CHEM 2510 / Topic 5: Collecting and Preparing Samples

How do you generally get a sampling error?

From non-representative samples / non-homogeneous samples.

What'‘s one way you can specifically get a sampling error?

> Sample not mixed well → some parts richer/poorer in analyte.

> You only test one region (like top layer) → results skewed.

> You generalize that one spot’s result to the entire thing.

> Why might a method give poor results even if indeterminate and determinate errors are minimized?

> What’s a common issue when using a method for the first time?

> Samp errs aren’t completely considered.

> Results are inacc & imprec.

How can you fix sampling errors?

Fix by true rep spl coll.

What are the five elements to consider when designing a sampling plan?

> Loc w/in t-pop.

> Spl type.

> Min spl amt needed for analysis.

> # of spls for analysis.

> Possible ways to minimize variance.

What are two main types of samples?

Homogenous & hetereogeneous.

What are the differences btwn homogenous and heterogenous samples, respectively?

> X evenly distributed in M; any portion reps the whole.

> X unevenly distributed in M; varies by space/time.

Why are determinate sampling errors insignificant in homogenous samples?

> X evenly dist thru whole spl.

> Every subspl = same true conc ≠ bias result.

> Small var = random (indet), not syst.

> Det samp errs = insignif.

What is the main issue w/ heterogenous samples?

> X unevenly dist in M.

> Subsamp ≠ rep whole.

> Samp bias → syst (det) errs.

> Reduced acc & prec.

What are the four samp approaches regarding how to decide where/when to sample?

> Random.

> Judgemental.

> Systematic.

> Convenience.

> How does random samp work?

> What uniquely gives random samp an adv as a samp technique, & what is said adv?

> Spls coll’d at random from t-pop.

> No assumption abt t-pop → Least biased samp appraoch.

What are the disadv of random samp?

> ↑ # of spls for analysis + representatation.

> ↑ time ↑ money than other samp methods.

> How does judgemental samp work?

> What uniquely gives judgemental samp an adv as a samp technique, & what is said adv?

> Spls coll’d from t-pop using avail info abt X dist w/in pop.

> Assumption present abt t-pop (selective) → More biased samp approach.

> How does systematic samp work?

> What uniquely gives systematic samp an adv as a samp technique, & what is said adv?

> b/w random & judgemental samp, wherein spls coll’d from t-pop @ regular intervals in time & space.

> Provides even pop coverage → ↓ bias/judgement.

How does convenience samp work?

Easily obtained spls → spls coll’d from t-pop w/ obtainability.

What are the three samp approaches regarding how to physically collect/measure the spl?

> Grab samp.

> Composite samp.

> In situ samp.

> When is a single grab spl sufficient to rep an entire pop?

> What main type of spls do grab spls work well w/?

> What are the main advantages of grab samp?

> When sys is stable & uniform, one grab sample from any time and place can rep whole pop, even if coll’d at random w/in stable & uniform pop.

> Homog spls.

> Simple, fast, & can be used in any samp method.

For grab spls, if parameters change, how do you adjust to get grab spls?

Collect multiple grab spls via systematic samp to show variation.

> How is a composite spl made?

> What does a composite spl represent?

> What is the main adv & disadv of composite spls?

> Coll grab spls @ diff times/places → mix uniform to a single composite.

> Avg rep of sys from mult snapshots

> When overall trend > indiv var.

> ↓ cost/time; loses time detail.

> When should weighted comps be used?

> When are unweighted comps best used?

> What data do weighted comps need?

> What’s the pro and con btwn weighted & unweighted comps?

> When flow/time varies a lot.

> When sys stable + uniform.

> Flow or time info for each grab spl → Used to set mix ratios.

> Weighted = ↑ acc but risk calc/mix errs ; Unweighted = ↓ effort but less rep.

Why is a weighted comp spl truer than an unweighted one?

> Larger flows/time periods = ↑ influ in mix.

