Chem Sep midterm Flashcards
2 MAJOR FORCES OF SEPERATION
Sepeartive and dispersive transport
Essential feature of transport
redistribution of components in space
Rules/limit of seperation
1) No absolute separations
a. Separation limitations and Detection limits
Limits in separation include
a. Physical (eg controlling t or p)
b. Chem limits (equilibrium)
2 major forms of entropy
Mixing and dilution
Seperative transport of a component into different regions
Delta(H) - T Delta(S) - see quiz
What is chemical potential and what does it depend on
Gibbs free energy change upon entering a system - depends on intrinsic affinity to the phase (enthalpy) and solution (diffusion/concentration termenetropy? (RTLn(C))
Stronger affinity menas what for enthalpy
Lower
What are the laws of thermodynamics
0) Heat is transferable - transitive
1) Energy can’t be created or destroyed - just transferred
2nd law : Entropy – total entropy of an isolated sys can never decrease over time – is constant if process is reversible
What is U - to
Q-w (heat transferred in vs work done
standard entropy vs entropy
standard entropy is a trait of the molecule while entropy of a reaction is something we calculate
Equation for change in entropy
Change in Q/T
For LLE -practice solving for Q
Uint vs u ext
mathematically equal (need to become 0) but different in unit abrupt whereas uext continuous
What is the distribution isotherm
Graph of concentration in one solvent vs concentration in another (so slope is K) - at one temperature - shows that for most concentrations - this is a lienar and predictable relationship (except when concentration too high
what is k
moles in stationary/moles in mp
Binomial distribution know it
What does craig appartus tell us about chroamtography
Tells us how it’s distributed - can’t give us shape and position however
Why is the Craig Apparatus and chroamtography able to separate compounds (what equations and relations make this so)
So if we think of our craig apparatus dist as gaussian peak - our mean is RP, and our stdev is ROOT(rpq) so we see our mean increases proportionally with R while our spread increases only with root R so our distance is increasing faster than the spread of our peaks
What are p and q in terms of k
p is k’/(1+k’) and q is 1/(1+k’) and k is just q/p
What is dead time a function of
column dimensions and mobile phase velocity
What is Rt based off of
column, mobile phase type and velocity, temperature and characteristic of the analyte
Dilution equation?
Delta(S) = nRln((Vfinal)/(Vinitial))
How do you get Vm and Vr in basic chromatography
= Ft so Ftm gets Vm, F*Tr gets Vr and can get adjusted retention volume as Vr - Vm
k = (in terms of RT)
adjusted RT/ TM
All the things k =’s
q/p, tr’/tm
How to derive k = tr’/tm from k = q/p
Determine velocity i(average) in terms of average velocity of the mobile phase and p and q and solve for p and q. Convert those velocities into tr and tm through distance L. DO OUT ON PAPER
What is alpha Selectivity factor or RRT)
KB/Ka or kb/ka or also RTb/RTa (always greater than 1) also deltav/average(V)
What is z in the gaussian dist
sample x minus the mean divided by stdev (so basically difference from mean, normalized or expressing it in #’s of stdevs)
W at different heights in terms of stdev
Base = 4 stdev, at half its 2.35 stdeev
Gaussian distribution as applied to concentration profile of a peak
c(t) = cmax * e^-((t-tr)^2)/(2stdev^2)
How does theoretical plates relate to how Craig apparatus is able to separate?
