Math Problem Statement
A chromatographic procedure separates 4.0 mg of unknown mixture on a column with a length of 40 cm and a diameter of 0.85 cm. What size column would you use to separate 100 mg of the same mixture? column diameter = blank1 - Numeric Answer
cm If the flow rate on the original column is 0.22 mL/min, what flow rate should be used on the larger column? flow rate = blank2 - Numeric Answer
mL/min
Solution
To determine the column diameter and flow rate for the larger column:
Step 1: Scale the Column Diameter
Chromatographic separations scale proportionally with the column's cross-sectional area to handle a larger sample. The cross-sectional area is proportional to the square of the column diameter. The ratio of the sample masses gives the required ratio of the areas.
For a column with a circular cross-section:
So, the ratio of diameters to is given by:
Substituting the values:
Answer for Diameter:
Step 2: Scale the Flow Rate
The flow rate scales proportionally to the column cross-sectional area. This means:
Since:
The new flow rate is:
Answer for Flow Rate:
Summary:
- Column Diameter:
- Flow Rate:
Let me know if you need a detailed explanation of the calculations!
Related Questions:
- What is the relationship between column diameter and sample capacity in chromatography?
- How does flow rate affect chromatographic resolution?
- What other factors should be considered when scaling up chromatography columns?
- Why does cross-sectional area play such a crucial role in chromatographic scaling?
- Can the same separation efficiency be maintained when scaling up a chromatographic column?
Tip: Always verify that the separation efficiency is preserved when scaling up chromatography, as larger columns might require adjustments in packing material or other parameters.
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Math Problem Analysis
Mathematical Concepts
Proportional Scaling
Area of a Circle
Flow Rate Scaling
Formulas
Area = π(d/2)^2
(d2^2) / (d1^2) = (Mass2 / Mass1)
(Flow Rate2) / (Flow Rate1) = (Area2 / Area1)
Theorems
Scaling of Chromatographic Columns
Suitable Grade Level
Grades 11-12
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