Question

A fictional company has been producing propene oxide, C3H6O, from propene, C3H6, with a 96.0% yield. The process requires the use of a compound called m-chloroperoxybenzoic acid, C7H5O3Cl, which can be abbreviated as mCPBA. The entire reaction takes place in the solvent dichloromethane, CH2Cl2:

C3H6+C7H5O3ClCH2Cl2−−−⟶96.0% yieldC3H6O+C7H5O2Cl

The initial propene concentration in the solvent is 21.0 g/L.

Consider the prices of the following substances.

Substance	Price per unit	Unit
propene	$10.97	kg
dichloromethane	$2.12	L
mCPBA	$5.28	kg
propene oxide	$258.25	kg

Also consider that the cost of waste disposal is $5.00 per kilogram of propene oxide produced.

Part A

A relatively simple way of estimating profit is to consider the the difference between the cost (the total spent on materials and waste disposal) and the earnings (the price at which the product can be sold).

Calculate the profit from producing 43.00 kg of propene oxide.

Express your answer numerically in dollars using three significant figures.

$

Alternative method

The company is developing a "greener" method of making propene oxide from propene using hydrogen peroxide, H2O2, in supercritical water with a vanadium catalyst. In the reaction 1.00 kg of vanadium catalyst and 32.0 kg of water are used for each kilogram of propene. 75 % of the vanadium catalyst can be collected and reused in a subsequent batch:

C3H6+H2O2V, H2O−−−⟶89.0% yieldC3H6O+H2O

Consider the prices of the following substances.

Substance	Price per unit	Unit
propene	$10.97	kg
hydrogen peroxide	$1.96	kg
vanadium catalyst	$57.50	kg
supercritical water	$1.85	kg
propene oxide	$258.25	kg

There is virtually no waste produced with this green process and there is no waste disposal fee, but the yield is only 89.0%.

Part B

Calculate the profit from producing 43.00 kg of propene oxide by this alternative green process.

Answer 1

Part a

The given reaction

C3H6+C7H5O3ClCH2Cl2−−−>96.0% yieldC3H6O+C7H5O2Cl

From the stoichiometry of the reaction

1mol mCPHA reacts with = 1 mol of propene = produces 1 mole of C3H6O

172.57grams mCPHA reacts with = 42.08grams of propene = produces 58.08grams of C3H6O

172.57 kg mCPHA reacts with = 42.08 kg of propene = produces 58.08 kg of C3H6O

to produce 1 kg of C3H6O

Required mass of C3H6 = 42.08 / 58.08 kg = 0.72452 kg C3H6

Required mass of mCPHA = 172.57 / 58.08 kg = 2.9712 kg mCPHA

Yield of the reaction = 96%

After scaling up to produce 1 kg of C3H6O

Mass of C3H6 required = (0.72452 kg ) (100/96)

= 0.75471 kg C3H6

mass of mCPHA required = (2.9712 kg) (100/96) mCPHA

= 3.095 kg mCPHA

Cost of C3H6 per kg of C3H6O produced

= (0.75471 kg C3H6) x ($10.97 per kg)

= $8.279

Cost of mCPHA per kg of C3H6O produced

= (3.095 kg mCPHA) x ($5.28 per kg)

= $16.342

Volume of dichloromethane per kg of C3H6O produced

= (0.75471 kg C3H6) / (0.0210 kg C3H6 / L dichloromethane)

= 35.939 L dichloromethane

Cost of dichloromethane per kg of C3H6O produced

= (35.939 L dichloromethane) x ($2.12 per L)

= $ 76.19

Cost of waste disposal per kg of C3H6O produced = $5.00/kg

total cost per kg of C3H6O produced

= $8.279 + $16.342 + $76.19 + $5.00

= $105.81

Profit = 1 kg C3H6O produced - total cost to produce 1 kg C3H6O

= ($258.25 / kg C3H6O) - ($105.81 / kg)

= $152.44 profit /kg

To produce 43 kg of C3H6O

Profit = (43.00kg) x ($152.44 /kg) = $6554.92

Profit = $6.55 x 10^3

Part b

The given reaction

C3H6+H2O2V, H2O−−−>89.0% yieldC3H6O+H2O

42.08 kg C3H6 reacts with = 34.0147 kg H2O2 = 58.08 kg C3H6O produced

to produce 1 kg of C3H6O

Mass of C3H6 required = 42.08 / 58.08 kg

= 0.72452 kg

Mass of H2O2 required = 34.0147/58.08 kg

= 0.58565 kg

Yield of the reaction = 89%

Mass of C3H6 required = 0.72452/0.89 = 0.81407 kg

Mass of H2O2 required = 0.58565/0.89 = 0.65803 kg

Cost of C3H6 per kg of C3H6O produced

= (0.81407 kg C3H6) x ($10.97 per kg)

= $8.930

Cost of H2O2 per kg of C3H6O produced

= (0.65803 kg H2O2) x ($1.96 per kg)

= $1.289

Kg of propene required per kg of C3H6O produced = 0.81407 kg

Cost of vanadium catalyst used for 0.81407 kg of propene = (0.81407 kg V) ($57.50 per kg) = $46.809

75 % of the vanadium catalyst can be collected

Only 25% of V is used

Cost of V used in the reaction = 0.25 x $46.809 = $11.70

Cost of H2O used in the reaction for 0.81407 kg of propene

= (32 kg H2O) x ($1.85 per kg) x 0.81407

= $48.193

Total cost per kg C3H6O produced = $8.930 + $1.289 + $11.70 + $48.193

= $70.112

Profit = 1 kg C3H6O produced - total cost to produce 1 kg C3H6O

= ($258.25 / kg C3H6O) - ($70.112 / kg)

= $188.138 profit /kg

To produce 43 kg of C3H6O

Profit = (43.00kg) x ($188.138 /kg) = $8089.93

Profit = $8.09 x 10^3