**Part (a) Number of Stages at Total Reflux (NTR)**

To determine the number of stages at total reflux (NTR), we can use the Fenske-Schmidt equation:

```
ln(x_D/x_F) = NTR * ln(α)
```

where:

• x_D is the mole fraction of LK in the distillate (0.75) • x_F is the mole fraction of LK in the feed (0.6) • α is the relative volatility of LK to HK (α_LK/α_HK = 4/1 = 4)

Plugging in the values, we get:

```
ln(0.75/0.6) = NTR * ln(4)
```

Solving for NTR, we get:

```
NTR = 1.08
```

This means that at total reflux, we need 1.08 stages to achieve the desired separation.

**Part (b) Minimum Reflux Ratio (R_min)**

To determine the minimum reflux ratio (R_min), we can use the Underwood equation:

```
R_min = (q - qD)/(xD - xB)
```

where:

• q is the molar flow rate of the feed (100 kmol/h) • qD is the molar flow rate of the distillate (qD = L * xD, where L is the molar flow rate of the reflux) • xB is the mole fraction of LK in the bottoms (xB = 0)

Since we want to recover 99.5% of the LK in the distillate, we can calculate qD as follows:

```
qD = (0.995)(0.6)(100 kmol/h) = 59.7 kmol/h
```

Plugging in the values, we get:

```
R_min = (100 kmol/h - 59.7 kmol/h)/(0.75 - 0)
```

Solving for R_min, we get:

```
R_min = 1.19
```

This means that the minimum reflux ratio required to achieve the desired separation is 1.19.

**Part (c) Actual Number of Stages and Feed Stage Location**

To determine the actual number of stages (N) and the feed stage location (N_F), we can use the Gilliland correlation:

```
N = NTR + (NTR - 1) / (R_actual - R_min)
```

where:

• R_actual is the actual reflux ratio (R_actual = 1.2 * R_min = 1.43)

Plugging in the values, we get:

```
N = 1.08 + (1.08 - 1) / (1.43 - 1.19)
```

Solving for N, we get:

```
N = 1.78
```

Since we cannot have a fraction of a stage, we round up to 2 stages. Therefore, the actual number of stages required is 2.

The feed stage location can be determined using the following equation:

```
N_F = N + (x_F - x_D)/(xD - xB)
```

Plugging in the values, we get:

```
N_F = 2 + (0.6 - 0.75)/(0.75 - 0)
```

Solving for N_F, we get:

```
N_F = 1.25
```

Since we cannot have a fraction of a stage, we round up to 2 stages. Therefore, the feed stage location is at stage number 2.

**Conclusion**

To design the distillation column so that it can recover 99.5% of the LK in the distillate with a mole fraction of 0.75 in the distillate, we need 2 actual stages with a feed stage location at stage number 2. The minimum reflux ratio required is 1.19, and the actual reflux ratio is 1.43.