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.

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 26.00 kg of propene oxide.

Answer 1

Solution :-

Lets first calculate the moles of the C3H6O

Moles = mass / molar mass

Moles of C3H6O = (26.00 kg *1000 g /1 kg )*(1 mol / 58.08 g ) = 447.6584 mol

Mole ratio of the C3H6O to C3H6 is 1:1 therefore moles of the C3H6 needed for the reaction are calculated as

(447.6584 mol C3H6O * 1 mol C3H6 / 1 mol C3H6O)* (100 % / 96 % ) = 466.3108 mol C3H6

Now let convert this moles to mass of C3H6

Mass of C3H6 = moles * molar mass

                      = 466.3108 mol * 42.08 g per mol

                      = 19622 g

19622 g * 1 kg / 1000 g = 19.622 kg C3H6

Now lets calculate the moles of the mCPBA needed

Mole ratio is 1 : 1

So moles of the mCPBA needed to give 100 % reaction = 447.6584 mol * 100 % / 96 % = 466.3108 mol

Lets convert this to its mass

Mass C7H5O3Cl = moles * molar mass

                              = 466.3108 mol * 172.56 g per mol

                             = 80467 g

80467 g * 1 kg / 1000 g = 80.467 kg

Now lets calculate the volume of the dichloromethane

Concentration is 21.0 g / L

Therefore 19622 g * 1 L / 21.0 g = 934.4 L CH2Cl2

Now lets calculate the cost of the each starting material

Propene = 19.622 kg * 10.97 $ / 1 kg = 215.2533$

mCPBA = 80.467 kg * 5.28$ / 1 kg = 424.87 $

CH2Cl2 = 934.4 L * 2.12 $ / 1 L = 1980.93 $

And cost for the waste disposal = 26 kg propene oxide * 5.00 $ / 1 kg = 130 $

So total cost = 215.2533 $ + 424.87 $ + 1980.93 $ + 130 $ = 2751 $

Now lets calculate the value of the 26.00 kg product

26.00 kg * 258.25 $ / 1 kg = 6714.5 $

Now lets calculate the profit

Profit = total earning – total cost

           = 6714.5 $ - 2751 $

           = 3963.5 $

So we can round it to 3964 $

So the total profit = 3964 $