A binary distillation column is operating with a mixed feed containing 20 mol% vapour. If the feed quality is changed to 80 mol% vapour, the change in the slope of the q-line is __________________
Understanding the q-line Slope in Distillation
The q-line represents the feed condition in a binary distillation column. Its slope is determined by the feed quality, specifically the fraction of liquid in the feed.
The parameter 'q' is defined as the fraction of liquid in the feed stream.
The slope of the q-line ($m_q$) is given by the formula:
$m_q = \frac{q}{q-1}$Calculating Initial q-line Slope
The initial feed condition is 20 mol% vapour. This means the feed is 80% liquid.
- Initial liquid fraction, $q_1 = 0.80$
- Initial slope, $m_{q1} = \frac{q_1}{q_1 - 1} = \frac{0.80}{0.80 - 1} = \frac{0.80}{-0.20} = -4.0$
Calculating Final q-line Slope
The feed quality is changed to 80 mol% vapour. This means the feed is now 20% liquid.
- Final liquid fraction, $q_2 = 0.20$
- Final slope, $m_{q2} = \frac{q_2}{q_2 - 1} = \frac{0.20}{0.20 - 1} = \frac{0.20}{-0.80} = -0.25$
Determining the Change in q-line Slope
The change in the slope is the final slope minus the initial slope.
- Change in slope, $\Delta m_q = m_{q2} - m_{q1}$
- $\Delta m_q = (-0.25) - (-4.0)$
- $\Delta m_q = -0.25 + 4.0 = 3.75$
The change in the slope of the q-line is 3.75.
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 ____________
