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CHAPTER O COMMON CONCENTRATION UNITS Moles of Analytic...

CHAPTER O COMMON CONCENTRATION UNITS Moles of Analytic Process (6 Steps · Molarity : solute/Lof soln. : Mostly for liquids Moles of solute 1 Form. a question · Molality : / kg of soln. : used in system W/ temp. Mass of solute. Choose method 2 · Mass : /Mass of Soin. X 100 : In solid soln Vol of solute * 100. Gather sample 3 · Vol %: , vol of soln. : When a liquid dissolved in 4. Prepare sample another Mol of solute. Measure analyte 5 · Mole fraction (x) : /mol of soluted mol of soln :. Evaluate data 6 primarily for gases parts per million (ppm) : massofsoutmassofsoa SAMPLING · parts per billion (ppb) Get ↳ a good sample , if not bad results., ppm & ppb used for dilute soln. from wrong CH 3 EXPERIMENTAL ERROR sampling error /not enough or place) may. relative to measurement error. SIGNIFICANT FIGURES be large Leading zeros aren't significant Trailing zeros only. To replicate samples microanalysis (0. 1g) & significant w/ a decimal; In between zeros are significant macroanalysis (10 0 0034060 SSF - > 3 4060 x10 scientific notation g) · :.. · 2500 : 2 SF · 10002 : 5 SF 8 SF Amount of analyte : 1 ppb Cultratrace) to 100 % (major 0 023 : 2 SF 0 00012030010 : · ·.. · 101 2. : 4 SF SAMPLE PREPARATION EX. When measuring (e g. W/. a ruler or graduated cylinder I homogenize estimated. Report all certain digits + one digit. solvent addition 2 shaking & centrifugation , (UPLC). Phase separation > 3 - organic fraction , chromatography Rounding Rules. solid 4 phase extraction (SPE) Rule about dropping S: Keep if preceding is even & increase S. Washings - > UPLC , Mass Spectrometry (TOF-MS) if it's odd · 0 467450 round to. 0 S. · 0. 128350 to.1 0 CH I CHEMICAL MEASUREMENTS. 0 47. 0 13. sl units 0 467. 0 128. Length-meter (m) Plane angle-radian (rad) 0. 4674 0. 1284 - so Mass-Kilogram (kg) solid angle-steradian (srl Not Time-second (s) 0 12825 round to 0 1283 ·.. Electric Current-Ampere (A) Temperature - Kelvin (k) Arithmetic Luminous Intensity-Candela (cd) Multiplication & division : fewest sig figs Amount of substance-mole (mol E 25 40 1 6589021 = 42 13611334 = 42 14. g · ·..... (45F) (8SF) (4SF) PREFIXES Addition & Subtraction : fewest decimal places 102" - yotta (4) 10 - deci (d) · E.. g 14 124 +. 12 29485 = 26 41885.. = 26 419. (3DP) (SDP) (3DP) 102 - zetta (2) 102 - centi (c) 1018 - exa(t) 103 - milli (m) Logarithm : # Sig figs = # decimal places -3 10 peta(P) - 10"- micro (M) · E. g pH -10g. = (H ) = + - 10g(3. 0 x 10 M) = 2 522878745. = 2 53. (2SF) (2DP) 102 - tetra (T) 109- nano In 109-Giga (G) 10-1 pico (p) - Antilogarithm # decimal : places = # Sig figs 10" Mega (M) - 10 - Femto (f) E g (H+ ] antilog(-pH) ·.. = = 10 Ph = 10 7 40 - = 3 981071706.. x108 (2DP( 8 103-KilO(k) 10-18 - atto - (a) = 4 0 x 10. (2SF) 102-necto (h) 10: 3 - zepto(2) 10 -deca(da) 10 - 24 - yocto(y) TYPES OF ERRORS To determine which instrument to use, use one w/ low systematic error : bias , determinate error tolerance & doesn't take too much time. · one-sided , correctable To discover sample size up -> error down analyze PROPAGATION OF UNCERTAINTY FROM RANDOM ERROR · : , Standard (NIST) , analyze blank sample , analyze W/ Addition & subtraction : use absolute uncertainty of ind. diff. methods terms (include units) (e) · E. g Uncalibrated balance. · final eit e. Random error : indeterminate error · e. (1 27 10 03)g g... - 10. 154 10. 004)g = 1 1161. ?g · - error , not correctable e = 003 + 0042 = 0 0303. can be minimized 1 12 10 03 mmol ·.. (2DP) (2DP) Gross error (blunder) : extreme instance of systematic or random error Multiplication & division : Use relative uncertainty (ve) · e. g. contaminated sample , instrument failure, ·. fina+.. over-titration e. g 10 246 10 003) MX (5 0010 01) mL 1 23 I ? ·. = mmol..... ACCURACYO PRECISION 0 246 M.. 0 005). = 0 00123 mol. = 1 23. mmo Accuracy : how close a measured value is to the true value convert e to e %: true value Often not known 10. 2461(100)Mx(5 0000). · Related to systematic error 10 24611.. 2%) Mx(5 00 10 20 % ).. mc = 1 23. I ? mmol %e = 11. 2 % )2 + 10 20 % ). = 1 2%. Precision : indicates the reproductibility or agreement btwn > 1 23 mmol -. (11. 2%) = 1. 23010 015. mmol (3DP) (3DP) measurements im e · Related to random error Mixed Operations : Use PEMDAS.it e s g ·. I Real Rule 3 measur How to report : 1. 230 10 015. or 1. 23 10 02. Relative uncertainty : 0 015. 1 230. = 0 012. or 0. 