Paraphrase each sentence of the report until the similarity be less than 5% of the report submitted below. keep all numbers and tables and figures as same. please make sure to paraphrase in a good way because we have a similarity check.

The main purpose of this experiment is to calculate the theoretical number of stages of an immiscible liquid-liquid extraction system using McCabe-Thiele diagram. Furthermore, to evaluate overall mass transfer coefficient and to find the height of the operating unit.

The procedure followed in the calculation of theoretical number of stages was based on McCabe-Thiele diagram, merely by plotting the equilibrium curve using the mass ratio data (Y,X) and at least one operating line.

The theoretical number of stages were determined and it was found from McCabe-Thiele diagram that the transfer unit have 1.2 equilibrium stages and a height equal to 2.6 m with percentage error equal to 54.6%. Moreover, the experimental value of mass flow rate ratio (Fd/Fs) was calculated then it was compared to the theoretical value to give percentage error of 30.85 %.

Finally, it was concluded that there are different sources of errors including the adjustment of the flow rate. In addition, it was found that as speed of the rotation of the spinning band increased, a better extraction process would be obtained.

Separation process is classified to be one of the most significant processes in any chemical industry to present and purify chemicals compound before stepping inside any chemical reactor and after it. There are several methods used to separate chemical compounds including continuous distillation column, adsorption, stripping and extraction. To remove one or more solutes from a liquid, immiscible liquid-liquid extraction will be the suitable method by transferring the solutes into another liquid phase.
Here are equations that were used in the calculation of this experiment:
X=x/(1-x) Where X = mass ratio solute in diluent (kg A / kg D). (1)
Y=y/(1-y) Where Y = mass ratio solute in solvent (kg A / kg s) . (2)
∆[y]_ln=((y_1^*-y_1 )-(y_(N+1)^*-y_(N+1) ))/(ln⁡((y_1^*-y_1)/(y_(N+1)^*-y_(N+1) ))) (3)
Where y* = extract mass fraction on solute at equilibrium.
K_ca=(W_T (y_1-y_(N+1)))/(∆[y]_ln .V) Where Kca¬ = overall mass transfer (4)
Coefficient (1/s), V = volume of separation column (m3), WT = flow rate of the light phase (m3/s).
H’=W_T/(K_ca .s) Where H’ = height of the unit (m). (5)
H_th=H^’ x N Where N: Number of stages (6)

Table 1: Equilibrium Data for water, Isopropanol and Toluene System and their mass rations.
x y X Y
0.0463 0.0058 0.0485 0.0058
0.0656 0.0092 0.0702 0.0093
0.1013 0.0149 0.1127 0.0151
0.1262 0.0226 0.1444 0.0231
0.1572 0.0356 0.1865 0.0369
0.1872 0.0516 0.2303 0.0544
0.2259 0.0959 0.2918 0.1061
0.2612 0.1538 0.3535 0.1818
0.2955 0.2131 0.4194 0.2708
0.3224 0.2964 0.4758 0.4213

Table 2: Gas Chromatography Analysis of the Feed, Heavy and Light with their mass fractions.
GC analysis Area Ratio Mass Ratio Mass Fraction
Feed (Xo) 0.2523 0.4383 0.3047
Heavy (XN) 0.1235 0.2146 0.1767
Light (Y1) 0.0724 0.0659 0.0618
(YN+1) 0 0 0

Table 3: Comparing experimental ratio (FD/FS) exp to theoretical ratio (FD/FS) Th.
(FD/FS)th 0.295
(FD/FS)exp 0.39
Error% 30.85

Table 4 : Main result Obtained From McCabe-Thiele Diagram and Calculated From experiment.
# of stages (N) 1.2
Y1* 0.3200
y1* 0.2424
Yn+1* 0.0700
yn+1* 0.0654
Δ[y]ln 0.1134
V (m3) 0.0001130
WT (m3/s) 0.00000007600
Kca (eq9) (s^-1) 0.000366
S (m2) 0.0001
H’ (m) 2.2
HTh (m) 2.6
H (m) 1.2
Error % 54.6

Figure 1: McCabe-Thiele Diagram for Dilute Extraction
Discussion of Result:
For separation by extraction, we cannot use the mass fraction like in normal distillation column because the solution is too dilatant however, instead of that we use mass ratio. The mass fraction for the equilibrium data were converted to mass ratio as shown in table (1).

Using the GC analysis with the area ratio %, the mass ratio in the feed(X0), heavy phase (XN) and light phase (Y1) were evaluated then were converted to mass fraction as shown in table (2).

As shown in figure (1), equilibrium data were plotted against operating line then both of the number of theoretical stages and the slope of the operating line (Fd/Fs) were obtained and they were equal to 2.1 stages and 0.295 respectively.

As shown in table (3), the experimental value of mass flow rate ratio (Fd/Fs) was compared to the theoretical value to give percentage error of 30.85 %.

As shown in table (4), the overall mass transfer coefficient was equal to 0.000366 s-1 and the actual height of the unit was evaluated to be 2.6 m with an error equal to 54.6%.

It can be noticed from the experiment that the effect the speed of the spinning band is to enhance the overall mass transfer coefficient and as result a better separation.

In conclusion, quite large errors were estimated regarding both the height of the column (54.6%) and the experimental ratio (Fd/Fs) (30.85 %). The actual height of the unit column is 1.9 m, while the theoretical height of the unit was 2.6 m. In addition, the overall mass transfer coefficient was determined to be 0.000366 s-1 and the number of theoretical stages were 1.2 stages.
However, there were different sources of the errors that were obviously reflected on the results. First, the feed was nearly improperly prepared, which could be seen in the GC analysis. Moreover, it was challenging to adjust the flow rates of the two phases at low rates. Additionally, the most key source of error was because the system could not reach punctually the steady state condition.

Appendices :
A1. Raw Data.
A2. Gas Chromatography Analysis
A3. Sample of Calculations.


Sample Solution

Sample solution

Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell. 

In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.

God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.

Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.

To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.



Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.

Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies4(8), 487.

Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.