To determine the reflux-to-distillate ratio in the distillation column, we will apply the concepts of relative volatility and the McCabe-Thiele method for ideal trays and constant molal overflow. Here are the steps involved:
- The relative volatility \( (\alpha) \) of component A with respect to B is given as 2. This value indicates how easily A will separate from B in the vapor phase.
- The steady-state compositions of A in the vapor phase leaving the first, second, and third trays are 94%, 90%, and 85%, respectively.
- These compositions can be represented as mole fractions:
- The vapor leaving the first tray, \(y_1 = 0.94\)
- The vapor leaving the second tray, \(y_2 = 0.90\)
- The vapor leaving the third tray, \(y_3 = 0.85\)
- Using relative volatility, the equilibrium relationship for each tray can be represented as: \(y = \frac{\alpha x}{1 + (\alpha - 1)x}\)
- We can determine the liquid composition leaving each tray using the relationship: \(x_i = \frac{y_i}{\alpha - (\alpha - 1)y_i}\)
- For tray 1: \( x_1 = \frac{0.94}{2 - (2 - 1) \times 0.94} = 0.87 \)
- For tray 2: \( x_2 = \frac{0.90}{2 - (2 - 1) \times 0.90} = 0.82 \)
- For tray 3: \( x_3 = \frac{0.85}{2 - (2 - 1) \times 0.85} = 0.76 \)
- The operating line for the rectifying section is given by: \(y = \frac{L}{L + D}x + \frac{D}{L + D}x_D\)where \( L \) is the reflux rate and \( D \) is the distillate rate.
- The slope of the operating line is equal to the reflux ratio: \(R = \frac{L}{D}\)
- Using the compositions found above (from trays),
- The line passes through these points: \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\).
- From these points, an average slope can be determined, and hence the reflux ratio is approximately calculated as 2.7.
Therefore, the reflux-to-distillate ratio is determined to be 2.7. This matches with the correct option
| Option | Reflux Ratio |
| 1 | 1.9 |
| 2 | 2.7 |
| 3 | 1.2 |
| 4 | 1.1 |
Important Questions from Distillation
A binary mixture of butane and butadiene is to be separated in an extractive distillation using furfural. Furfural lowers the activity of butadiene more than it does for butane. Consider the distillation sequence shown in the figure.
Match the component labels in Group I with chemical species in Group II.
Group I Group II P. Component X 1. Butane Q. Component Y 2. Butadiene R. Component Z 3. Furfural A continuous distillation column is used to separate an equimolar mixture of diethylamine (DEA) and methanol. The feed enters the column as saturated liquid at a flow rate of $30 \text{ mol s}^{-1}$. It is desired to obtain $92 \text{ mol}\%$ DEA as distillate. The rate of withdrawal of the distillate from the column is $10 \text{ mol s}^{-1}$. The equilibrium curve for the conditions in the column is given below. The latent heat of vaporization of the reboiler contents is $35 \text{ kJ mol}^{-1}$. Neglect heat loss to the surroundings and assume constant molal overflow. Which one of the following is the minimum reboiler heat duty (in kW)?
- A binary AB liquid mixture containing 30 mol% A is subjected to differential (Rayleigh) distillation at atmospheric pressure in order to recover 60 mol% A in the distillate. Assuming a constant relative volatility $ \alpha_{AB} = 2.2 $, the average composition of the collected distillate is _______ mol% A (rounded off to nearest integer).
- Identify the WRONG statement amongst the following:
A binary feed consisting of $25$ mol% liquid and $75$ mol% vapour is separated in a staged distillation column. The mole fraction of the more volatile component in the distillate product is $0.95$. The molar flow rate of distillate is $50$% of the feed flow rate and the McCabe-Thiele method can be used to analyze the column. The q-line intersects the operating line of the enriching section at $(0.35, 0.5)$ on the x-y diagram. The slope of the stripping section operating line (up to one decimal place) is ____________