04 23. = 0 01. measured value - true value Relative error = ~true value *100 Like error g (0 246 10 003)Mx (5 0010 01) mL 231 ? · e...... = 1. mo 0 003 True value from (1) ) (in volume. a standard (NIST) , (2) accepted relative u. = = 0 012. (in conc. = 0 002. value, (3) spike-and-recovery experiments In final Real rule of Sig figs uncertainty, report 2 SF When : UNCERTAINTY OF MEASUREMENTS 1st non-zero # is 1 Or 2 , if not only ISF. Match the # of Number I uncertainty e.. g 18 46 1 0 02 m.. decimal places in number I uncertainty. L If not known , assume 11 of last deimal place CH 4 STATISTICS. e. g 9 37 1 ? > True value btwn - 9 36 & 9 389 N # measurements EXi =.. - g.. 1 1. M/1 0-1.. 2 M) 1 10 M. (1 09-1.. /1 M) 1. 100 M/1 099-1 101M) = mean.. Y= N Report result as I precision Absolute uncertainty (e) : e.. 10 g. 02 mL in reading of SO mL - burette standard deviation : smaller = better (more precise) - Relative Uncertainty = absolute uncertainty 0 02 m. = 0 0011 S · = magnitude of measurement 6m). Relative Standard deviation (coefficient of variation) % relative uncertainty (1 e). = loox relative uncertainty = 100 x 0 0011. = 0 11 %. · RSD = 100% Confidence Interval Cl =* # It from -table : as EX. CALIBRATION Calibration : Finding a relationship between instrument Signal & analyte concentration standard deviation : = 0. bamg Standard solutions : solutions w/ a known concentration of RSD = =. 100 = x100 = 2 3. analyte 2 3 %) - + 29 6 10 7 (N = 4) 29 6 mg/RSD = mg ·.... 4 = 102 3.. 0. 95 % Cl 1 1. m Blank solutions : solutions w/ no deliberately added analyte 29 6 11 1 (contains sample matrix) Used mg (95 % (1) in control exp e. to g ·..... check for interference & impurities CONFIDENCE INTERVAL If NE co , use sample mean (X) CALIBRATION PLOT Linear range (0-c ) , confidenceInterval = I · Analyte conc. range w/ linear response t is crossing at degrees of freedom Dynamic range (0-C) y = mx + b (N-1) & confidence level ( %) Analyte conc range w/ non-zero · m = Slope (sensitivity (. response A as % confidence level : "We're 95 % sure the true value (M) lies Within the confidence interval" or "the 95 % confidence · Recommended S or more calibration points interval would include the true value (M) in 95 % of the · Don't extrapolate beyond the measured range of standards " infinite sets of N measurements. · Measure Standard Soln. in random order · Measure Standards over the entire conc. range of interest For 29 6 11.. 1 mg (95 % (1) , we expect i to be within 28 5-30 7.. mg. Avoid serial dilutions of a single stock soln. For best results use linear range only · , STATISTICAL TESTING OF HYPOTHESES Null hypothesis postulates the 2 observed quantities are CH S QUALITY ASSURANCE/ CALIBRATION METHODS. the same TYPES OF DATA Raw data : Individual values of a measured quantity No statistical diff between 2 sets of data if e. weight g from a balance , volume by graduate pipet ·.. a * * > calculated tabulated Treated data : Conc. or amounts found by applying a F tests compares the precision calibration procedure to raw data. of 2 Sets (Ftabulated + Results : values after applying statistics to treated data Falculated · What's ultimately reported Student t test JARGON OF QUALITY ASSURANCE case 1 : test to compare measured & "real" values (NIST standard operating procedure (SoP) : Steps used to analyze · standards W sample /storage , chain of custody instrument , calibration #+ calculated = (X M)5 - & maintenance) · Case 2 : t test to compare 2 methods (F test 1st It calculated Control chart : Visual representation of confidence intervals Grubbs test : test for (IGtabulated False positive & false · Outliers in table) negative questionable value - * # G calculated S Sensitivity : Slope of calibration curve Matrix : everything in a sample other than analyte (changes sensitivity ( sample= matrix + analyte Accuracy Check Dynamic Range : Conc. interval over which there is a Method blank of sample matrix signal change (not linear : analysis measurable Calibration check : w/ known Robustness : ability of analytical method to be unaffected measuring signal analyte an 10-20 unknown by small deliberate changes operating parameters (pH , C T conc. every samples in , , volume Blind sample : known samples used as unknowns Limit of detection : smallest quantity of analyte that can be Spike : a known quantity of analyte added to a sample detected by a given analytical method SPIKE LIMIT OF DETECTION (LOD) & QUANTITATION - R is