Students and faculty from Brigham Young University Developed and delivered a sma
ID: 940025 • Letter: S
Question
Students and faculty from Brigham Young University Developed and delivered a small-scale process to Tonga for making biodiesel fuel from coconut oil. The central component of the process was the reactor where the coconut oil (triglycerides containing a variety of fatty acids - represented as R_1, R_2, and, R_3) is reacted with methanol in the presence of sodium hydroxide (acting as a catalyst, thus not consumed) as shown in the following reaction. The conversion of coconut oil is essentially 100%, and the products are biodiesel, which is a collection o fatty esters (the collection of several varieties are represented here by the designation R_x), and glycerol. For the small-scale process (assume steady-state), 140/hr of coconut oil is fed to the reactor, along with 540 g/hr solid (pure) NaOH. Based on previous testing, methanol is also fed at a molar flow rate equal to 4.2 times the molar flow rate of coconut oil. A single outlet stream leaves the reactor. The properties of all components are as follows: What is the mass fraction of biodiesel in the reactor output? Later stages of the process separate the components of this reactor output to provide a stream of essentially pure biodiesel. What is the volumetric flow rate of that stream?Explanation / Answer
as per the reaction, 1 mole of coconinut oil reacts with 3 moles of methanol to give 3 moles of trigylcerides and 1 mole of glycerol.
flow rate of coconut oil = 140 lLhr
density of coconut oil =878g/L
mass of coconut oil= 140*878 g/hr=122920g/hr
moles of coconut oil = mass/molecular weight= 122920/659=186.525 moles/hr
Moless of methanol required =3*186.525 =559.57 moles/hr
Methanol is excess,
moles of bio-diesel formed = 186.525*3 ( 3 times the molar flow rate of coconut oil)=559.5751 moles/hr
mass of bio-diesel formed= moles of bio-diesel* Molecular weight = 559.5751*221 g/mol =123666.1 g/hr
Mass of glycerol formed = moles of glycerol* molecular weight= 186.525*92
moles of glycerol formed = 186.525 moles/ hr*92 g/mole= 17160.3 g/hr
total mass of product= 123666.1+17160.3 g/hr=140826.4 g/hr
Mass fraction of bio-diesel= 123666.1/140826.4=0.878
volumetric flow rate of bio-diesel = mass flow rate (g/hr)/density (g/L)=123666.1/880=140.53 L/hr