> Unweighted = equal votes → under/overrep parts.

> Weighting by vol/time → mirrors real contrib.

> Gives truer sys avg, closer to real cond.

> What can be done before mixing grab spls for better rep?

> What’s the main purpose of comp spls?

> Why not use comp spls for fast-changing systems?

> How should comp spls be handled before analysis?

> Weighting grab spls → more rep avg.

> Used for avg conc studies.

> Analyte may react, decompose, evaporate, etc. → comp ≠ true rep.

> Mix throughly & store cold overnight sealed.

> How is in-situ samp done?

> What is the key adv of in-situ samp?

> Analytical sensor placed directly in target pop → Spl taken & analyzed w/in pop; not physically removed.

> Real-time, cont monitoring of X w/o indiv grab spls.

> What are 3 other advs of in-situ samp?

> What are 3 key disadvs of in-situ samp?

Advs:

> No handling → ↓ contam risk.

> Instant data → hi time-res.

> Ideal for field/enviro studies.

Disadvs:

> Only works for sensor-measurable analytes.

> Sensors need cal & maint.

> Sensor can get dirty or unstable → ↓ acc.

> What happens if spl size too small?

> What happens if spl size too big? 

> Too small → composition of spl differ from t-pop → significant samp err.

> Too big → ↑ time ↑ money for analysis for just tiny improvement in samp err.

What equation tells you how close your sample mean is to the true mean?

\mu=x\pm\frac{tS_{s}}{\sqrt{n}}

wherein

> u = true pop mean

> x = mean of spls

> t = statistical factor (depending on confidence level, e.g. 95%)

> S_s = stdev of samp

> n = # of spls

When the confidence interval eq is rearranged, what’s the new equation to get the # of spls you need?

n=\frac{t^2S_{s}^2}{\left(\mu-x\right)^2}

> What makes up the overall variance of an analysis?

> How can samp var improve?

> How can method var be improved?

> What’s the goal of minimizing overall variance?

> Combo of samp var & method var.

> Collect ↑ # of spls of proper size.

> Analyze each spl ↑ times → better precision.

> To ↑ acc + prec by balancing samp & method.

> What are the three steps to implement sample plan?

> What risk occurs after removing spl from its pop, and why is that a prob?

> Remove spls from target pop → Preserve spls → Prep spls for analysis.

> May undergo chem/phys change → Changed sample ≠ true rep of pop.

> What determines a method’s selectivity?

> What does K_A,I rep?

> What’s the signal equation accounting for interference? What does it tell you?

> How do y’know if interferent signal is negligible?

> Rel sens toward X compared to Int.

> Selectivity coeff → characterizes method’s ability to separate X from Int.

> S_{samp}=k_{A}\left(C_{A}+K_{A,I}\cdot C_{I}\right) → tells you how much Int contributes to S_tot.

> If C_A > K_A,I • C_I → Int’s effect on S_tot is basically negligible as long as X’s effective S > Int’s contribution.

What does it mean when n “stabilizes” during iteration?

> When recalculating n gives same (or nearly same) value.

> Means t & n now consistent → true sample size found.

> What’s the goal of any analytical method involving separation?

> What’s the key thing you need for separation to happen?

> What is separation efficiency?

> Remove X / Int from M.

> Diff in phys / chem property of X & Int.

> How well sep method resolves one component from others.

What’s the formula for R_A?

R_{A}=\frac{C_{A}}{\left(C_{A}\right)_0}

> R_A = separation efficiency / analyte recovery (usually %)

> C_A = analyte amt post-sep collected.

> (C_A)_o = analyte amt pre-sep.

What’s the formula for R_I?

R_{I}=\frac{C_{I}}{\left(C_{I}\right)_0}

> R_I = interferent recovery (%)

> C_I = interferent amt post-sep collected

> (C_I)_o = analyte amt pre-sep

> What’s the formula for S_I,A (separation factor)?