so theoretical plates = (tr/stdev)^2 and this is analogous to R (so the more we have tr goes up higher, and stdev increase proportional to root (N)
What is effective plate # and relation to N
RRT/stdev squared; Neff = N *(k/1+k)^2
Equations for H (height in theoretical plates)
L/N, variance/L, X/N, variance/X, X*W2/(16tr^2)
so in sum things it could be related to are L, N, X, W, Tr
Calculate resolution
(difference in Tr divided by average W)
Resolution scales
Adequate is 0.8, 1-1.5 is great, 1.5 is baseline(>99% separation)
Write out how migration distance effect on Rs depends on Delta X (start with resolution equation in terms of X)
Resolution plot that comes from showing Rs proportional to ROOT(X)
Y axis is resolution, and X is distance of migration (X) - and we have a plot for DELTA X (the top of the Rs equation ) - being proportional to X so it’s linear, and we have a curve for the bottom (average W) which since its proportional to ROOT(X) is a curve - and where they meet is where R - 1 (makes sense) and - after that point we see that our DELTA X line is bigger than the average W curve showing that our R will be greater than one after that point with increased migration distance
How does selectivity play into our resolution plot
So in the top part of resolution DELTA X - we determined equaled Delta v tr, in which we sub tr for X/V which gives us (Delta(v) /V)X in our first plot we just had X as a line and now delta v/V is OUR SLOPE FOR THE LINE and this delta v/v is our selectivity so as our selectivity is greater(alpha = tr’/tr’ or K/K or k/k) the slope is higher and we reach a resolution of one with less migration distance of X
How does Plate height play into our Rs plot
For our resolution plot equation - we instead of just saying the denominator is proportional to ROOT(T) we take it literally - we went from Average W to 4ROOT(H*X) which if we we square the inside but take a root of it we can rearrange to to 16H so smaller plate height better -
How does N enter the resolution equation
So when we have DeltaV/V *ROOT(X/16H), X/H = N so it becomes Delta v/v * (N/16)^(1/2)
derive the purnell equation
Start with resolution but in terms of rt - Assume W for both are so average W = W, and replace that with sigma and replace sigma with the theoretical plate equation (in terms of N and rt) THen , replace the rt’s with tm(k+1)’s , work that out and sub in alpha = k2/k1 (IDK how the math works but it works)
What are the purnell factors and how do they affect resolution
Selectivity, N and K; as k increases our peaks have more affinity for SP - move farther along - some resolution but broader peaks, as N increases, we get sharper peaks - same Rt sep but less sigma so better resolution, and Selectivity - makes a big difference eg change mobile phase now they will move differently from each other
How do the effects of the fundamental purnell factors change as they increase
Alpha is fairly linear throughout - better returns, N and K have points where their slopes become really shallow - pretty early for N and K, earlier and shallow for K though
are the fundamental factors *purnell) independant?
no
What is peak capacity
The number of peaks we can fit along a length (essentially L/W*Rs) an be turned into root(N)/ 4
more accruate peak capacity equations
nc = 1 + (ROOTN)/4 * ln(Vmax/VmiN)
Explain alternate isotherms
Langmuir -so we have stronger interactions with SP and MP SO as concentration goes up - the SP gets SATURATED - and at these higher concentrations then - we see k go down - so tr goes down and vi goes up. So the center of our peak moves Faster - in DISTANCE - this creates a tailing peak but iN RT (keep in mind faster means lower RT) - this makes a shark fin tailing peak -
Anti LANGMUIR- the opposite - more affinity for MP - see the opposite happen - creates fronting peaks
Write out the Vi and Tr equations for isotherms in terms of k
so vi = vm/(1+K) and tr = tm(1+k) so we see tr increases with k and vi goes down as k increases.
Tailing asymmetry equiations
asymmetry factor: b/a at 10% (b being behind the peak so > 1 is tailing.
ALSO tailing factor - a+b/2a (at 5% height) - 1 = even no tailing)
pros and cons of fluid
(a) The strength of flow: provides the most powerful and versatile
mechanism of transport available for separative displacement.
(b) The weakness of flow: its nonselectivity and nonuniformity.
Know the relationship between volume, tr and tm, Flow rate length etc
Start with vm = L/tm end with L*F/V (note little v is velocity) big V is volume. Can do with dead volume or just mobile phase flow and also do with SOLUTE flow rate (tr)
What does flow depend on in terms of viscosity
viscosity , area of contact between fluid layers, dv/dy (how velocity changes with y)
How do we calculate Reynauds factor
INERTIA/VISCOSITY (inertia = pvd (solvent density * velocity * pipe diameter).
3 types of flows and expected Reynaud factors?
