unit 1: analytical process and data handling Flashcards
activity (ax)
the effective concentration, taking into account the effect of ionic strength π΄π₯ = [π₯]πΎ subπ₯
absolute uncertainty
typically the standard deviation of multiple measurements or from (1) a calibration, (2) the manufactureβs stated tolerance (equation below), or (3) gradations on the device or instrument. π = Β± π‘ππππππππ /β6 = Β± π /β6
Activity coefficient (Ξ³x)
dimensionless quantity that measures the deviation of the behavior from ideality; can be calculated using the extended Debye-HΓΌckle equation (below, only applicable for solutions with ΞΌ β€ 0.1 M) or activity coefficient tables (table 8.1 in 10th edn of Harris)
ππππΎ = (β0.51π§ ^2 βπ ) /(1 + ( πΌβπ /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 ΞΌ
blank
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)
callibration curve
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
π’π₯ = (π π¦ /|π|) (β (1/ π) +( 1/ π )+ (π¦ β π¦Μ )^2)/ π^2 β(π₯π β π₯Μ ) ^2
confidence interval
π₯Μ Β± (π‘π / βn)
confidence limits
The upper and lower bounds of the confidence interval
f-test
Answers the question: are the two standard deviations significantly different from one another? Can inform if one method is more precise than another πΉππππ = (π 1)^2 / (π 2)^ 2
figures of merit
metrics that give a measure of how βgoodβ the method/technique is
gaussian distribution
(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 (ΞΌ) and population standard deviation (Ο) - calculated from infinite (all) measurements and can completely define the Gaussian - Sample mean (π₯) and sample standard deviation (s) - calculated from a subset of measurements and are used to approximate the Gaussian
grubbs
Statistically determine if a data point is an outlier and should be removed πΊπππππ’πππ‘ππ = |ππ’ππ π‘πππππππ π£πππ’π β π₯Μ | / s
interferent
any substance (not the analyte) whose presence interferes with the signal
internal standard
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. π΄π /[π] = πΉ ( π΄π /[π] )
ionic atmosphere
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
Ionic strength (ΞΌ)
measure of the total concentration of ions in solution, with more highly charged ions βcountedβ more π = (1/2) β (ππ)(π§π)^2
Note: equation only applicable for dilute (less than ~0.2 M) solutions with ions of low charges (>|2|)
Limit of Detection (LOD)
concentration of analyte that gives a signal that is significantly different than the blank πΏππ·πππππππ‘πππ‘πππ = 3π πππππ π or the concentration at S/N = 3
Limit of Quantification (LOQ)
smallest quantity of analyte that can be measured with reasonable accuracy πΏπππππππππ‘πππ‘πππ = 10π πππππ π or the concentration at S/N = 10
linear range
concentration range over which the calibration curve is linear
linearity
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 β concentration range over which the calibration curve is linear Dynamic range β concentration range over which there is a measureable response
matrix
components in a sample that are not the analyte(s) of interest
matrix effect
change in the analytical signal caused by anything other than the analyte of interest
measures of precision
Variance (s2 or Ο2 ): has the units of the measurement squared; are additive Standard deviation (s or Ο): has units of the measurement; are not additive; measures the width of the Gaussian Relative standard deviation (RSD = s/root π₯): often reported in ppt (x 1000) or as the coefficient of variation (CV, x 100) or %RSD (x 100)
method of validation
the process that proves the acceptability of a method for its intended purpose
prop of unc- addition and sub
Use the absolute uncertainties of individual terms to determine the uncertainty in the final result: ππ = βππ₯^2 + ππ¦^2 + πz^2