observations. Determine the Mean and Standard Deviation (s); Determine the degrees of freedom (n-1); Find the t value from the student-t table at the requested confidence level (90%, 95%, and etc.); Calculate to obtain the confidence interval using the above formula. Student t Table Comparison of Means with Students t Determine whether two sets of data are the same; Assignment: survey of Analytical chemistry Determine, at a specific confidence level (e.g. 90%), that the difference between two data sets are only due to random measurement error. Comparison of a Measured Result with a Known Value Testing Standard Reference Material bought from National Institute of Standards and Technology. tcalculated ? x ? known value s n If tcalculated > ttable, data sets are different at the confidence level you are using. Comparison of Two Sets of Replicate Measurements Involved with two steps: 1. Comparison of Standard Deviations with the F test; 2. Use the appropriate equation based on whether the population standard deviation is the same (not significantly different) for both sets of measurements. Comparison of Standard Deviations with the F test Fcalculated ? 2 s1 2 s2 *Remember: s1 is always larger than s2 If Fcalculated > Ftable, the standard deviations are significantly different from each other. F Table Comparison of Two Sets of Replicate Measurements ? Assume the population standard deviation is the same (not significantly different) for both sets of measurements. tcalculated ? x1 ? x2 s pooled n1n2 n1 ? n2 where s pooled ? ? set 1 ( xi ? x1 ) 2 ? ? set 2 ( x j ? x2 ) 2 n1 ? n2 ? 2 ? s12 ( n1 ?1) ? s22 ( n2 ?1) n1 ? n2 ? 2 If tcalculated > ttable, data sets are different at the confidence level you are using. Comparison of Two Sets of Replicate Measurements ? The population standard deviations for both sets of measurements are NOT the same (significantly different). tcalculated ? x1 ? x2 s12 / n1 ? s22 / n2 ? ( s12 / n1 ? s22 / n2 ) 2 ?? Degrees of freedom = ? ( s12 / n1 )2 ( s22 / n2 )2 ? ? 2 ? ( n1?1 ? n2 ?1 ) ?? If tcalculated > ttable, data sets are different at the confidence level you are using. Comparison of Two Methods tcalculated ? d sd n sd ? ? n ?1 ( di ?d )2 Assignment: survey of Analytical chemistry If tcalculated > ttable, data sets are different at the confidence level you are using. Comparison of Two Methods (continued) sd ? ( 0.04?0.06) 2 ? ( ?0.16?0.06) 2 ? ( 0.17?0.06) 2 ? ( 0.17?0.06) 2 ? ( 0.04?0.06) 2 ? ( 0.10?0.06) 2 6?1 = 0.12 tcalculated ? 00..06 12 6 ? 1.20 ttable = 2.571 ? tcalculated < ttable ? The difference of two methods is NOT significant at the 95% confidence level. The Q-test Deciding when to reject data points Q experimental (Qexp) = ?xq xn ?/w ?xq xn ? = ? (suspect value nearest value) ? w = spread = (largest value smallest value) Note: includes xq Qexp is then compared to a tabulated Q value called Q critical (Qcrit) If Qexp > Qcrit then the questionable point should be discarded Q-test Table Q-test Example Can a questionable result be dropped from this data set? 9.32, 9.75, 9.62, 9.92, 9.43, 9.57, 9.87, 9.79, 10.4 Which value is the questionable value? Answer: minimum or maximum values. Q-test Example (continued) 9.32, 9.75, 9.62, 9.90, 9.43, 9.57, 9.87, 9.79, 10.4 Lets test 10.4. Qexp = ?xq -xn ?/w = ?(10.4 9.90) ?/(10.4 9.32) = 0.463 Examine Q table for n = 9 Evaluate whether Qexp > Qcrit Reject with 90% confidence, but not at 95% confidence Example During a UV-vis experiment for the detection of benzene in hexane, Bob made four measurements for an unknown sample. The obtained absorbance results were as follows: 0.69, 0.75, 0.50, 0.78. A calibration curve was prepared for a series of standards containing various concentrations of this analyte, and the equation of the best fit line relating absorbance to concentration was determined to be Y = 1.5 X + 0.02, where Y is the absorbance and the concentration, X, is in parts per million (ppm). Calculate the concentration of the unknown sample. Please find the mean, standard deviation, 90% confidence interval for the mean. Describes the ability to discriminate between small differences in analyte concentration by a method or instrument; Sensitivity = the slope of a calibration curve; Signal (S) Sensitivity Slope = S/[A] = sensitivity Analyte Concentration [A] Assignment: survey of Analytical chemistry The larger slope value, the better sensitivity. Detection Limit Defined as the minimum amount (e.g., concentration) of the analyte that can be confidently detected above the background or noise signal. Two Types of limitations: ? Blank (e.g. analyte in reagents) ? Instrument (e.g. instrumental electrical noise) Determination of the Detection Limit from a Blank Detection Limit (DL) based on a blank signal is defined as: The concentration corresponding to 3x the standard deviation of a blank signal. DL = Concentration with a signal of 3sblank Determination of the Detection Limit from Instrumental Noise The detection limit can also be estimated as the concentration corresponding to a signal with 2-3 folds of instrumental noise. normally called as signal to noise ratio (S/N) of 2-3. Dynamic Range lowest concentration: detection limit; highest concentration: the end of linear region. Working Range Signal (S) The range in analyte concentration that can be reliably quantified from the lowest to the highest concentration. Limit of Linearity Detection Limit Analyte Concentration [A] Quantification Plot a figure with signal (e.g. area, height, absorbance, etc.) vs. analyte amount (weight, concentration, etc.); Linear signal response with the amount (or concentration) of analyte is desired. Quantification If peak is symmetrical, we can use peak height in the detection process (but better or safer to use peak area). Quantification Three common approaches to quantification ? Calibration (Standard, Working) Curve ? Standard Addition ? Internal Standard Calibration Curve Generate a plot of response versus known amount (e.g. concentration) of the analyte of interest Method of Least Squares Most widely used technique for find Assignment: survey of Analytical chemistry Get a 10 % discount on an order above $ 100 Use the following coupon code : NURSING10