Plug, Turbulent and Laminar
Plug - infinite -
Turbulent - > 2100 (has laminar zone on edges and turbulent area in middle)
Laminar - < 2100 - center is vmax (Hagen Poiseuille Flow
What is the Hagen Poiseuille equaiton and what does it tell us
Vmax in terms of pressure drop (for laminar flow)
How do you calculate the velocity of a particle x distance from center in a laminar flow
vmax (1-(x^2)/(r^2)) r being radius of tube
Talk about the basis for Hagen-Poiseuille and how it takes it’s final form
It’s essentially- Change in pressure = Flow * Resistance . It dictates average v is proportional to radius of pipe (squared), and change in pressure and inversely correlated with Length of pipe and viscosity
Volumes in a column and how they’re divided into porsoities
so theres overall voluKnowme, interparticle volume and intraparticle volume (so volume inside our particles vs outside it (stagnant vs flowing) - our porosities are then
EE- INTERPARTICLE POROSITY (volume outside of particle/empty column)
EP - INTRAPARTICLE(volume in particle/empty column)
and TOTOAL POROSITY) -EE + EP (void volume of column/ empty column)
* NOTE DIFFERENCE IN VOID VOLUME VS EMPTY COLUMN
Common porosities
EP often .4, EE often .4 and E tot often .8
How does REYNAUDS # change in packed bed and what are the relative #’s expected for flows
instead of d being diameter of pipe - it’s particle diameter
Turublent is > 100
1-100 is a mix of turbulent and laminr
Laminar is < 1
How does Hagen Poiseuille change in packed bed
So instead of r for radius of pipe we have B -specific permeability constant, also instead of in denominator we also have EE (so Bo is R^2/8 (AN OPEN TUBE) which is why it replaces both of those values)
THIS IS DARCYS LAW
For a packed column , what does B depend on and what is an approximation for B in common column types
B depends on EE and particle diameter (positively with both), for a regularly packed column its roughly d^2 / 1000 for a bed packed with spherical particles d^2 /500
Relations in the OVERALL DARCY equation (subbing in the karman conzeny eq for Bo)
Vavg is proportional to changein pressure, particle diameter ^2, inverse proportional with viscosity and length, and generally proportional to EE
relationship between v avg and vm in packed bed
V avg is the set flow I guess and v m is the Actual flow
Vavg* (EE/Etot) = Vm and if we use ee = .4 and eep = .4 we get vavg = vm*2 (VM is less than v avg
Bo in terms of vm?
vm *n * ETot * L divided by delta P
Given Darcy equation whats the relation between change in pressure and dp
inversely related (dleta P = vavg * (constant/dp^2))
Know how to put Vm into Darcys equation (relate Bo to Vm)
Start with Darcys, sub in vavg = VM *(ETOT)/(EE)) rearrange for BO
Mass Transfer and Diffusion definitions
Mass transfer: movement of mass from one place to another
Diffusion: movement of mass from region of high concentration to low
concentration.
How to get the mean for a random walk
binomial distribution
How do you get the overal mean of several random walks
Kl - (k-1)l
How do you get variance of random walk
know how to do this
How do you get drift velocity from random walk
n * delta t = t from this can sub in for N in terms of T and X/T = v
How do you get einsteins equation from random walk
The variance equation - sub in t/Delta T for N and sub in D
diffusion coefficient in terms of l
D = (l^2)/2delta(t)
Rewrite band broadening (gaussian function) in terms of diffusion (einsteins)
replace all the sigma ^2 with 2dt
but otherwise same equation Ct = cmax etc
How to get plate height theory of columen efficiency (from random walk)
given our diffusion being variance = 2dt, D also = l^2 /2delta(2) so if we sub that in we get l = sigma - SO we can take H = variance/L - sub in N*l for variance and then n/L = H so l^2/H = H so l = h
How do we caluclate N for particles moving across plane in one direction
N(x-l/2) = 1/2( Nx - Nx-l)
How do we derive ficks first law
so we need 3 equations N moving across a plane is L/2 * dN/dx, N = c(x)LYZ and J = N/(YZdelta(T)) and for the J equation first sub in L/2dN/dx for N and then sub in c(x*LYZ for dN - sub in D for l^2/2t and done
How do we derive ficks 2nd law
We start with N/YZdelta t = J - turn it inot delta N and delta J and sub in N - c(x) *LYZ, and divide both sides by L this makes dN/dt = dJ/dx then sub in for J (-D dc/dx)
what does ficsk 2n dlaw say
Fick’s 2nd law of diffusion describes the rate of accumulation (or depletion) of concentration within the volume as proportional to the local curvature of the concentration gradient.
