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What does standardizing analytical methods do?
Determine if method (incl calib) gives accurate, precise, and consistent results under fixed parameters.
What does calibration do?
Determine rs btwn measured signal & amount of target analyte in sample.
What are the three methods to connect signal and analyte concentration, a.k.a. calibrate quantitatively?
> External standardization.
> Internal standardization.
> Standard addition.
How does one do an external standard method? What is its goal?
> Prep known std sols w/ range of [std]s individually.
> Measure signals.
> Plot S vs [std].
> Use cc to det [analyte] in the sample.
> What must the range of standards in external standardization encompass?
> What rs should analyte signal vs. [analyte] show? Why is it important?
> How is the unknown [analyte] found?
> Expected [analyte] & w/in instrument’s working range.
> Every ↑ in [analyte] gives same ↑ in signal → linear.
> By estimating unknown value w/in known data range.
> What does slope (k) of a cc rep?
> Why is a linear working range desirable?
> What happens when cc becomes non-linear?
> Sensitivity.
> b/c method’s sensitivity stays constant across that [ ] range.
> Sensitivity changes → small [ ] diffs no longer gives proportional signal changes → error in calculated unknowns.
What is the equation for a linear calibration curve?
y = kx + C
y = instrument signal
k = slope/sensitivity
x = [analyte] in sample
c = background signal
> When should spl be diluted in standardization? Why should you dilute said spl?
> What happens if the spl is not diluted & lies outside linear range?
> What should you do if sample response is too low?
> When its response > linear range → brings signal w/in linear range where response is still ≈ concentration.
> Non-linearity.
> Concentrate it to move signal w/in working range.
How does one do an internal standard method? What is its goal?
> Add diff cpd in known amt to all spls & stds.
> Use ratio of (analyte signal / IS signal) to correct vars & improve prec.
What are the four criteria of a good internal standard?
> Stable.
> Not present in spl.
> No interfering w/ target analyte/s.
> Similar physical-chemical properties to target analyte/s.
Note: Any losses occurring w/ target analyte(s) will also occur w/ IS.
> Why must IS have similar chemical properties to the analyte?
> What happens to responses & accuracy if their properties differ too much?
> b/c only cpds behaving similarly during analysis will be affected equally by vars → signal ratio reliable for correction.
> Responses change unevenly not based on vars but on properties → signal ratio becomes inaccurate.
> When is the internal standard added to sample? Why?
> What is the ideal response of the IS & analytes?
> What’s the ideal IS?
> Before any manipulation, b/c IS will track all losses occurring during manipulation, e.g. extraction / purification.
> 1:1.
> One that’s chemically similar to analyte but has stable isotope enrichment.
> What’s the formula for Response Factor in internal standardization?
> What does it represent?
> What does a relative Response Factor > 1 mean?
> What does a relative Response Factor < 1 mean?
> RF = Peak area / Spl amount
> How strongly detector responds to cpd amt, e.g. analyte/IS.
> Analyte = stronger signal than IS → detector more sensitive to analyte.
> IS = stronger signal than analyte → detector more sensitive to IS.
What is the formula correlating RRF, IS & X concentrations, and IS & X signals?
(SX / SIS) = (RRF)(CX)/(CIS)
> What is the formula for the dilution factor?
> Why does the DF work in concentration calculations?
> DF = Vfinal / Vinitial
> M1V1 = M2V2 → M1 / M2 = V2 / V1 = DF
Note: Multiplying by DF restores original concentration before dilution.
> What’s a primary reagent?
> What’s a primary std sol?
> What’s a secondary reagent?
> What’s a secondary std sol?
> Primary reagent: Pure, stable, non-hygroscopic cpds used for std sol prep.
> Primary std sl: Sol made from primary reagent w/ accurately known [ ].
> Secondary reagent: Less pure, unstable, hygroscopic cpds whose [ ] cannot be precisely known.
> Secondary std sol: Sol whose [ ] is determined by standardization vs a primary std.
> What’s the goal of prepping std solutions?
> How’s a std solution prepared?
> Create std sols (by serial, stepwise dilution from pure analyte) w/ known [analyte] in each sol for calibration & quantitative analysis.
> Accurately weight analyte → dilute to known vol (usually in vol flask).
Note: std sols can be made from a primary or secondary std.
> What’s a stock or primary std?
> What’s a secondary standard solution?
> Concentrated solution prepared directly from a pure analyte and used to make other stds.
> Solution containing dilution of a portion of a primary std.
How does one perform the standard addition method? What is its goal?
Add known amounts of analyte directly into the sample, measure total signal after each addition, then extrapolate back to zero to find the analyte concentration originally present in the sample (matrix).
Why does the x-intercept (negative value) in standard addition give the original [analyte]?
When you extend line back to where signal = 0, that point shows how much analyte would need to be removed to erase the signal—meaning that amt was already in the sample before any std was added.
How is standard addition different from internal standardization?
IS has a different substance added to the sample; standard addition has the target analyte (the same substance) added to the sample.
Does external standardization correct for matrix effects? Why or why not?
> The calibration standards are in a clean or different matrix than the real sample.
> Signal response can shift if the sample has interfering substances.
Note: External assumes matrices are the same but is faster. Additions proves it by measuring within the same matrix but is slower.
How can you quantify the analyte in the sample using standard addition?
Increase in signal produced by addition of known amt of target analyte to the sample.
What are the three approaches to standard addition?
> Single addition to a single solution.
> Multiple point addition to multiple solutions.
> Multiple point addition to a single solution.
How does one perform standard addition via a single addition to a single solution?
> Start with unknown sample containing target analyte.
> Measure its initial signal.
> Add known amounts of standard analyte to same solution, step-by-step.
> After each addition → measure signal again.
> Plot signal vs added analyte concentration
What is the formula when dealing w/ single addition to a single solution?
[X]i / [S]f + [X]f = IX / IS+X
> [X]i = unknown [analyte]
> Ix = intensity of signal from unknown amt of analyte
> [S]f = final [standard]
> [X]f = diluted [analyte]
> IS+X = intensity of unknown analyte + standard
What’s the matrix effect?
> Interference from other components in the sample that change the signal of the analyte.
> e.g. ions, solvents, pH, etc.
How does one perform standard addition via a multiple addition to multiple solutions?
> Begin with several identical aliquots of unknown sample w/ same matrix and analyte amt.
> Add different known amounts of standard analyte to each aliquot (except the blank).
> Dilute each solution to the same final volume to keep matrix constant.
> Measure the signal for every solution.
> Plot signal vs. [added standard analyte].
> Extrapolate line back to x-axis → intercept gives original [analyte].
When do you do multiple addition to multiple solutions?
> When only small vol of sample is available.
> When larger volumes of sample are available, it is possible to take a known aliquot out of sample.
Note: You’d be adding a successive known amounts of target analyte to sol and fill to same final volume.
How does one perform standard addition via a multiple addition to a single solution?
> Begin w/ one unknown sample containing target analyte.
> Add a known small amount of standard analyte to the same solution.
> Repeat additions successively while recording signal after every addition.
> Plot signal vs. total concentration of added analyte.
> Extrapolate to find original analyte concentration before any addition.
What is the formula when dealing w/ multiple additions to a single solution?
(IX+S) (Vi + VS / VI) = IX + (IX / [XI]) [SI](VS / VI)
> LHS = function to plot on y-axis.
> RHS = function to plot on x-axis.