We can analyze the chromatography experiment based on the provided data. Here's the step-by-step breakdown:

1. Dead Time ($t_m$)

The dead time, $t_m$, is the time the solvent takes to elute, which is given as 16.5 seconds.

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2. Capacity Factor ($k'$)

The capacity factor for each compound is calculated using: $k' = \frac{t_r - t_m}{t_m}$ where $t_r$ is the retention time (elution time).

• For Compound 1: $k'_1 = \frac{120 - 16.5}{16.5} \approx 6.27$

• For Compound 2: $k'_2 = \frac{225 - 16.5}{16.5} \approx 12.64$

• For Compound 3: $k'_3 = \frac{310 - 16.5}{16.5} \approx 17.76$

• For Compound 4: $k'_4 = \frac{608 - 16.5}{16.5} \approx 36.85$

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3. Column Efficiency (Number of Theoretical Plates, $N$)

The number of theoretical plates is calculated using: $N = 16 \left(\frac{t_r}{w_b}\right)^2$ where $w_b$ is the peak width at the base.

• For Compound 1: $N_1 = 16 \left(\frac{120}{28}\right)^2 \approx 2943$

• For Compound 2: $N_2 = 16 \left(\frac{225}{70}\right)^2 \approx 1652$

• For Compound 3: $N_3 = 16 \left(\frac{310}{55}\right)^2 \approx 5072$

• For Compound 4: $N_4 = 16 \left(\frac{608}{98}\right)^2 \approx 6107$

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4. Selectivity ($\alpha$)

The selectivity is calculated for consecutive peaks as: $\alpha = \frac{k'_2}{k'_1}, \frac{k'_3}{k'_2}, \frac{k'_4}{k'_3}$

• Between Compound 1 and 2: $\alpha_{1,2} = \frac{12.64}{6.27} \approx 2.01$

• Between Compound 2 and 3: $\alpha_{2,3} = \frac{17.76}{12.64} \approx 1.41$

• Between Compound 3 and 4: $\alpha_{3,4} = \frac{36.85}{17.76} \approx 2.07$

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5. Resolution ($R_s$)

The resolution between peaks is calculated as: $R_s = \frac{\Delta t_r}{w_b}$ where $\Delta t_r$ is the difference in retention times between adjacent compounds, and $w_b$ is the average of the two base widths.

• Between Compound 1 and 2: $R_{s,1,2} = \frac{225 - 120}{\frac{28 + 70}{2}} = \frac{105}{49} \approx 2.14$

• Between Compound 2 and 3: $R_{s,2,3} = \frac{310 - 225}{\frac{70 + 55}{2}} = \frac{85}{62.5} \approx 1.36$

• Between Compound 3 and 4: $R_{s,3,4} = \frac{608 - 310}{\frac{55 + 98}{2}} = \frac{298}{76.5} \approx 3.89$

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6. Peak Asymmetry (Optional)

If peak asymmetry data is needed, it would require additional information about the peak tailing factor.

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Summary of Key Results:

• $k'$ values: $6.27, 12.64, 17.76, 36.85$
• $N$ values: $2943, 1652, 5072, 6107$
• $\alpha$ values: $2.01, 1.41, 2.07$
• $R_s$ values: $2.14, 1.36, 3.89$

Would you like detailed steps for any calculation, or additional analysis such as peak areas or interpretation of chromatographic performance?

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5 Questions for Deeper Exploration:

1. How does the selectivity $\alpha$ influence the separation efficiency of the column?
2. Why might Compound 2 have the lowest number of theoretical plates?
3. Can we infer anything about the polarity of the compounds from their retention times?
4. How would increasing the flow rate impact the resolution of the peaks?
5. What other factors can affect the column efficiency in this experiment?

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Tip:

Always ensure the column's performance metrics (like $N$, $R_s$) meet the method's validation criteria to maintain accurate and reproducible separations.