Instrumental and Analytical

What are the 10 steps of the analytical method?
1) Define the problem (quant. vs.qual)
2) Choose the method of analysis
3) Obtain appropriate sample
4) Determine amount of sample
5) Get sample into correct form
6) Eliminate interfering species
7) Run assay
8) Data reduction
9) Statistical analysis
10) Interpret the meaning of results
What’s the general framework for instrumentation?
Stimulus –> Sample–> Response
Difference between accuracy and precision.
Accuracy= how close measurements are to the true value.

Precision = how close measurements are to each other

Explain the two types of errors
1) random: indeterminate–> equal high and low precision.
2) systematic: determinate–> generates from a fixed cause, and is either high or low. affects our accuracy but its generally correctable.
What’s relative standard deviation
Comparing two numbers with standard deviations.
Relative : s/ avg. x
% rel std same thing times one hundred percent
What’s the difference between x, s and Mu, delta in the context of confidence intervals?
x, s = experimental sample mean and standard deviation; limited number of results; N < 20
Mu, delta = population/true; infinite number of measurements; N >20
What are two systematic errors that affect accuracy (bias)?
1) constant: size of sample doesn’t effect this; its the same magnitude (ex: calibration throws off subsequent measurements)
2) proportional: magnitude of error is proportional to sample; interferent in sample.
Corrections for systematic error
1) constant –> run a blank.
2) proportional –> run a standard (standard= sample with a known concentration of analyte).
When would choose a type 1 t-test?
When we want to see if experimental data agrees with a known value.
tcalc = (Mu – x)(sq. root of N / s)
If tcalc < ttable we get statistically valid results.
When would we use a type 2 t- test?
Compare 2 sets of experimental data which are replicates of a single sample:
same method w/ 2 diff. analysts or 2 methods with the same analyst.
You get 2 sets of data, each w/ Xa Xb and Mu a and Mu b.
When would you used a case 3 t-test?
Compare 2 sets of data where individual measurements are made of multiple samples.
tcalc = d/ sd *(sq. root of N)

where d = difference between set 1 and 2.

Why would we do an f-test?
Allows us to compare error distributions of 2 sets of experimental data.
fcalc = sa^2/ sb^2 (bigger one on top)
If fcalc > ftest, they have different error distributions.
Why would you use the Q-test?
Only if there is a particular data point that isn’t part of the parent popluation.
Qcalc = d (differnece between questionable point and its nearest neighbor) / w (difference between qst. pt. and the farthest point)

IF q calc < q table, you must keep the point

What are the 5 general principles in sample pretreatment?
1) Should be done w/o losing analyte
2) Should include bringing analyte into the best chemical form.
3) should remove interferents from the matrix.
4) should be done w/o introducing additional interferents
5) should bring the analyte into the proper concentration range
What are some sources of loss in your sample?
1) Adsorption: sticks to the surface (metal on glass)
2) Decomposition
3) non-quantitative transfer
How can you maximize your recovery?
Optimize the chemical form, Minimize interferences, and optimize concentration
Standards:
2 Types of Instruments
1) Direct measure: mass, volume
2) Indirect measure: instrument measures signal
Describe an external standard
The sample is different from the standard (in physically different locations).
-when matrix is either simple or well defined.
– one set of calibration solutions.
For external standards, what does the calibration curve depend on?
The instrument, condition of the instrument at the time of analysis, and other materials in the matrix
When would you use/apply standard addition?
When matrix is very complex, or when it contains proportional interferences.
spike varying amts. of standard
1) known conc. of standard 2) const. amt of sample, 3) varying amt of standard 4) const total volume
For standard addition, on a graph of IR versus volume of standard, what does “Vs0” refer to?
The negative of this value gives you the amount of standard you would’ve had to add to give you the same signal as the standard.

Cx = -(Vs)0 Cs/ Vx

Describe the Internal Standard method
spike a compound that’s similar but different from our analyte
-add a known amt of internal standard (diff from analyte)
What are the criteria for a good internal standard
1) similar molecular properties to analyte
2) distinguishable analytical signal
What is sensitivity?
How close 2 samples can be in concentration and still produce a measureably different instrumental response
Describe calibration sensitivity
Sensitivity can be determined by slope of the calibration curve.
-We want 2 samples close together, but produce a large difference in IR to be able to distinguish and measure them.
Describe analytical sensitivity
Gamma = m/ s, where s= std. dev. of sample IR.

-If you have another sample that falls within the same std. deviation of one sample, you won’t be able to distinguish them.

Detection limit
The smallest concentration which produces a signal which can be statistically differentiated form the blank.
Smin = Sblank + 3sblank

cmin = Smin -b/ m

Dynamic range
Range of concentration over which the instrumental response/ signal is linearly related to the concentration
Selectivity
ability of your method to distinguish signal from analyte versus signal from interferents.