> What does S_I,A tell you?

S_{I,A}=\frac{R_{I}}{R_{A}}=\frac{C_{I}\cdot\left(C_{A}\right)_0}{\left(C_{I}\right)_0\cdot C_{A}}

How well X was sep’d from Int.

Note: Not just how much analyte you got (like recovery) but how cleanly it was separated.

> What’s it mean to get an R_A = 1?

> What’s it mean to get an R_I = 0?

> What’s it mean to get an S_I,A = 0?

> 100% X recovered.

> 0% Int carried over.

> Perfect sep w/ pure X.

How does dialysis work?

> Sample is placed inside a cellulose bag w/ a pore size ≈ 1–5nm.

> Bag is submerged in a surrounding liq w/ diff composition.

> If conc inside ≠ outside → conc gradient forms.

> Small solute molecules pass thru pores until concs equalize.

> Large molecules stay inside bag.

> In SEC, what is the stationary phase usually made of?

> What dictates smaller pore size?

> Cross-linked dextrin / polyacrylamide.

> ↑ cross-linking ↓ pore size

How does centrifugation work?

> Sample is placed in a centrifuge tube → spun at high rpm.

> Heavier/denser molecules feel stronger outward pull & settle faster at the bottom as pellet.

> Lighter particles remain suspended as supernatant.

> In centrifugation, what does sedimentation rate mean?

> What does medium mean?

> What does medium density mean?

> Speed at which molecules settle to the bottom under gravity.

> Liq your spl is in.

> Thickness & denseness of medium.

> How does particle mass or density affect sedimentation rate?

> How does medium density affect sedimentation rate?

> How does centrifugal force (rpm) affect sedimentation rate?

> ↑ mass of particles ↑ density of particles → particles sink faster → ↑ sedimentation rate.

> ↑ medium thickness ↑ medium denseness → fluid slows settling → ↓ sedimentation rate.

> ↑ rpm ↑ spin force → ↑ sedimentation rate.

Differentiate RPM and RCF.

> RPM (revolutions per minute): How fast the rotor spins / how many spins per minute.

> RCF (relative centrifugal force): How strongly particles are pulled outward.

What’s the rs btwn RPM, radius, & g-force?

CF\left(g\right)=1.12\cdot R\cdot\left(\frac{RPM}{1000}\right)^2

> CF (centrifugal force) = RCF (relative centrifugal force) = g-force.

> 1.12 = conversion factor.

> R = distance from centre of rotor to sample (bottom of tube).

> RPM = revolutions per minute.

How does masking work?

> Spl = X & Int.

> Add masking agent → binds only Int.

> Int → part of stable complex → no longer reacts / produces S for analysis.

Masking hides interferent by binding it to masking agent that “masks it” so it can’t interfere.

> Why isn’t masking a true separation technique?

> How do diuretics, dextran, and epitestosterone relate to masking?

> X & Int stay together → never physically sep’d.

> All three are examples of masking techniques → they don’t remove substance, they just make it harder to detect.

How do diuretics affect chemical concentration in urine?

> Increase urine production.

> Body excretes more water → Urine becomes diluted.

> Any drugs or chemicals present appear at lower concentration.

> How does dextran affect chemical concentration in blood?

> What happens to the T/E ratio when epitestosterone is added?

> Acts as a plasma expander (adds volume to bloodstream).

> Increases blood fluid volume.

> Same amount of chemical now spread out in more liquid.

> Measured concentration drops.

What happens to the T/E ratio when epitestosterone is added?

> Testosterone testing relies on the T/E ratio (normally ≈ 1:1).
> Doping raises T → ↑ ratio.

> Adding synthetic E balances ratio back ↓ → makes excess testosterone harder to detect,

How does partitioning between phases work?

> Solu placed in contact w/ two immiscible phases.

> Solu distributes b/w phases based on relative solubility / interactions.

> Solu transfers back & forth b/w phases.