what does ficks first law say
Fick’s first law tells us HOW MUCH flux to expect
For a particle in solution moving at velocity and is colliding upon - what is the equation representing its distance and its velocity
x = vo*t + (1/2) f/m * (t^2)
v = v + (1/2) f/m * t
What is stokes law
friction coefficeint = 6 pi r n(viscosity)
Derive friction equations and use those with diffusion to get einstens famous equation (and expand with components that make up friction)
so from velocity equation the f term is 1/2 * f/m t and friction is kind of inverse 2m/t - friction also equals 6 pi r viscosity. D = l^2/2t so when you do D * friction you get mL^2/t^2 and l^2/t^2 = v^2 so we get mv^2 so we can say Dfric = Kb *T, we can divide both sides by friction and sub in 6 pi r viscosity (which is STOKES EINSTEIN
What is mobility (u)
1/fric
What is c (or dc)
density or change in density
How are boltzmanns and R and avogadros related
R = kb * T * Na
What does diffusion depend on in a system
solute solvent and temp
Typical diffusion constant valules
around 1 in gases and around 10^-5 to 10^-7 in liquid
Issues with diffusion in a packed bed
Tortuosity and bottleneck problems, tortuosity is that there are many winding paths and bottleneck is some of these paths are narrower - decrease rate of diffusion
friction coefficient
Na * friction coefficent (MOLAR DRAG CONSTNAT
Know how to derive molecular transport equation
what is transient
M/f (1/A0 time it takes for acceleration
does the transient matter
typically very small reduces the whole term essentially to 0 - that’s us reaching steady state velocity - acceleration died down really quick because too much friciton/collisions etc
Derive the Flux of molecular transport
What do the terms in flux of molecular transport mean
U is mean displacement from external and internal forces and D dc/dx is our dilution entropy term
What is diffusion interms of molar drag coefficeint
D = RT/f ( this works because D(fric) = Kbt and f = (fric)Na so substituting it gives Na*Kb on top which gives R
For our overall Flux molecular transport equation - how does that relate to Ficks first law
It’s ficks first law with UC so if there are no external or internal forces - becomes ficks first law (no U force)
How do we relate our overall flux transport o Ficks 2nd law
see notes
What is w
w replaces Uc - representssimply the sum of all direct (non-diffusional) displacement
velocities– those caused by bulk displacement at velocity v plus those
caused by chemical potential gradients which impel solute at velocity U
Transport equation on a gasussian curve
so at one point in a peak we see dc with respect to dt is going up and we see that s proportional to -W dc/dx = so going from high concentration to low? as we go along its less BUT ITS negative - so the stuff moving out is less and more is coming in
3 PROCESSES that affect band broadening
(1) Longitudinal diffusion
(2) Eddy multi path diffusion
(3) Partition between stationary phase and mobile phase
To understand band broadening in a column using random walk - whats our first step
Determine step length and Number of steps
Whats longitudinal diffusion in an open tube vs a packed bed and how is it derived
Open tube: 2 dm/v (comes from einstein equation variance = 2dt = 2dmL/v and variance/L = Hl
FprPacked bed - it’s the same equation but we multiple velocity by (1 + ep/ee)
eventually turned into Hl - 2yDm/v (with y being that term we added)
In terms of eddy diffusion - what are ways CRITICAL VELOCITY BIASES arise
molecules traveling faster at center of narrow flow channels
molecules travel faster in some channels than other due to shape, openness etc
molecules travel faster in some region due to packing differences
molecules travel faster outside of pores than in them
How to use random walk to define EDDY DIFFUSION
1st assume constant v in our segment which is the size of our site (so # of segments = L/S) - can change v between S’s but not within - SO to determine our step size - we compare the S of a normal velocity (average) to a fast one and the difference is our step size (so the difference would be (Vf-v)t - and we sub in for t with S/v so we get (vs-v) S/vf and we can replace all the v terms with w so its jus W^2 *S =HE
2 ways a molecule is removed from velocity bias (eddy diffusion )
Flow - they’ll naturally flow to the next S which may be faster , slower or the same - DIFFUSIOn - they can diffuse between fast an slow paths randomly
