CHEM 2510 / Topic 5: Collecting and Preparing Samples

How do you generally get a sampling error?

When the portion you collect doesn’t truly represent the whole sample, e.g. when sample’s composition ≠ population composition.

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 an analytical 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?

> Sampling errors aren’t completely considered.

> Results are inaccurate & imprecise.

How do you reduce sampling-related errors?

Ensure representative & homogenous samples.

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

> Location within target population should samples be collected.

> Type of sample should be collected.

> Minimum amt of sample needed for analysis.

> # of samples 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?

> Analyte evenly distributed in matrix; any portion represents the whole.

> Analyte unevenly distributed in matrix; varies by space or time.

Why are determinate sampling errors insignificant in homogenous samples

> Analyte evenly dist. thru whole samp.

> Every subsamp. = same true conc.

> Samp. ≠ bias result

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

> Det. samp. errs = insignif.

What is the main issue w/ heterogenous samples?

> Analyte unevenly dist in matrix.

> Subsamp ≠ rep whole.

> Samp bias → syst (det) errs.

> acc & prec.

What are the four approaches to sampling?

> 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 collected at random from target population.

> No assumption abt target pop → Least biased samp appraoch.

What are the disadv of random samp?

> ↑ # of spls for analysis and 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?

> Samples collected from target pop using avail info abt analyte distribution w/in pop.

> Assumption present abt target 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?

> Btwn random & judgemental samp, wherein spls collected from target pop @ regular intervals in time & space.

> Provides even pop coverage → reduces bias/judgement.

How does convenience samp work?

> Easily obtained spls → samples collected from target pop w/ obtainability.

What are the three common methods to obtain spls?

> Grab samp.

> Composite samp.

> In situ samp.

> Where is a grab spl taken from?

> How is a grab spl used?

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

> What is/are the advantage/s of grap samp?

> One single spl removed from target pop @ specific time & space.

> When sys is stable & uniform, one grab sample can rep whole pop, even if collected at random w/in stable & uniform pop.

> Homogenous 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 systematica samp to show variation.

> What is a composite spl?

> How is a composite spl made?

> What does a composite spl represent?

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

> Mix of several grab spls → single composite.

> Coll grab spls @ diff times/places → mix uniform

> 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 → Gives rep avg of uneven sys.

> When sys stable + uniform → Simple equal-vol approach.

> 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?

> Unweighted = equal votes → under/overrep parts.

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

> 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.

> What is an in-situ spl?

> How is in-situ samp done?

> What’s the key adv of in-situ spls?

> What’s the key purpose of in-situ samp?

> Spl taken w/in pop → not physically removed.

> Analytical sensor placed directly in target pop.

> Cont monitoring w/o indiv grab spls.

> Real-time / cont monitoring of analytes.

> What are key advs of in-situ samp?

> What are the key disadvs in 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.

> Sensory can get dirty or unstable → ↓ acc.

> What happens if spl too small?

> What happens if spl too big? 

> Too small → composition of spl differ from target pop → significant samp error.

> Too big → composite ↑ time ↑ money for analysis for just tiny improvement in sampling error.

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 diff in sens toward analyte vs interferent.

> Selectivity coeff → characterizes method’s ability to separate analyte from interferent.

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

> If C_A > K_A,I • C_I → interferent’s effect on tot signal is basically negligible as long as analyte’s effective signal is much greater than the interferent’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 analyte / interferents from matrix.

> Diff in physical / chemical property of analyte & interferent.

> How well a separation 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 analyte was separated from interferent.

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% analyte recovered.

> 0% interferent carried over.

> Perfect separation with a pure analyte.

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.

How does size-exclusion chromatography (SEC chromatography) work?

> Porous beads, as stationary phase w/ pore size ≈1–10µm, are packed in the column.

> Sample is added and will pass via gravity / pump at fixed flow rate.

> Small molecules must pass through the beads, getting into heavy “traffic,” because they have no choice. This heavy traffic causes small molecules to go elute slowly. It is very unlikely for small peptides to pass around the traffic.

> Big molecules do not fit in the pores of the beads, and pass around the traffic, causing them to elute faster.

> 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 during centrifugation under gravity.

> Thickness & denseness of medium.

> Liq your spl is in during centrifugation.

> 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 has both analyte & interferent.

> Add masking agent → binds only the interferent.

> Interferent → part of stable complex → no longer reacts / detected in analysis.

Note: 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?

> Analyte & interferent stay together → never physically separated

> 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?

> Solute placed in contact with two layers (called “phases”)

> Solute divides itself between them depending on which it “likes” more.

> Rate of transfer btwn both laters balances → Equilibrium reached, i.e. S_{phase_1}\rightleftharpoons S_{phase_2} .

Note: 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}}

Note: 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 btwn 2 phases, aka the concept.

> Extraction = applying said eq to physically move solute btwn 2 phases, aka 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.

Note: 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.

Note: 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?

Each extraction leaves less solute in the aqueous phase, so later pulls transfer only tiny leftovers → diminishing returns.

Note: First few extractions do most of the work.

How does liquid-solid extraction (LLE) work?

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