unit 1: analytical process and data handling

Question 1

activity (ax)

Answer 1

the effective concentration, taking into account the effect of ionic strength 𝐴𝑥 = [𝑥]𝛾 sub𝑥

Question 2

absolute uncertainty

Answer 2

typically the standard deviation of multiple measurements or from (1) a calibration, (2) the manufacture’s stated tolerance (equation below), or (3) gradations on the device or instrument. 𝑒 = ± 𝑡𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒 /√6 = ± 𝑎 /√6

Question 3

Activity coefficient (γx)

Answer 3

dimensionless quantity that measures the deviation of the behavior from ideality; can be calculated using the extended Debye-Hückle equation (below, only applicable for solutions with μ ≤ 0.1 M) or activity coefficient tables (table 8.1 in 10th edn of Harris)

𝑙𝑜𝑔𝛾 = (−0.51𝑧 ^2 √𝜇 ) /(1 + ( 𝛼√𝜇 /305) )

Some trends: 1) For a given ionic strength, deviations from ideality increase with charge 2) For a given species, deviations from ideality increase with ionic strength 3) Small effects are seen for differences in hydrated radius; the effect of charge is greater 4) The activity coefficient of an uncharged molecule is approximately 1 (ideal) at any μ

Question 4

blank

Answer 4

contains everything that is in the standards and sample solution, but no analyte; often further classified as a method blank (blank that has been process through the entire method) or a reagent blank (blank that contains just contains everything except analyte and has not been process through the entire method)

Question 5

callibration curve

Answer 5

Translate signal output into a concentration. Plots concentration vs. signal, uses a least squares linear regression (or weighted linear regression) to determine a line that fits the calibration; using this line we can know the relation between any signal (y) and the concentration (x). Uncertainty in a calibration curve

𝑢𝑥 = (𝑠𝑦 /|𝑚|) (√ (1/ 𝑘) +( 1/ 𝑛 )+ (𝑦 − 𝑦̅)^2)/ 𝑚^2 ∑(𝑥𝑖 − 𝑥̅) ^2

Question 6

confidence interval

Answer 6

𝑥̅± (𝑡𝑠/ √n)

Question 7

confidence limits

Answer 7

The upper and lower bounds of the confidence interval

Question 8

f-test

Answer 8

Answers the question: are the two standard deviations significantly different from one another? Can inform if one method is more precise than another 𝐹𝑐𝑎𝑙𝑐 = (𝑠1)^2 / (𝑠2)^ 2

Question 9

figures of merit

Answer 9

metrics that give a measure of how “good” the method/technique is

Question 10

gaussian distribution

Answer 10

(also called a bell curve or normal error curve) Experiments repeated many, many times with purely random uncertainty will have results that cluster about the average (mean) and the distribution will resemble the Gaussian Distribution - Population mean (μ) and population standard deviation (σ) - calculated from infinite (all) measurements and can completely define the Gaussian - Sample mean (𝑥) and sample standard deviation (s) - calculated from a subset of measurements and are used to approximate the Gaussian

Question 11

grubbs

Answer 11

Statistically determine if a data point is an outlier and should be removed 𝐺𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 = |𝑞𝑢𝑒𝑠𝑡𝑖𝑜𝑛𝑎𝑏𝑙𝑒 𝑣𝑎𝑙𝑢𝑒 − 𝑥̅| / s

Question 12

interferent

Answer 12

any substance (not the analyte) whose presence interferes with the signal

Question 13

internal standard

Answer 13

Calibration method that accounts for differences in instrumental response, or to account for sample loss during the method Uses an internal standard that is similar enough in chemical makeup that it will go through the analytical method in the same way, but different enough to detect it as distinct from the analyte of interest. 𝐴𝑋 /[𝑋] = 𝐹 ( 𝐴𝑆 /[𝑆] )

Question 14

ionic atmosphere

Answer 14

region of charge around an ion; charge of the ionic atmosphere is less than the charge of the ion at the center - Decreases the attraction between ions - Higher ionic strength leads to higher charges in the ionic atmosphere - Higher charges in the ionic atmosphere results in weaker attractions between cations and anions in solution

Question 15

Ionic strength (μ)

Answer 15

measure of the total concentration of ions in solution, with more highly charged ions “counted” more 𝜇 = (1/2) ∑ (𝑐𝑖)(𝑧𝑖)^2

Note: equation only applicable for dilute (less than ~0.2 M) solutions with ions of low charges (>|2|)

Question 16

Limit of Detection (LOD)

Answer 16

concentration of analyte that gives a signal that is significantly different than the blank 𝐿𝑂𝐷𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 = 3𝑠𝑏𝑙𝑎𝑛𝑘 𝑚 or the concentration at S/N = 3

Question 17

Limit of Quantification (LOQ)

Answer 17

smallest quantity of analyte that can be measured with reasonable accuracy 𝐿𝑂𝑄𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 = 10𝑠𝑏𝑙𝑎𝑛𝑘 𝑚 or the concentration at S/N = 10

