Quantitative Chemical Analysis
Quantitative Chemical Analysis
9th Edition
ISBN: 9781464135385
Author: Daniel C. Harris
Publisher: W. H. Freeman
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Chapter 25, Problem 25.13P

(a)

Interpretation Introduction

Interpretation:

The plate number has to be calculated for the two peaks given in the chromatogram.

(a)

Expert Solution
Check Mark

Explanation of Solution

For L-enantiomer:

Retention time ( tr ) for L-enantiomer is given as 4.70min .

Half-width is given as 0.28min .

The relation between plate number, retention time and half-width is given as,

N = 5.54(trw1/2)2

Plate number can be calculated as shown below,

N = 5.54×tr2w1/22 = 5.54×(4.70)2(0.28)2 = 5.54×22.090.0784 = 5.54×281.76 = 1560.95 = 1561

The plate number is calculated as 1561 for L-enantiomer.

For D-enantiomer:

Retention time ( tr ) for L-enantiomer is given as 5.37min .

Half-width is given as 0.35min .

The relation between plate number, retention time and half-width is given as,

N = 5.54(trw1/2)2

Plate number can be calculated as shown below,

N = 5.54×tr2w1/22 = 5.54×(5.37)2(0.35)2 = 5.54×28.83690.1225 = 5.54×235.40 = 1304.11 = 1304

The plate number is calculated as 1304 for D-enantiomer.

(b)

Interpretation Introduction

Interpretation:

The resolution has to be calculated for the two peaks given in the chromatogram.

(b)

Expert Solution
Check Mark

Explanation of Solution

Retention time ( tr ) for L-enantiomer is given as 4.70min .

Retention time ( tr ) for L-enantiomer is given as 5.37min .

Half-width for L-enantiomer is given as 0.28min and therefore width is equal to 0.56min .

Half-width for D-enantiomer is given as 0.35min and therefore width is equal to 0.70min .

The resolution can be calculated using the formula as given below,

Resolution = (tr)D(tr)L(WD+WL)/2 = 5.374.70(0.56+0.70)/2 = 0.67(1.26)/2 = 0.670.63 = 1.06

(c)

Interpretation Introduction

Interpretation:

The resolution has to be predicted for the average plate number in the chromatogram.

(c)

Expert Solution
Check Mark

Explanation of Solution

Retention time ( tr ) for L-enantiomer is given as 4.70min .

Retention time ( tr ) for L-enantiomer is given as 5.37min .

tm is given as 1.62min .

The average plate number for the D-enantiomer and L-enantiomer can be calculated as shown below,

Average plate number = 1561+13042 = 28652 = 1432

Retention factor can be calculated as shown below,

k = trtmtm = 5.371.621.62 = 3.751.62 = 2.31

Relative retention is calculated as shown below,

α = 5.37min4.70min = 1.142

The resolution can be calculated using the formula as given below,

Resolution = N4×α1α×(k1+k)

Where,

N is the plate number

α is the relative retention

k is the retention factor

Resolution = 14324×1.14211.142×(2.311+2.31) = 37.844×0.1421.142×(2.313.31) = 9.46×0.124×0.697 = 0.817

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