Advanced Separation Science Flashcards
What is the equation for Resolution?
Rs = 2(tᵣ₂ - tᵣ₁) / W₂ + W₁
What is the equation for k’?
k’ = tₛ / tₘ = (tᵣ - ₘ) / tₘ
What is k’?
k’ is the capacity factor
It is an experimental factor that is used to compare migration rates of solutes in columns.
The longer a component is retained by a column, the greater the capacity factor is.
Why is it useful to use k’?
It is useful for monitoring performance.
It is useful for working out how many column volumes of MP are needed to elute the analyte.
What is the selectivity factor α?
For a separation to occur, analytes must have different capacity factors.
The selectivity factor is the ratio of the capacity factors.
How can we calculate α?
α = k’₂ / k’₁
α = tₛ₂ / tₛ₁
What is another equation of the capacity factor k’?
k’ = nₛ / nₘ = CₛVₛ / CₘVₘ
What is the equation for the partition coefficient K?
k’ = K x (Vₛ / Vₘ)
As the ratio of phase volumes is constant for a given column and mobile phase, the capacity factor for any analyte is directly proportional to its partition equilibrium constant.
What is σ?
The standard deviation in length units
What is tau?
Standard deviation in time units
Tau = W/4
What is the equation for σ² (variance)?
σ² = 2Dt
D = diffusion coefficient
When does fronting occur?
From overloading the solute
What does tailing occur?
Small quantities of solute are retained more strongly than large quantities.
We can correct by masking strong adsorption sites on SP.
What is plate height?
The constant of proportionality between the variance (σ²) of the band, and the distance it has travelled.
What is the equation for plate height involving σ²?
H = σ² / x and H = σ² / L
x = distance solute has travelled
It is the measure of variance per unit length
What is efficiency, N?
For a solute emerging from a column of length L, the number of plates in the entire column, N, is the length divided by the plate height.
What is the equation for efficiency N?
N = L/H = Lx / σ² = L² / σ²
What is the van Deemter equation?
H = A + B/u + Cu
A = multiple flow paths
B/u = longitudinial diffusion
Cu = mass transfer/equilbiration time
How can the contribution of multiple flow paths be reduced?
Smaller stationary phase particles.
Multiple flow paths is absent in open tubular (capillary) columns
How can longitudinal diffusion be reduced?
Faster linear flow which reduces the amount of time spent on the column
What is mass transfer/equilibration time?
Finite time for analyte to equilibrate between the mobile and stationary phases
How can the mass transfer/equilibration time be reduced?
Decreasing the stationary phase thickness/column radius
Increase the temperature
What flow rate do we want to run a column at?
The flow rate which gives us the lowest value of H.
How does ln(k’) and k’ change with boiling point T for a homologous series of analytes?
ln(k’) scales with 1/T
k’ increases as the boiling point T increases
How does ln(k’) and k’ change for all analytes?
ln(k’) scales with 1/T
k’ decreases as T increases
What are two types of column?
Packed (with zeolite or alumina)
Open tubular (capillary)
What is the flow resistance in a packed column?
High
What is the flow resistance in an open tubular column?
Low
What is the length of a packed column?
2-3 metres
What is the length of an open tubular column?
15-100 metres
What is the phase ratio (vₛ / vₘ) for a packed column?
High
What is the phase ratio (vₛ / vₘ) for an open tubular column?
Low
What is the efficiency of a packed column?
Low
Due to high ‘A’ term (van Deemter equation) and short column
What is the efficiency of an open tubular column?
High
Can you overload a packed column?
No
Can you overload an open tubular column?
Yes, if too much analyte is injected.
What is eluent strength εᵒ?
The solvent adsorption energy, defined as 0 for pentane on bare silica
What happens has εᵒ increases?
Solutes elute more rapidly
In RP, less polar solvents have a higher εᵒ.
How does log k’ decrease with the volume fraction of the organic modifier (OM)?
It decreases linearly with volume fraction of organic modifier
What is the benefit of having non-porous silica?
The phase ratio (Vₛ/Vₘ) is much lower, and k’ decreases by a factor of 10-100.
Why does non-porous silica decrease k’?
The bonding can only occur on the external surface, instead of internal pores.
How fast is transverse diffusion in GC?
It is fast
How fast is transverse diffusion in LC?
It is slow
How does having a slow transverse diffusion rate impact H?
It decreases H
How does particle size impact plate height?
Large particles increase A (less uniform flow through the column)
Large particles increase C (takes longer to diffuse through the inner pores)
