SME
Analytical Chemistry · Problem type
Plates needed for a resolution
Use this for “Two compounds have α = 1.08 and k₂ = 3.2 on a column. How many plates give a resolution of 1.5?”
Table
Plates (N)
Resolution (R)
This is an example. Type your own values to start a new problem.
R
=
N
4
×
−
1
α
×
k₂
1
+
Formulas
R
=
√
N
4
×
α
− 1
α
×
k₂
1 +
k₂
1.88
=
√
4,900
4
×
1.15 − 1
1.15
×
4.6
1 + 4.6
Assumptions
•
Purnell: R = (√N ÷ 4) × ((α − 1) ÷ α) × (k₂ ÷ (1 + k₂)), with N the plates, α the selectivity and k₂ the later peak’s retention factor.
•
R grows with √N: four times the plates (a column four times as long) doubles the resolution.
•
A selectivity close to 1 is the hardest to fix with plates, since (α − 1) ÷ α is then small.
Step-by-step
WE KNOW
N = 4,900, α = 1.15, k₂ = 4.6
FIND
resolution (R)
Step 1 · Find resolution (R)
Use R = √N ÷ 4 × (α − 1) ÷ α × k₂ ÷ (1 + k₂)
Multiply
the
three
terms:
efficiency
√
N
4,
selectivity
α
− 1
α
and
retention
k₂
1 +
k₂
.
R
=
√
4,900
4
×
1.15 − 1
1.15
×
4.6
1 + 4.6
R
=
√
4,900
4
×
0.15
1.15
×
4.6
5.6
R
=
70
4
×
0.15
1.15
×
4.6
5.6
R
=
17.5
×
0.15
1.15
×
4.6
5.6
R
=
2.625
1.15
×
4.6
5.6
R
=
2.283
×
4.6
5.6
R
=
10.5018
5.6
R
=
1.88
→
R
≥
1.5:
baseline
separation.
Check
Put the numbers back in. Both sides should match.
1.88
=
√
4,900
4
×
1.15 − 1
1.15
×
4.6
1 + 4.6
✓
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