Plate number and plate height concepts MCQs With Answer

Introduction: This set of MCQs on plate number and plate height concepts is designed for M.Pharm students studying Advanced Instrumental Analysis (MPA 201T). The questions emphasize both theoretical understanding and practical calculation of chromatographic efficiency — including relationships between plate number (N), plate height (H), retention time, peak width (base and half-height), and the Van Deemter contributions (A, B, C terms). You will encounter calculation-based items, interpretation of chromatograms, and conceptual scenarios involving packed and open-tubular columns, particle size effects, extra-column broadening, and reduced parameters. Use these MCQs to test and reinforce your ability to evaluate and optimize column performance for pharmaceutical separations.

Q1. Which expression correctly relates plate number (N) to retention time (tR) and peak width at baseline (w) for a Gaussian peak?

• N = 16 (tR / w)^2
• N = 5.54 (tR / w)^2
• N = 16 (tR / w1/2)^2
• N = 5.54 (tR / w1/2)^2

Correct Answer: N = 16 (tR / w)^2

Q2. Plate height (H) for a column of length L with plate number N is given by which formula?

• H = N / L
• H = L / N
• H = sqrt(LN)
• H = L * N

Correct Answer: H = L / N

Q3. For a chromatographic peak with retention time 5.00 min and width at half-height (w1/2) = 0.20 min, which expression gives the correct N using the half-height formula?

• N = 5.54 (tR / w1/2)^2
• N = 16 (tR / w1/2)^2
• N = 5.54 (tR / w)^2
• N = 16 (tR / w)^2

Correct Answer: N = 5.54 (tR / w1/2)^2

Q4. Which parameter most directly decreases the plate height (H) in a packed column operated in the kinetic regime (controlled by mass transfer resistance)?

• Increasing particle diameter (dp)
• Reducing mobile phase linear velocity
• Decreasing particle diameter (dp)
• Increasing extra-column dead volume

Correct Answer: Decreasing particle diameter (dp)

Q5. The Van Deemter equation H = A + B/u + C*u contains terms A, B, and C. What physical process does the B/u term represent?

• Eddy diffusion (multiple flow paths)
• Longitudinal diffusion
• Mass transfer resistance in stationary phase
• Extra-column dispersion

Correct Answer: Longitudinal diffusion

Q6. Reduced plate height (h) is defined as H/dp where dp is particle diameter. What is the primary advantage of reporting h instead of H?

• Removes dependence on column length
• Normalizes efficiency for different particle sizes
• Eliminates effects of retention time
• Directly gives resolution between peaks

Correct Answer: Normalizes efficiency for different particle sizes

Q7. If two identical columns are connected in series, how does the overall plate number N_total compare to the plate number of a single column N_single?

• N_total = N_single (no change)
• N_total = 2 * N_single
• N_total = N_single / 2
• N_total = sqrt(2) * N_single

Correct Answer: N_total = 2 * N_single

Q8. A chromatogram shows a peak with tR = 10.0 min and baseline width w = 0.50 min. Calculate N using the correct baseline formula (no calculation required here; choose the correct numeric form result).

• N = 16 (10.0 / 0.50)^2 = 16 * 20^2 = 6400
• N = 16 (10.0 / 0.50)^2 = 16 * 10^2 = 1600
• N = 5.54 (10.0 / 0.50)^2 = 5.54 * 20^2 = 2216
• N = 5.54 (10.0 / 0.50)^2 = 5.54 * 10^2 = 554

Correct Answer: N = 16 (10.0 / 0.50)^2 = 16 * 20^2 = 6400

Q9. Which change will most likely shift the Van Deemter minimum to a higher linear velocity for a given column?

• Decrease diffusion coefficient of analyte (Dm)
• Use smaller particle size (dp)
• Increase mobile phase viscosity with temperature drop
• Decrease stationary phase film thickness

Correct Answer: Use smaller particle size (dp)

Q10. Extra-column broadening contributes to observed peak width. Which strategy will reduce extra-column peak broadening most effectively?

