The company is developing a \"greener\" method of making propene oxide from prop
ID: 501002 • Letter: T
Question
The company is developing a "greener" method of making propene oxide from propene using hydrogen peroxide, H_2O_2, in supercritical water with a vanadium catalyst. In the reaction 1.00 kg of vanadium catalyst and 32.0kg of water are used for each kilogram of propene. 75% of the vanadium catalyst can be collected and reused in a subsequent batch: Consider the prices of the following substances. There is virtually no waste produced with this green process and there is no waste disposal fee, but the yield is only 89.0% Calculate the profit from producing 53.00 kg of propene oxide by this alternative green process. Express your answer numerically in dollars using three significant figures.Explanation / Answer
"In the reaction 1.00 kg of vanadium catalyst and 32.0 kg of water are used for each kilogram of propene." they gave the amount of catalyst & water per kg of C3H6, where as I had read in as 1 kg of C3H6O
to produce 1 kg of C3H6O, I had calculated that they needed 0.81407 kg C3H6
so, to produce 1 kg of C3H6O,
"In the reaction 1.00 kg of vanadium catalyst and 32.0 kg of water"...:for each kilogram of propene."
becomes, to produce 1 kg of C3H6O:
" In the reaction" 0.81407 "kg of vanadium catalyst" ("and 32.0 kg") (0.81407) "of water for each" 0.81407 "kg of propene."
which then to produce 1 kg of C3H6O would require::
" In the reaction" 0.81407 "kg of vanadium catalyst" 26.05kg "of water"
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1 mol C3H6 & 1 mol H2O2 --> 1 mol C3H6O
using molar masses, that equation becomes:
42.08 grams C3H6 & 34.015 grams H2O2 --> 58.08 grams C3H6O
which is: 42.08 kg C3H6 & 34.015 kg H2O2 --> 58.08 kg C3H6O
to produce 1 kg of C3H6O, this becomes:
42.08 / 58.08 kg C3H6 & 34.015 / 58.08 kg H2O2 --> 58.08 /58.08 kg C3H6O
which is: 0.72452 kg C3H6 & 0.5857 kg H2O2--> 1 kg C3H6O
but because the reaction gives only a 89.0 % yield,
we scale up the reactants to get that desired 1 kg of C3H6O
(0.72452 kg ) (100/89) C3H6 & (0.5857 kg) (100/89) H2O2 --> 1 kg C3H6O
which is: 0.81407 kg C3H6 & 0.65804 kg H2O2 --> 1 kg C3H6O
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costs per kg of C3H6O produced:
since 1.00 kg of vanadium catalyst is used for each kilogram of propene,
75 % of the vanadium catalyst can be collected,
its expense is
(25%) (0.81407kg Va cat) ($57.50 per kg) = $11.70
(0.81407 kg C3H6) ($10.97 per kg) = $8.9303
(0.65804 kg H2O2) ($1.96 per kg) = $1.2898
(26.05 kg of water) ($1.85 per kg) = $48.193
total cost of materials: $70.11 per kg C3H6O produced
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profit: ($258.25 / kg C3H6O) - ($70.11 cost per kg) = $188.14 profit /kg
“Calculate the profit from producing 53.00kg of propene oxide”
(53.00kg) ($188.14 /kg) = $9,971
rounded off to 3 sig figs is: $9,971