Question 18

linear range

Answer 18

concentration range over which the calibration curve is linear

Question 19

linearity

Answer 19

measure of how well does the calibration curve follows a straight line, demonstrating the proportionality between response and concentration Measures: R2 , how close the x intercept is to 0 (after blank subtraction) Linear range – concentration range over which the calibration curve is linear Dynamic range – concentration range over which there is a measureable response

Question 20

matrix

Answer 20

components in a sample that are not the analyte(s) of interest

Question 21

matrix effect

Answer 21

change in the analytical signal caused by anything other than the analyte of interest

Question 22

measures of precision

Answer 22

Variance (s2 or σ2 ): has the units of the measurement squared; are additive Standard deviation (s or σ): has units of the measurement; are not additive; measures the width of the Gaussian Relative standard deviation (RSD = s/root 𝑥): often reported in ppt (x 1000) or as the coefficient of variation (CV, x 100) or %RSD (x 100)

Question 23

method of validation

Answer 23

the process that proves the acceptability of a method for its intended purpose

Question 24

prop of unc- addition and sub

Answer 24

Use the absolute uncertainties of individual terms to determine the uncertainty in the final result: 𝑒𝑇 = √𝑒𝑥^2 + 𝑒𝑦^2 + 𝑒z^2

Question 25

Propagation of Uncertainty – Multiplication and Division

Answer 25

Use the relative uncertainties of individual terms to determine the uncertainty in the final result: %𝑒𝑇 = √%𝑒𝑥^2 + %𝑒𝑦^22 + %𝑒𝑧^22 Reminder: %𝑒𝑥 = 𝑒𝑥/𝑥

Question 26

random uncertainty

Answer 26

(Harris calls this random error) - uncertainty that causes data to be scattered evenly about an average value - effects the precision of the measurement

Question 27

relative uncertainty

Answer 27

Relative uncertainty: %𝑒 = 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 / 𝑚𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑚𝑒𝑎𝑠𝑢𝑚𝑒𝑚𝑒𝑛𝑡 × 100 (as a percent) 𝑒𝑝𝑝𝑡 = 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 / 𝑚𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑚𝑒𝑎𝑠𝑢𝑚𝑒𝑚𝑒𝑛𝑡 × 1000

Question 28

repeatability and reproducability

Answer 28

Repeatability – precision of the same person, in the same lab, on the same instrument

Reproducibility (inter laboratory precision) – precision of different people in different labs with different equipment on a similar sample and the same method.

Question 29

robustness

Answer 29

ability of the method to be unaffected by small, deliberate changes in operating conditions/parameters

Question 30

sample

Answer 30

solution containing an unknown amount of analyte

Question 31

sensitivity

Answer 31

ability of an instrument/technique to discriminate, based on signal, between similar concentrations; slope of the calibration line

Question 32

specificity

Answer 32

ability of an analytical method to distinguish the analyte of interest from everything else present in the sample

Question 33

standard

Answer 33

solutions containing a known amount of analyte

Question 34

standard addition

Answer 34

X-not at 0. Calibration method that accounts for matrix effects; known quantities of the analyte of interest are added or “spiked” into the sample When using standard addition where all solutions have a constant volume, the final concentration of unknown is the absolute value of the x intercept.

Question 35

Systematic error

Answer 35

an error that consistently makes the measured value different from the true value - effects the accuracy of the measurement

E = xi - xt
𝐸𝑟 = (𝑥𝑖−𝑥𝑡) / 𝑥𝑡 × 100

Question 36

t-test case 1

Answer 36

Answers the question: are the two means significantly different from one another? Case 1 T-Test: Comparison of an experimental mean with a known value 𝑥̅± 𝑡𝑠 / √𝑛

Question 37

t-test case 2

Answer 37

Case 2 T-Test: Comparison of two experimental means Must perform an F-test first to determine which set of equations to use. If standard deviations are not significantly different:
𝑡𝑐𝑎𝑙𝑐 = (|𝑥̅1−𝑥̅2| / 𝑠𝑝𝑜𝑜𝑙𝑒𝑑 ) * (√ 𝑛1𝑛2 /𝑛1+𝑛2 )

( check eq sheet for porper format) 𝑠𝑝𝑜𝑜𝑙𝑒𝑑 = √ 𝑠1 2(𝑛1−1)+𝑠2 2 (𝑛2−1) 𝑛1+𝑛2−2 If standard deviations are significantly different: 𝑡𝑐𝑎𝑙𝑐 = |𝑥̅1−𝑥̅2| √(𝑠1 2 /𝑛1)+(𝑠2 2 /𝑛2) 𝑑𝑒𝑔𝑟𝑒𝑒𝑠 𝑜𝑓 𝑓𝑟𝑒𝑒𝑑𝑜𝑚 = (𝑠1 2 /𝑛1+𝑠2 2 /𝑛2) 2 (𝑠1 2/𝑛1) 2 𝑛1−1 + (𝑠2 2/𝑛2) 2 𝑛2−1

Question 38

t-test case 3

Answer 38

Case 3 T-Test: Paired T-Test, Different methods used on the same set of samples 𝑡𝑐𝑎𝑙𝑐 = |𝑑̅|√𝑛 / 𝑠𝑑