analyte LOD : smallest amount of analyte detectable by an analytical linear calibration method w/ a plot : Signal-SlopexC Spike & recovery exp 196-104 % recovery acceptable). % recovery kiked Sample-Coriginal sample x 100 LOD =ope Cadded mM-15 0 MM recovery. e % x 100 = 107 % S is the standard deviation of a blank or a low-conc... g. 10 0 mM. Conclusion : 107 % too much , method needs improvement sample JARGON OF METHOD VALIDATION Limit of Quantitation : LoQ = e Method Validation process of : proving an analytical method is acceptable for its intended purpose REPORTING LIMIT Reporting limit : the conc. below which regulations say Selectivity being : able to distinguish analyte from all other that an analyte is reported as "not detected , even species present in a sample though Canalyte * O. e the reporting limit of trans fat is 0. g Sg per serving ·. Linearity : measures how well a calibration plot follows a - Manipulation : by reducing the serving size , straight line (R should be close to 1. 000) manufacturers can claim Og trans fat (but products do have trans fat Accuracy : closeness to the true value · use reference materials JARGON OF METHOD VALIDATION (CALIBRATION METHODS · different methods to compare Calibration plot : Signal Vs. Known Canalyte Plot The Signal. · blank method w/ a spike for unknown samples are used to determine unknown · standard additions Canalyte Precision : how well replicate measurements agree w/ one another instrument precision : repeated w/ one instrument · · intra-assay precision : I person/I day/the same instrument intermediate precision : diff people/diff day / diff. ·.. instruments standard addition : Sample is spiked w/ known quantity Interlaboratory precision : diff people/diff of the same analyte & the labs original quantity of analyte is ·.. - uncertainty of analysis increases w/ a decrease in determined from the increase in Signal analyte content in a sample Internal Standard : Sample is spiked w/ known quantity of Range : Conc. interval w/ acceptable linearity (R210. 995) , compound other than analyte. The analyte signal is accuracy (spike recovery , (100 14 % )) , and precision (RSD, 12% ) compared to signal from the internal standard to determine the analyte content in a sample Linear range : Conc. interval over which calibration plot is linear.  USE OF STANDARD ADDITION (SPIKE) CH 6 THE EQUILIBRIUM CONSTANT. Good when a sample matrix is unknown & there are at + bB = c + dDk = matrix effects Doesn't correct for interference (if they're in sample) EQUILIBRIUM CONSTANT, K · Reaction / Products favored if K (Analyte] before spike Signal before Spike [Analyte] after spike Signal after spike Equilibrium constants are dimensionless · If A is a solute , (A] means [A] / IM Unknown (x] : -Signal · If D is a gas , (D) means (pressure of D in bars)/lbar : written as Pp (x]f (Xi) = Same (s)) = (S] , Standard, ↑ Dilution factor - Each quantity in the ratio is given as a concentration at Standard state Ex. Problem · conc. of solutes : M Problem: Saliva containing enzyme myeloperoxidase (MPO) · conc. of gas : bars yielded a current of 9.6 nA. The 10.0 μL of 2.0 nM MPO conc. of pure solids/liquids , and solvents areomitted solution was added to 90.0 μL of saliva. This spiked saliva gave be they are unity a current of 15 nA. What was the initial (original) concentration of MPO in saliva? MANIPULATING EQUILIBRIUM CONSTANTS K (Eames St = Is nag Reaction reversed : new K is reciprocal of original K Si = 9 6 nA. (S) = (si) Standard3 K forward = "reverse Vfinal lon (5) 2 OnM) =. () ; Reaction multiplied by n : Kraised to the nth power h (x3 = (x , 10 a). + 0. 2) Xi(1 - 0 576) = 0 128.. knew = (original X = (0 424) = 0 128 0 128 (0 576) 0. Xi X= =. - -.. = Reactions added Overall K is product of individual Ks : 0 302 n Xi = Xi Xi(0 576) = 0 128. -.. ksum = k, xkz... * kn INTERNAL STANDARD Internal Standard : diff but similar to analyte ,. no rxn w/ EX. H20 = H* + OH + 1 Kw = SH ](OH -] = - analyte , no interference w/ analyte 1 0 x 10 signal. use when sample loss can occur during sample prep KNaOH , amount of sample injected in chromatograph varies NHy (aq) + H20NHITOH Response factor f * Signal from analyte X from standard NHy [NHz(aq) + Ht Fy Signal S = Conc of conc of Standard S. analyte x. H =H + o + k = 1 0. x10-1 = kw = Ex NH + NH3 #20k 4 10 = sensitivity toward x- sensitivity towards = + = YknHy =. 8 x Ex Problem. NHYTH + NHE K = Kw X N KNHH5 6 X1. ResponseFacto- 0 0827 M. F = 0 90.