Things are going smoothly at PhilsPills Pharmaceutical pilot plant during the ov

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: (1) The mass fraction of Compound X in the reactor stream was supposed to be 0.25 and (2) When the mole fraction of Compound X in the reactor reaches 0.3, the reaction mixture will explode.

a) 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.

b) 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.

c) 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 0.3)?

Explanation / Answer

Specific gravity of cyclohexane = density of cyclohexane / density of water

Density of cyclohexane = Specific gravity of cyclohexane X density of water

                                           = 0.779 X 1 g / ml = 0.779 g/ml

simillarly

Specific gravity of compound x = density of compound x / density of water

Density of compound x = Specific gravity of compound x X density of water

                                           = 1.30 X 1 g / ml = 1.30 g/ml

Let us consider one minute flow cyclohexane 11 liters and Compound X to 5 liters.

Mass = volume X density

Mass of cyclohexane =11000 ml X 0.779 g/ml = 8569 g

Mass of compound x = 5000 X 1.30 g/ml = 6500 g

Moles = mass / mol. Wt.

Moles of cyclohexane = 8569 g / 84 g/mol = 102.011mol-1

Moles of compound x = 6500 g / 216 g/mol = 30.09 mol-1

Mass fraction of cyclohexane

= Mass of cyclohexane / (Mass of cyclohexane + Mass of compound x)

= 8569 g/ (8569 g + 6500 g) = 0.568

Mass fraction of compound x

= Mass of compound x / (Mass of cyclohexane + Mass of compound x)

= 6500 g/ (8569 g + 6500 g) = 0.432

Mole fraction of cyclohexane

= Moles of cyclohexane / (Moles of cyclohexane + Moles of compound x)

= 102.11mol-1/ (102.011mol-1 + 30.09 mol-1) = 0.773

Mole fraction of compound x

= Moles of compound x / (Moles of cyclohexane + Mass of compound x)

= 30.09 mol-1/ (102.011mol-1 + 30.09 mol-1) = 0.227

Frank should have remembered two little things:

(1) The mass fraction of Compound X in the reactor stream was supposed to be 0.25 and

(2) When the mole fraction of Compound X in the reactor reaches 0.3, the reaction mixture will explode.

Answers

a) Yes Frank select the right flow rates. Mole fraction of Compound X in the reactor is 0.227 hence the reaction mixture will not explode.

b) Mass fraction of compound x = Mass of compound x / (Mass of cyclohexane + Mass of compound x)

0.25= 6500 g/ (Mass of cyclohexane + 6500 g)

0.25(Mass of cyclohexane + 6500 g)= 6500 g

0.25 X Mass of cyclohexane = 6500 – 1625 g = 4875 g

Volume = mass / density = 4875 / 0.779 g/ml = 6285 ml = 6.285 Litre

flow rate of the solution of cyclohexane be set at to achieve the desired mass fraction of Compound X of 0.25, Keeping the flow rate of Compound X at 5 liters/min is 6.285 litres/min

c) Mole fraction of compound x

= Moles of compound x / (Moles of cyclohexane + Moles of compound x)

0.3 = Moles of compound x / (102.11mol-1 + Moles of compound x)

0.3(102.011mol-1 + Moles of compound x) = Moles of compound x

30.603 = Moles of compound x - 0.3Moles of compound x

Moles of compound x = 30.603 / 0.7 = 43.71

Mass of compound x = moles X molar mass = 43.71 X 216 = 9443.2 g

Volume = mass / density = 9443.2 / 1.3 g/ml = 7264 ml = 7.264 Litre

Keeping the flow rate of cyclohexane at 11 liters/min, the minimum flow rate of Compound X that will cause the reaction mixture to explode (Compound X mole fraction 0.3) is 7.264 Litre min-1

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