Things are going smoothly at PhilsPills Pharmaceutical pilot plant during the ov
ID: 476549 • Letter: T
Question
Things are going smoothly at PhilsPills Pharmaceutical pilot plant during the overnight shift until Frank, aka FumbleFingers, dropped the instruction sheet for the new reactor into the Bunsen burner he was using to warm up his tea. Needless to say, the instruction sheet was completely destroyed, and his tea was spilled on the lab bench in his panic to save the instruction sheet. Instead of calling his supervisor who will be none too pleased to receive a late-night phone call, Frank decides to hope memory is correct and sets the reaction parameters. He adjusts the cyclohexane (MW = 84 g/mol, specific gravity = 0.779) to 11 liters/min and the Compound X (MW = 216 g/mol, specific gravity = 1.30) to 5 liters/min. Frank should have remembered two little things: The mass fraction of Compound X in the reactor stream was supposed to be 0.25 and When the mole fraction of Compound X in the reactor reaches 0.3, the reaction mixture will explode. Did Frank select the right flow rates? If not, did he learn about his mistake immediately? (i.e. did the reaction mixture explode?) Explain how you arrived at these conclusions. What flow rate should the solution of cyclohexane be set at to achieve the desired mass fraction of Compound X of 0.25? Keep the flow rate of Compound X at 5 liters/min. Keeping the flow rate of cyclohexane at 11 liters/min, what is the minimum flow rate of Compound X that will cause the reaction mixture to explode (Compound X mole fraction greaterthanorequalto 20.3)?Explanation / Answer
Let us consider 1 min flow
The amount of cyclohexane and compound x flowing in 1 min are 11 litres and 5 litres
Specific gravity of substance = density of substance / density of water
Density of substance = specific gravity X density of water
Density of substance cyclohexane = specific gravity of cyclohexane X density of water
= 0.779 X 1 g/ml = 0.779 g/ml
Conversion of volume into mass
Mass of cyclohexane = density X volum = 0.779 g/ml X 11000 ml = 8569 g
Density of substance cyclohexane = specific gravity of cyclohexane X density of water
= 1.3 X 1 g/ml = 1.3 g/ml
Calculation of mass fraction
Mass of cyclohexane = density X Volume = 1.3 g/ml X 5000 ml = 6500 g
Mass fraction of x = mass of x/( mass of x + mass of cyclohexane)
= 6500/(8569 +6500) = 6500/15059 = 0.43
Calculation of mole fraction
Moles of cyclohexane = mass/ mol. Wt. = 8569/84 = 102.01
Moles of compound x = mass/ mol. Wt. = 6500/216 = 30.09
Mole fraction of x = moles of x/( moles of x + moles of cyclohexane )
= 30.09/(102.01 + 30.09) =30.09/132.1 = 0.2277
Answers
a) The flow rates selected by frank was wrong as the mass fraction was greater than expected 0.25, the reaction mass did not explode as the mole fraction was below 0.3 see above calculation of mass fraction ana mole fraction
b)
Mass fraction of x = mass of x/( mass of x + mass of cyclohexane)
0.25 = 6500/(8569 +mass of cyclohexane)
8569 +mass of cyclohexane = 6500/0.25 = 26000
Mass of cyclohexane = 26000 – 8569 =17431
Volume = Mass of cyclohexane / density
= 17431 / 1.3 = 13408.46 ml = 13.4 litres/min
therefore flow rate of cyclohexane should be 13.4 lit/min
c)
Mole fraction of x = moles of x/( moles of x + moles of cyclohexane )
0.3 = moles of x /(102.01 + moles of x)
0.3(102.01 + moles of x) = moles of x
30.6 + 0.3moles of x = moles of x
moles of x - 0.3moles of x = 30.6
0.7 moles of x = 30.6
Moles of x = 30.6/0.7 = 43.7 mol
Mass = 43.7 X 216 =9443 g
Volume = mass / density = 9443/ 1.3 = 7264 lit/min
Keeping flow rate of cyclohexane 11 lit/min the volume of compound x that will cause explosion will be 7264 Lit/min
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