• Use longer transfer tubing with larger internal diameter
• Place detector further from the column outlet
• Minimize injector-to-column and column-to-detector dead volumes
• Use higher injection volumes at the same concentration

Correct Answer: Minimize injector-to-column and column-to-detector dead volumes

Q11. For an open tubular (capillary) GC column compared to a packed column of same length, which statement about H is generally true?

• H is typically larger for capillary columns because of wall effects
• H is typically smaller for capillary columns due to absence of eddy diffusion
• H is identical for both column types when particle size is scaled
• H only depends on gas velocity and not on column type

Correct Answer: H is typically smaller for capillary columns due to absence of eddy diffusion

Q12. Which experimental observable will directly decrease when the plate number N increases for a fixed column length?

• Retention time (tR) of a compound
• Peak width (w) of a compound
• Column dead volume
• Mobile phase viscosity

Correct Answer: Peak width (w) of a compound

Q13. The reduced linear velocity v is defined as u*dp/Dm (where u is linear velocity). Which use of reduced parameters is correct?

• They change with column length but not with particle size
• They allow comparison of column behavior across different particle sizes and mobile phases
• They are only useful for gas chromatographic systems
• They eliminate the need for Van Deemter analysis

Correct Answer: They allow comparison of column behavior across different particle sizes and mobile phases

Q14. Given two peaks with identical tR but one has twice the baseline width of the other, how does their plate number N compare?

• The broader peak has four times higher N
• The broader peak has half the N
• The broader peak has one-quarter the N
• The plate numbers are identical

Correct Answer: The broader peak has one-quarter the N

Q15. In chromatography, which effect is NOT a contributor to the Van Deemter C-term (mass transfer resistance)?

• Diffusion into and out of stationary phase particles
• Resistance due to finite film thickness of stationary phase
• Longitudinal molecular diffusion in mobile phase
• Resistance to mass exchange between mobile and stationary phases

Correct Answer: Longitudinal molecular diffusion in mobile phase

Q16. You measure peak width at half-height w1/2 = 0.10 min and retention time tR = 2.00 min. Which numeric N corresponds to the half-height formula?

• N = 5.54 (2.00 / 0.10)^2 = 5.54 * 20^2 = 2216
• N = 16 (2.00 / 0.10)^2 = 16 * 20^2 = 6400
• N = 5.54 (2.00 / 0.10)^2 = 5.54 * 10^2 = 554
• N = 16 (2.00 / 0.10)^2 = 16 * 10^2 = 1600

Correct Answer: N = 5.54 (2.00 / 0.10)^2 = 5.54 * 20^2 = 2216

Q17. Which change will most directly reduce the A-term (eddy diffusion) in a packed HPLC column?

• Use a more uniformly packed stationary phase with smaller, monodisperse particles
• Increase mobile phase temperature
• Use larger-diameter particles with wide size distribution
• Increase flow rate to very high velocities

Correct Answer: Use a more uniformly packed stationary phase with smaller, monodisperse particles

Q18. If observed plate height H_obs is larger than theoretical H_col (column contribution), what is the most plausible explanation?

• There is significant extra-column broadening adding to observed H
• The column length was measured incorrectly, but extra-column effects are negligible
• The analyte diffusion coefficient is infinite
• The instrument detector has zero contribution to band broadening

Correct Answer: There is significant extra-column broadening adding to observed H

Q19. Resolution (Rs) between two peaks depends on N, selectivity (α) and retention factor (k). If N is increased fourfold while k and α remain constant, how does Rs change approximately?

• Rs doubles (increases by factor of 2)
• Rs increases by factor of 4
• Rs decreases by factor of 2
• Rs remains unchanged

Correct Answer: Rs doubles (increases by factor of 2)

Q20. In high-efficiency UHPLC systems using sub-2 μm particles, which practical limitation often prevents realizing the theoretical very low H values?

• Excessively low backpressure
• Insignificant extra-column volumes that sharpen peaks
• Instrumental dispersion and extra-column broadening
• Unchanged Van Deemter A-term dominance

Correct Answer: Instrumental dispersion and extra-column broadening

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