## Question:

A. What is the linear velocity in cm/sec?

B. What are the k values for heptane and ethyl acetate?

C. What is the \alpha value for the ethyl acetate-heptane pair?

D. What is the resolution between heptane and ethyl acetate using the values for the retention times and peak widths?

E. What are the N and H (in mm) values for ethyl acetate (use the values for retention time and peak widths given on page 1)? Why is the H value that you calculated different from our approximation that under some conditions H = column diameter

F. What is the wt% of heptane and ethyl acetate in the sample using the normalization with response factor approach?

G. f we increase the temperature will the retention times for heptane and ethyl acetate increase or decrease

H. If we consider heptane to be the internal standard and its weight is 1 g and the sample weight is 10 g; calculate the wt% of ethyl acetate using the internal standard calculation.

I. What is the N value required to achieve a resolution of 1 between heptane and ethyl acetate?

J. What is the phase ratio of the column?Below you have 2 reports from isothermal chromatographic runs. The first, Run A, is for

methane, which is non retained and has a k value of 0 . The second, Run B, is for a mixture of

heptane and ethyl acetate. We previously determined that heptane has a relative response factor

of 1.00 and ethyl acetate has a relative response factor of 2.00 . The column used for this

analysis has a length of 25m, and an internal diameter of 0.25mm and a film thickness of 3.0

μm. Using the data in the two reports calculate the following

Run A

Run B

a) What is the linear velocity in cmsec ?

OR

Run A

Below you have 2 reports from isothermal chromatographic runs. The first, Run A, is for methane, which is non retained and has a k value of 0. The second, Run B, is for a mixture of heptane and ethyl acetate. We previously determined that heptane has a relative response factor of 1.00 and ethyl acetate has a relative response factor of 2.00. The column used for this analysis has a length of 25 m, and an internal diameter of 0.25 mm and a film thickness of 3.0 μm. Using the data in the two reports calculate the following

Component

Methane

Retention Time, seconds 100

Peak Width (seconds) 1.0

Peak Area

500

Run B

Component

Retention Time,

seconds

Baseline Peak Width (seconds)

Peak Area

Heptane

590

9

1000

Ethyl acetate

600

10

2000

a)

What is the linear velocity in cm/sec?

## ANSWER:

**A. What is the linear velocity in cm/sec?**

The linear velocity can be calculated using the following formula:

```
v = F / (πr² * 3.14159)
```

where:

- v is the linear velocity (cm/sec)
- F is the flow rate (cm³/sec)
- r is the radius of the column (cm)

The flow rate can be calculated using the following formula:

```
F = A / t
```

where:

- A is the peak area (arbitrary units)
- t is the retention time (seconds)

The radius of the column can be calculated using the following formula:

```
r = d/2
```

where:

- d is the inner diameter of the column (mm)

Plugging in the values, we get:

```
v = (500 / 100) / (π(0.25/2)² * 3.14159) = 3.3953 × 10^20 cm/sec
```

Therefore, the linear velocity is 3.3953 × 10^20 cm/sec.

**B. What are the k values for heptane and ethyl acetate?**

The k value for a compound is defined as the ratio of the time the compound spends in the stationary phase to the time it spends in the mobile phase. The k value can be calculated using the following formula:

```
k' = (t_R - t_M) / t_M
```

where:

- k’ is the adjusted retention factor
- t_R is the retention time (seconds)
- t_M is the dead time (seconds)

The dead time is the time it takes for a non-retained compound to pass through the column. It can be calculated using the following formula:

```
t_M = L / (F * v)
```

where:

- L is the length of the column (cm)

Plugging in the values for heptane, we get:

```
k' = (590 - 100) / 100 = 4.9
```

The k value for heptane is 4.9.

Plugging in the values for ethyl acetate, we get:

```
k' = (600 - 100) / 100 = 5.0
```

The k value for ethyl acetate is 5.0.

**C. What is the \alpha value for the ethyl acetate-heptane pair?**

The α value is the selectivity factor for two compounds. It is defined as the ratio of the k’ values for the two compounds. The α value can be calculated using the following formula:

```
α = k1' / k2'
```

where:

- α is the selectivity factor
- k1′ is the adjusted retention factor for the first compound
- k2′ is the adjusted retention factor for the second compound

Plugging in the values, we get:

```
α = 5.0 / 4.9 = 1.02
```

The α value for the ethyl acetate-heptane pair is 1.02.

**D. What is the resolution between heptane and ethyl acetate using the values for the retention times and peak widths?**

The resolution (Rs) is a measure of the separation between two peaks. It is defined as the difference between the retention times of the two peaks divided by the average peak width. The Rs can be calculated using the following formula:

```
Rs = 2(t_R2 - t_R1) / (w1 + w2)
```

where:

- Rs is the resolution
- t_R1 is the retention time of the first peak (seconds)
- t_R2 is the retention time of the second peak (seconds)
- w1 is the peak width of the first peak (seconds)
- w2 is the peak width of the second peak (seconds)

Plugging in the values, we get:

```
Rs = 2(600 - 590) / (10 + 9) = 0.20
```

The resolution between heptane and ethyl acetate is 0.20.

**E. What are the N and H (in mm) values for ethyl acetate (use the values for retention time and peak widths given on page 1)? Why is the H value that you calculated different from our approximation that under some conditions H = column diameter**