What is the maximum amount of ethanol (in grams) that can be produced when 1.0 kg of ethylene (C2H4) and 0.014 kg of steam are placed into the reaction vessel?
Ethanol (C2H5OH) is synthesized for industrial use by the following reaction, carried out at very high pressure.
C2H4(g) + H2O(g) C2H5OH(l)
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jmyi
To determine the maximum amount of ethanol (in grams) that can be produced, you need to use stoichiometry and the concept of limiting reactants.
1. Start by writing and balancing the chemical equation:
C2H4(g) + H2O(g) → C2H5OH(l)
2. Convert the masses of ethylene and steam from kg to grams:
1.0 kg of ethylene = 1000 g
0.014 kg of steam = 14 g
3. Determine the molar mass of ethylene (C2H4) and steam (H2O):
- Molar mass of C2H4 = 2(12.01 g) + 4(1.01 g) = 28.05 g/mol
- Molar mass of H2O = 2(1.01 g) + 16.00 g = 18.02 g/mol
4. Use the molar mass to convert the masses of ethylene and steam to moles:
- Moles of C2H4 = 1000 g / 28.05 g/mol = 35.65 mol
- Moles of H2O = 14 g / 18.02 g/mol = 0.776 mol
5. Compare the mole ratio between the reactants and the product:
Based on the balanced equation, the mole ratio between C2H4 and C2H5OH is 1:1. This means 1 mole of C2H4 reacts with 1 mole of C2H5OH.
6. Determine the limiting reactant:
To find the limiting reactant, compare the moles of C2H4 and H2O. The reactant that produces fewer moles of product is the limiting reactant.
From the given amounts, C2H4 has 35.65 moles, while H2O has 0.776 moles.
Since H2O is the limiting reactant, it determines the maximum amount of product formed.
7. Calculate the moles of C2H5OH produced:
Since the mole ratio between C2H4 and C2H5OH is 1:1, the moles of C2H5OH produced are also equal to 0.776 moles.
8. Determine the molar mass of ethanol (C2H5OH):
Molar mass of C2H5OH = 2(12.01 g) + 6(1.01 g) + 16.00 g = 46.08 g/mol
9. Calculate the maximum amount of ethanol produced in grams:
Grams of C2H5OH = moles of C2H5OH × molar mass of C2H5OH
Grams of C2H5OH = 0.776 mol × 46.08 g/mol = 35.77 g
Therefore, the maximum amount of ethanol that can be produced is 35.77 grams when 1.0 kg of ethylene and 0.014 kg of steam are used.