S = maCa + mbCb + Sbl
selectivity coeffic. Kb,a = mb/ma If K is small, method is selective

We’re talking about light now. A high energy corresponds to what type of wavelength, and frequency?
A short wavelength, and a high frequency
From high energy to low energy, list the types of radiation that you can have.
Gamma, x-rays, UV, Visible, Infrared, Microwaves, and Radiowaves
For the index of refraction, if there are two mediums that light can pass through (air and water for example), in what medium will the angle between the normal be smallest?
In water; the greater the difference in the index of refraction, the more it bends.
Name two important facets of the Photoelectric Effect
1) Light must have a critical/threshold frequency (doesn’t matter what intensity the light is, the wavelength has to be shorter than the medium)
2) Light having greater than critical frequency causes ejected electrons to be ejected w/ increased KE
Atoms have ____ _____ energy levels, and can only absorb or emit certain frequencies of light.
Discreet, quantized
Energy of light must equal _______ between any ___ ___ levels in the atom or molecule.
the difference; 2 energy levels
Describe the three types of emission that can occur
1) Line spectra: arise from atomic transitions (vphoton = E1-E0/ h)
2) Band spectra: arise from molecules (they are broader)
3) Contiuum Spectra aka blackbody radiation (wavelength max = TK)
Name two types of absorbtion
1) Atomic: no vibrational levels, only electronic
2) Molecular: electronic, vibrational, and rotational
When we measure absorbance, what are we actually measuring?
The power in and power out. T = P/Po
A= -log T
What are the practical quantitative aspects of UV-Vis?
1) Selection of lambda max
2) Prepare solns which have constant temp, electrolyte concentration, interfering species, pH
3) Cells or cuvettes (ideally usd matched ones)
What do we run a user baseline?
To account or correct for differences in the cuvette
Important characteristics of UV-Vis
1) wide applicability to both inorganic and organic
2) detection limit (E-4, E-5)
3) moderate selectivity
4) good accuracy
5) easy data acquisition
How about qualitative aspects of UV-Vis?
Not done frequently because you get broad, few peaks
– can get some functional groups
-must choose solvent carefully (must be transparent at wavelengths of interest)
– polar solvents blur the spectrum
What’s the difference between single vs. double beam UV-Vis?
single beam= measure the reference than sample.
double beam = measure reference and sample at the same time
Photometer versus Spectrophotometer
Spectro: measure spectrum,
photo: can’t; measures absorbance at one wavelength.
Single versus Multichannel
Single channel: looks at one wavelenght at a time
Multichannel: all wavelengths at once
Null versus Direct read out
Direct: directly measures P and Po
Null: put optical wedge in until you get same intensity of P and Po.
What are some general characterisitics of the light source you need for UV-Vis?
1) stable intensity–> fairly intense
2) cover all wavelengths of interest (can’t do)
3) easily replaced and realigned (can do)
Deuterium versus Tungsten light source
Deuterium: UV-light source
Tungsten: pass current through filament, resistive heating –> blackbody radiation (350-2500 nm)
Describe two slit experiment
Interference pattern spacing: smaller spacing of slits yields larger spaces of diffraction pattern.
– the place where diffraction spots fall is lambda dependent
What does n*(lambda) = d(sin i + sin r) tell you?
It tells you where in space you get positive interference for a particular wavelength
Performance characteristics for monochromator
1) Inverse linear dispersion
2) Resolution
3) Effective bandwidth
4) Scattered light
Inverse linear dispersion. Describe it.
A small inverse linear dispersion is good (bad is large teheh)
IF you want a low D-1, you need a large space or large spectrum
What’s resolution
How close 2 spectral peaks can be together and still be distinguished
R = lambda/ delta lambda for 1 peak (detla lambda = Full Width Half Max

For 2 peaks, R = lambda ave/ delta lambda

What are factors that effect the resolution?
Distance between the blazes, diffraction order (n), size of the grating
R= nN
Describe effective bandwidth
Range of wavelengths exiting the monochromator. delta lambda eff = D-1 * w, where D-1 = inverse linear dispersion, and w = width of the slit
What size bandwidth will give you a greater sensitivity?
A larger bandwidth; more light, more sensitive. BUT, if you have an analyte and interferent, you need a small bandwidth in order to distinguish the two (sensitivity vs. selectivity)
What’s the effect of scattered light on beer’s law?
You get non-linearity, and an erroneous low absorbance.
Colored glass filter vs. Interference filter
1) colored glass: every thing else is absorbed except for colored wavelength
2) interference: destructive interference for all other wavelenghts except for wavelength of interest.
Sample and Reference cells
Measure P and Po simultaneously vs. in series
1) Simultaneously: minimize time between P and Po, difference in detector response between cause errors
2) series: chopper! mirror = sample, holes = reference
Purpose of detectors
Transduce our signal from a non-electronic domain to an electronic domain.
Photomultiplier Tube
Taking a small optical signal, and transducing it (a multiplying it) to a large electronic signal.
– each dinode multiplies the number of electrons, 1 photon = 10^7 electrons
Performance characteristics in PMT
1) Good sensitivity (small number of photons gives a reasonable current)
2) Consistent response regardless of lambda
3) High gain (1 photon –> lots of electrons)
Multichannel Detectors
PMT vs. Array
PMT: exit slit determines bandwidth; scan
Array: all multichannel is single beam,gives us spectrum chunk at one time
For array of detectors, what must you change about the monochromator?
You must remove the exit slit, so the light is open to all detectors (the width of each detector is the band width or the pixel)
Semiconductors
– solid w/ dissociated electrons. Electrons can move w/o being attached to a particular atom or molecule. Holes or electrons moves about = both can be an electrical conductor.
– electricity conducted by electrons (n-type) or holes (p-type)
An n-type semiconductor is doped w/ group __.
An p-type semiconductor is doped w/ group __.
n-type: group 5.
p-type: group 3.
What are the 4 limitations of Beer’s law?
1. Only works for dilute solutions.
2. Equilibrium pushes system to chemical deviations
3. Polychromatic deviations (this is why we measure absorbance at flat region).
4. Stray radiation (light which reaches the detector but hasn’t originated from the light source and through the sample).