Equations for molecules removed from velocity (flow vs diffusion dominated)
hf = 2 lambda *dp (flow)
Hd = (wdp^2)/Dm * v (diffusion - Dm is diffusion coefficient in MP)
In eddy diffusion how do Flow based and diffusion based interactive (derive the additive plates)
In terms of random walk steps - They are additive! So we can solve for S (L/N - and sub in N for N from D and N from F and from there add in the W term and simplify it
How do the combination of Eddy diffusion factor look graphically
on velocity vs H - HF is independent of velocity so its a horizontal line, Hd is a line - linear BUT HE - is in fact a curve that approaches 0
Get He equation not in terms of Hd and Hf (sub these values in
see notes
What does He relate to
dp (correlates to) - inverse correlate with diffusion- correlate positively with v
How does mass trasnfer effect flow -
largely in how it takes time- different distances from the phase IN addition to it just taking different amount of times in and out
Equations for Hs and Hm (resistance to stationary and mobile phase)
see notes
Relationship between Hr and Hs and Hm
additive! Hr - Hs + Hm
Know VAN DEEMTER TERMS andH’s correpsonding to them
Band broadening tips tips
Smaller particles for packed column
Smaller diameter for open column
Lower temperature and higher flow rate to reduce longitudinal diffusion
Most separation is operated in flow rates higher than the optimum flow rate, thus C term is significant in overall separation performance
What is minimum for van deemter and how derived?
Take derivative and solve - take 2nd derivative to see if min or max (its a min)
𝑣_𝑜𝑝𝑡=(𝐵⁄𝐶)^(1/2)
𝐻_𝑜𝑝𝑡=𝐴+〖2(𝐵𝐶)〗^(1/2)
What do the diffusion equations describe
The diffusion equation describes Brownian motion for
a large number of particles
What are the names of k, k’, Dc and K
k is the retention factor (capacity factor), Dc is the concentration distribution coefficient, K is the distribution partition coefficient (Distributio coefficent)?
In which system GC or LC is longitudinal diffusion more important
GC
So for Eddy diffusion plate height which equation is used when and what are the terms
Hf is used when flow is the dominant mechanism, (Hf = 2lambda dp) and Hd is used when diffusion dominates w*dp^2 * v / Dm (solution diffusion coefficient)
What is plate height eddy proprtional to
lamba (column packing factor 0.5-1.5), dp, and velocity - inverely proprtional to diffusion of mobile phase (x is also in this dp is to 1+x, v to x and dm to x - x = 0 for GC 1/3 for LC) -
The effects of Dm and v as compared He to Hl
Opposite - Hl = 2dm/v He is 2 lamba dp V/dm
What happens if slow mass trasnfer time
lagging peaks
Knox eq
He (flow term) + Hl (packed) + Hm + Hs and can write it interms of v (so the He term which is a is v ^1/3 , the B term for longitudinal is B/v and the Mass transfer terms are x v (cm + cs)*v
Which tings go up and down for which terms in van deemter (for v, D, dp, df (thickness off stationary) and k)
v - goes down Hl up for everything else (unless He is flow in which its independent)
D - up for Hl down for everything else
dpup for everything
df (up for Hs)
k - up for Hm down for Hs
In rate theory of bandbroadening - we ca new sum up all of these lplateheights
necause they are all our variancces and can be summed up
optimal velocity van deemter
ROOT(B/c)
Simplified van deemter equation
Htot - A +B/V +Cv
H opt
A + 2(BC)^1/2
Summary of band broadening
Smaller particle for packed column,
smaller diameter for open column,
low temp and high flow rate to reduce longitudinal diffusion,
A lot of separation ran higher than optimal flow rate so C term is significant
What are things in the Hs term
k, qs (shape factor 2.3 for thin layer on support), df - thickness of stationary, Ds - diffusion in stationary )inverse with Ds
Things in hm term
k, dp, v and dm (inverse
What is x in He and what does it depend on
0 for Gc, 1/3 for LC
What is W in moleular transport with flow
W is the sum of uint, uext and v from flow
physical interp of transport equation
so our equation is J = -W(Dc/dc) + D Dc^2/dx^2 so J or dc/dt is proprtional to -W(dc/dx) which makes sense
What does J =
dc/dt, ; N/(YZdt)); Ddc/dx; UC + (1/f)Ddc/dx
Why use a packed column isntead of a stationary columns and how does that effect the column dimensions