> @ equil, rates of transfer are equal

> Concs become constant, not necessarily equal.

S_{phase_1}\rightleftharpoons S_{phase_2}

Separates substances based on how they distribute (partition) between two immiscible phases, usually one polar & one nonpolar (like water & organic solvent).

> What’s the formula for K_D? What does it tell you?

> What does it mean to have a large K_D?

> What does it mean to have a small K_D?

K_{D}=\frac{\left\lbrack S\right\rbrack_{phase_2}}{\left\lbrack S\right\rbrack_{phase_1}}

> K_D = equilibrium constant for distribution → tells you which phase the solute prefers.

> Large K_D = solute prefers & goes to phase 2 from phase 1 / ↑ transfer to extracting phase (products).

> Small K_D = solute prefers & stays in phase 1 (reactants).

> How do you calculate the total moles of solute conserved in separation?

> How do you get [S]_aq post-extraction?

> How do you get [S]_org post-extraction?

> (moles_{aq})_0=(moles_{aq})_1+(moles_{org})_1

> \left\lbrack S\right\rbrack_{aq}=\frac{\left(moles_{aq}\right)_1}{V_{aq}}

> \left\lbrack S\right\rbrack_{org}=\frac{\left(moles_{org}\right)_1}{V_{org}}

0 = pre-extraction ; 1 = post-extraction (at eq).

What does the K_D​ formula in LLE represent?

K_{D}=\frac{\frac{\left\lbrack\left(moles_{aq}\right)_0-\left(moles_{aq}\right)_1\right\rbrack}{V_{org}}}{\frac{\left(moles_{aq}\right)_1}{V_{aq}}}

What’s the diff btwn partitioning & extraction?

> Partitioning = eq dist of a solute b/w two phases (the concept).

> Extraction = using partitioning to physically transfer a solu b/w phases (the application).

Why’s a spl extracted one or more times w/ portions of the second phase?

> After each extraction, a bit of solute stays in phase 1.

> Add fresh solvent (phase 2) → keeps taking more out → better recovery.

Multiple smaller extractions → pull out more solute than one big extraction.

How does liquid-liquid extraction (LLE) work?

> Target analyte initially present in 1-phase.

> Two liquids (aq + org) placed in sep funnel.

> Sep funnel shaken to ↑ contact → ↑ SA btwn phases.

> ↑ solute transfer → solute partitions btwn both layers until eq.

> ↑ density of phase (often aq layer) → settles at bottom.

> ↓ density of phase (often org layer) → floats on top.

> Target analyte may be present in both phases but favours one.

Extraction efficiency determined by equilibrium constant for analytes partitioning btwn 2 phases.

What’s the equation for (F_aq)₁? What does it tell you?

\left(F_{aq}\right)_1=\frac{\left(moles_{aq}\right)_1}{\left(moles_{aq}\right)_0}=\frac{V_{aq}}{\left(D\cdot V_{org}\right)+V_{aq}}

> (F_aq)₁ tells you what fraction of the solute stayed in aq phase after one extraction.

> D = distribution ratio (same as K_D)

> V_aq = aq phase volume.

> V_org = org phase volume.

> What’s the equation for (Q_aq)_n?

> What does it tell you?

> What does smaller Q_aq mean?

> What’s the relationship between n and separation quality?

\left(Q_{aq}\right)_{n}=\left\lbrack\frac{V_{aq}}{\left(D\cdot V_{org}\right)+V_{aq}}\right\rbrack^{n}

> Tells you the fraction of solute left in the aqueous layer after n extractions.

> Smaller Q_aq = more solute moved to organic phase.

> More extractions (↑n) → better separation.

Why does LLE efficiency level off with more extractions?

B/c each extraction reaches partition eq, and as the remaining solu decreases, subsequent equilibria transfer progressively smaller amts.

How does liquid-solid extraction (LLE) work?

Liquid sample passes through a solid adsorbent column that traps target analytes.