(a)
Interpretation:
The optimal velocity is to be stated.
Concept introduction:
The Van Deemeter equation relates the HPLC plate height and velocity of plate. The Van Deemeter equation is as follows.
Here, the HPLC height is
Answer to Problem 28.23QAP
The optimal velocity of HPLC plate is
Explanation of Solution
Differentiate Equation (I) with respect to plate velocity.
Substitute
(b)
Interpretation:
The minimum plate height is to be stated.
Concept introduction:
The Van Deemeter equation relates the HPLC plate height and velocity of plate. The Van Deemeter equation is as follows.
The relation between HPLC height is inversely proportional to plate velocity. So minimum height is obtained corresponding to optimal velocity in the Van Deemeter equation.
Answer to Problem 28.23QAP
The minimum plate height is
Explanation of Solution
Substitute
(c)
Interpretation:
The optimal velocity and minimum height of plate in terms of the diffusion coefficient in mobile phase, particle size and dimensional analysis is to be stated.
Concept introduction:
The mass transfer coefficient relates the particle size and diffusion coefficient in mobile phase. The diffusion coefficient relates the dimensional constant and diffusion coefficient in mobile phase.
Answer to Problem 28.23QAP
The optimal velocity is
Explanation of Solution
Write the expression for mass transfer coefficient in mobile phase.
Here, the diffusion coefficient in mobile phase is
Write the expression for diffusion coefficient.
Here, the dimensional coefficient is
Write the expression for optimal velocity in mobile phase.
Write the expression for minimum height in mobile phase.
Substitute
Substitute
(d)
Interpretation:
The optimal velocity and minimum height of plate at unity order for dimensional constants.
Concept introduction:
The mass transfer coefficient relates the particle size and diffusion coefficient in mobile phase. The diffusion coefficient relates the dimensional constant and diffusion coefficient in mobile phase.
Answer to Problem 28.23QAP
The optimal velocity is
Explanation of Solution
Write the expression for optimal velocity in terms of dimensional constants.
Substitute
Write the expression for plate height in terms of dimensional constants.
Substitute
(e)
Interpretation:
The preceding conditions for reduced plate height to one third, the optimal velocity in these conditions and effect on number of theoretical plates is to be stated.
Concept introduction:
The plate height and number of theoretical plates directly depends on the particle size and optimal velocity inversely depends on particle size.
Answer to Problem 28.23QAP
For one third reduction in particle size the plate height is reduced to one third. The optimal velocity becomes
Explanation of Solution
Write the expression for plate height.
Here, the initial plate height is
Substitute
The particle size is also reduced to one third to initial particle size for one third reduction in the plate height.
The optimal velocity is inversely proportional to the particle size, so optimal velocity become
Write the expression for number of theoretical plates.
From the above equation it is clear that number of theoretical plates reduced to one third to initial number of theoretical plates.
(f)
Interpretation:
The condition to reduce the plate height to one third without reducing the number of theoretical plates is to be stated.
Concept introduction:
The number of theoretical plates directly depends on the height of the plate and inversely to the column length.
Answer to Problem 28.23QAP
The column length is also reduced to one third with plate height to maintain same number of theoretical plates.
Explanation of Solution
Write the expression for number of theoretical plate with one third reduced plate height
To maintain the same number of theoretical plate length of column also be reduced to one third. We have to substitute
(g)
Interpretation:
The two sources of band broadening which also contribute to overall width of HPLC peaks is to be stated.
Concept introduction:
The band broadening is defined as the reduction in separation of solute molecules in the column. This also reduces the quality and accuracy of the separation. The band broadening occurs due to longitudinal movement of particles in the column.
Answer to Problem 28.23QAP
The two sources of band broadening which also contribute to overall width of HPLC peaks are diameter of the particles and diffusion coefficient in mobile phase.
Explanation of Solution
The band broadening is the measure of column efficiency. It is inversely proportional to the mass transfer coefficient. If the mass transfer is slow in the column then wide band is obtained and narrow band is obtained when the mass transfer in the column is high. The sources of extra column band broadening which contributes to overall width of liquid chromatography peaks are following.
(1) The diameter of particles in column.
(2) The diffusion coefficient of mobile phase.
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Chapter 28 Solutions
Principles of Instrumental Analysis
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