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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?
> 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 → to give linearity.
> 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 give 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 response w/in linear range where response is still ≈ concentration.
> Non-linearity.
> Concentrate it to move response w/in working range.
How does one do an internal standard method?
> Add diff cpd in known amt to all spls & stds.
> Use ratio of (X signal / IS signal) to correct vars & improve prec.
What are the four criteria of a good internal standard?
> Stable.
> Absent in spl.
> No interfering w/ target X.
> Similar physical-chemical properties to target X.
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
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?
> Calibration & quantitative analysis.
> Accurately weight analyte → dilute to known vol.
Standard solutions can be made from a primary or secondary standard.
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.
> 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]?
The x-intercept’s magnitude equals the original analyte concentration, because it represents the amount that was there before any standard was added.
How is standard addition different from internal standardization?
> IS has a different substance added to the sample.
> Standard addition has the same substance added to the sample.
What are matrix effects?
∆Sx by other stuff in spl (the matrix) that isn’t X itself.
Does external standardization correct for matrix effects? Why or why not?
> In external standardization, the cc is prepared using stds in a clean solv.
> If the spl contains a different matrix, matrix components can alter the S response.
> Because the spl and stds do not respond the same way, the cc no longer accurately relates S to C, leading to incorrect results.
External assumes matrices are the same but is faster. Additions proves it by measuring within the same matrix but is slower.
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 w/ unknown spl (contains X).
> Measure So.
> Add known amount of X std.
> Measure new S1.
> Draw line thru two points (assuming linear response).
> Extrapolate to x-int → gives -Cx.
∴ magnitude of x-int = [X]og
What is the formula when dealing w/ single addition to a single solution?
[target analyte] / [final standard] + [diluted target analyte] = IntensityX / IntensityS+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 is your special formula when dealing w/ single addition to a single solution?
C_{x}=\frac{I_{x}C_{s}V_{s}}{I_{s+x}\left(V_{x}+V_{s}\right)_{}-I_{x}V_{x}}
How does one perform standard addition via multiple addition to multiple solutions?
> Begin w/ several identical aliquots of unk spl w/ same matrix + X amt.
> Add diff kn amts of std-X to each aliquot (except blank).
> Dilute each sol to same final volume to keep matrix constant.
> Measure S for every sol.
> Plot S vs. added [std-X].
> Extrapolate to x-int → gives -Cx.
∴ Magnitude of x-int = [X]og
When do you use single-solution vs multiple-solution standard addition?
Single solution, successive adds
> Sample vol limited
Multiple solutions, multiple adds
> Sample vol plentiful
> Better stats, indep pts
How does one perform standard addition via a multiple addition to a single solution?
> Start w/ unkn spl (contains X).
> Measure S0.
> Add increasing kn std-X amts successively.
> After each addition, correct for dilution.
> Measure S after each addition.
> Plot S vs added [std-X]
> Extrapolate to x-int → gives -Cx.
∴ Magnitude of x-int = [X]og
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.