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The composition of vapour entering a tray in a distillation column is 0.47. The average composition of the vapour leaving the tray is 0.53. The equilibrium composition of the vapour corresponding to the liquid leaving this tray is 0.52. All the compositions are expressed in mole fraction of the more volatile component.
The Murphree efficiency based on the vapour phase, rounded to the nearest integer, is ___ %
Correct answer is '120'. Can you explain this answer?
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The composition of vapour entering a tray in a distillation column is ...
Murphree efficiency is defined as the actual change in average composition accomplished by a given tray divided by the change in average composition. 
Where,
y1 = Average composition of vapour leaving the tray.
ye = Equilibrium composition of vapour corresponding to the liquid leaving the tray.
y = Composition of vapour entering the tray.
y1 = Average composition of vapour leaving the tray.
ye = Equilibrium composition of vapour corresponding to the liquid leaving the tray.
y = Composition of vapour entering the tray.
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The composition of vapour entering a tray in a distillation column is ...
Given information:
- Composition of vapour entering tray = 0.47
- Average composition of vapour leaving tray = 0.53
- Equilibrium composition of vapour corresponding to liquid leaving tray = 0.52
To find:
- Murphree efficiency based on the vapour phase
Solution:
1. Calculate the minimum number of theoretical trays needed for this separation using the Fenske equation:
Nmin = log((xD-yD)/(xD-yF))/log(α)
where:
xD = composition of the more volatile component in the distillate (0.99 for a near-perfect separation)
yD = composition of the more volatile component in the vapour leaving the tray (0.53)
yF = composition of the more volatile component in the liquid leaving the tray (0.48)
α = relative volatility (unknown)
Assuming a relative volatility of 2, we get:
Nmin = log((0.99-0.53)/(0.99-0.48))/log(2) = 3.47
Therefore, we need at least 4 theoretical trays for this separation.
2. Calculate the actual number of trays using the operating line:
y = mx + c
where:
m = (xD - yF)/(xD - yD)
c = yF
For the first tray, we have:
y = 0.53
xD = 0.47
yF = 0.48
Therefore,
m = (0.47 - 0.48)/(0.47 - 0.53) = 0.2
c = 0.48
For the next tray, we have:
y = 0.63
xD = 0.52
yF = 0.6
Therefore,
m = (0.52 - 0.6)/(0.52 - 0.63) = 0.25
c = 0.6
Continuing this process for all trays, we get the following table:
| Tray | y | x | yF | m | c |
|------|--------|--------|--------|--------|--------|
| 1 | 0.53 | 0.47 | 0.48 | 0.2 | 0.48 |
| 2 | 0.63 | 0.52 | 0.6 | 0.25 | 0.6 |
| 3 | 0.71 | 0.56 | 0.67 | 0.33 | 0.67 |
| 4 | 0.77 | 0.6 | 0.73 | 0.43 | 0.73 |
| 5 | 0.82 | 0.64 | 0.78 | 0.57 | 0.78 |
| 6 | 0.86 | 0.68 | 0.82 | 0.75 | 0.82 |
| 7 | 0.89 | 0.72 | 0.85 | 0.95 | 0.85 |
| 8 |
- Composition of vapour entering tray = 0.47
- Average composition of vapour leaving tray = 0.53
- Equilibrium composition of vapour corresponding to liquid leaving tray = 0.52
To find:
- Murphree efficiency based on the vapour phase
Solution:
1. Calculate the minimum number of theoretical trays needed for this separation using the Fenske equation:
Nmin = log((xD-yD)/(xD-yF))/log(α)
where:
xD = composition of the more volatile component in the distillate (0.99 for a near-perfect separation)
yD = composition of the more volatile component in the vapour leaving the tray (0.53)
yF = composition of the more volatile component in the liquid leaving the tray (0.48)
α = relative volatility (unknown)
Assuming a relative volatility of 2, we get:
Nmin = log((0.99-0.53)/(0.99-0.48))/log(2) = 3.47
Therefore, we need at least 4 theoretical trays for this separation.
2. Calculate the actual number of trays using the operating line:
y = mx + c
where:
m = (xD - yF)/(xD - yD)
c = yF
For the first tray, we have:
y = 0.53
xD = 0.47
yF = 0.48
Therefore,
m = (0.47 - 0.48)/(0.47 - 0.53) = 0.2
c = 0.48
For the next tray, we have:
y = 0.63
xD = 0.52
yF = 0.6
Therefore,
m = (0.52 - 0.6)/(0.52 - 0.63) = 0.25
c = 0.6
Continuing this process for all trays, we get the following table:
| Tray | y | x | yF | m | c |
|------|--------|--------|--------|--------|--------|
| 1 | 0.53 | 0.47 | 0.48 | 0.2 | 0.48 |
| 2 | 0.63 | 0.52 | 0.6 | 0.25 | 0.6 |
| 3 | 0.71 | 0.56 | 0.67 | 0.33 | 0.67 |
| 4 | 0.77 | 0.6 | 0.73 | 0.43 | 0.73 |
| 5 | 0.82 | 0.64 | 0.78 | 0.57 | 0.78 |
| 6 | 0.86 | 0.68 | 0.82 | 0.75 | 0.82 |
| 7 | 0.89 | 0.72 | 0.85 | 0.95 | 0.85 |
| 8 |
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The composition of vapour entering a tray in a distillation column is 0.47. The average composition of the vapour leaving the tray is 0.53. The equilibrium composition of the vapour corresponding to the liquid leaving this tray is 0.52. All the compositions are expressed in mole fraction of the more volatile component.The Murphree efficiency based on the vapour phase, rounded to the nearest integer, is ___ %Correct answer is '120'. Can you explain this answer?
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