So in an open column - a solute is far from the stationary phase and interaction really depends on distance SO - for this open columns you need to make their diameters really small (also as a means of increasing relative Vs) For a packed column however, not necessarily the case - this everywhere - as such larger diameter - and has higher sample capacity then for potentially an equivalent Vs
What are poise units
g/(cms) or (Newtons )/m^2 or Pas (so a Pa is Newton/m^2) (newton is kgm / s^2) WATCH OUT FOR PROBLEM S TO MAKE SURE OTHER UNITS the same - like for Reynauds everything g/cm etc BUT in stokes radius - have Kb so every thing needs to be in Nm (so you would convert other numbers to match meters)
How to solve lengthening resolution problem
Rs /Rs = ROOT(N)/ROOT(N) so the first root N is the more retained - and then you KEEP THE SAME H from previous then h=l/n get new L
What causes a langmuir isotherm -
Saturation of solid phase so at higher concentration an unexpected amount remains in mobile phase and goes faster
How does anti-langmuir occur
Solute solute interactions strong - so as concentration increase - as more goes into stationary phase - actually creates a mixed phase that allows increased solubility of the solute so more go into the stationary phase than expected to slower than expected. Can also occur in GC if over inject (more concentration than can be possibly vaporized some stays in liquid phase in the stationary phase
spontaneous process (G and S
G negative, S positive(at least balanced by H
Limits on stokes law
In the limit of low Reynolds number, the mobility μ is the
inverse of the drag coefficient ζ. For spherical particles only of
radius r, Stokes’ law gives
When we are calculating mean displacement of a collision what do we assume
assume v0 is 0 so all of the force is from acceleration and friction
Why is diffusion in liquids slower
density and high chance of reactions between the solvents
What is step 2 of getting the stdev of random walk
N(ql^2 + (1-q)l^2 - triangebrack(x)^2)
How do we go from stdev of random walk to Plate column efficiency
assume q = 0.5 - then stdev simplifies into variance = Nl^2
dG for closed system
0
closed system dG equ
dG< PdV - SdT
What is the K used for lle and the like (
K distribution coefficient
in an overall closed system what’s true about uB and ua
need to equal each other (overall change in gibbs must be 0
Delta H in a partition between two liquids
For general separation system involving a partition of
components between phases
Intermolecular interactions
dominate
so H should be greater than S*Delta T
relation between N and N eff
Neff = N *(k/1+k)^2
What is H useful for in chormatogrpahy
H is useful in comparing the efficiencies of different sized columns
or different support materials.
* It is also heavily used in chromatography theory to relate various
chromatographic parameters to the kinetic processes occurring in
the column
H in terms of X and tr
H = XW^2/16tr^2
Estimatino for peak capacity assumes what
Rs = 1
how flow relates to V
flow = P/R
void volume/total column volume
For most porous supports, εtot ~ 0.8 (i.e., in average 80% of the
column is occupied by mobile phase and 20% by the solid support
bo for open tube
R^2 /8
EP vs EE
EP is intra particle, EE is interparticle
konzeny carman issues
really only works for irregular packing - typically produces a Bo greater than actual
u
1/zeta *wierd fric)
Molecular transport is written in what quanttity
molar (all of the terms are MOLAR terms - eg f is molar friction, M is one mole of substance, du dx is effective force per mole
What is Hd and Hf
2 lamba dp and wdp^2*v/Dm
what is lamba
column pakcing factor .5-1.5
x what is
system constnat (0 for gc 1/3 for lc
what is qc for a thin layer support
2/3
Different van deemter forms for GC and LC
Van deemter A + B/V + C *V is GC (longitudinal form) then the LC form is knox (and the Z is Z *V^1/3 assuming max gamma
What are the A B and C terms in van deemter
A is EDDY diffusion, B is longitudinal and C is mass trasnfer
Units for diffusion
cm/s^2
Units needed for solving for J *U int, uext etc
kg/m*s mL
Units of reynolds flow rate
mL(?)/sec!
packed gc column use gamma
yes for HL
how to do transient time calc
so its m/f However the M can be in u or daltons and this is taken care of because f is already molar (so if have zeta need to multiply it by avogadors - if have f - stay the same)
