Select the correct answer.
What is the theoretical yield of methanol [tex]$\left( CH _3 OH \right)$[/tex] when 12.0 grams of [tex]$H _2$[/tex] is mixed with 74.5 grams of CO? [tex]$CO +2 H _2 \rightarrow CH _3 OH$[/tex]
A. 14.88 grams
B. 47.65 grams
C. 74.50 grams
D. 85.12 grams
E. 92.04 grams
Answer (2)
Calculate the moles of H 2 and CO using their respective masses and molar masses.
Determine the limiting reactant by comparing the mole ratio of the reactants to the stoichiometric ratio in the balanced equation.
Calculate the theoretical yield of C H 3 O H based on the number of moles of the limiting reactant and the molar mass of C H 3 O H .
The theoretical yield of methanol is approximately 85.12 grams .
Explanation
Calculate Moles of Reactants First, we need to determine the number of moles of each reactant. The molar mass of H 2 is 2.016 g/mol, and the molar mass of CO is 28.01 g/mol. We have 12.0 grams of H 2 and 74.5 grams of CO .
Moles Calculation The number of moles of H 2 is calculated as follows: m o l e s H 2 = m o l a r _ ma s s H 2 ma s s H 2 = 2.016 g/mol 12.0 g = 5.95 mol The number of moles of CO is calculated as follows: m o l e s CO = m o l a r _ ma s s CO ma s s CO = 28.01 g/mol 74.5 g = 2.66 mol
Determine Limiting Reactant Next, we need to determine the limiting reactant. The balanced chemical equation is: CO + 2 H 2 → C H 3 O H From the balanced equation, 1 mole of CO reacts with 2 moles of H 2 . Therefore, we need to compare the mole ratio of the reactants to the stoichiometric ratio.
Limiting Reactant Calculation We can determine the limiting reactant by dividing the number of moles of H 2 by 2 and comparing it to the number of moles of CO :
2 m o l e s H 2 = 2 5.95 mol = 2.98 mol Since 2.98 mol > 2.66 mol, CO is the limiting reactant.
Calculate Moles of Methanol The theoretical yield of C H 3 O H is based on the number of moles of the limiting reactant, which is CO . Since 1 mole of CO produces 1 mole of C H 3 O H , the number of moles of C H 3 O H produced is equal to the number of moles of CO reacted, which is 2.66 mol.
Calculate Theoretical Yield Finally, we calculate the mass of C H 3 O H produced using its molar mass (32.04 g/mol): ma s s C H 3 O H = m o l e s C H 3 O H × m o l a r _ ma s s C H 3 O H = 2.66 mol × 32.04 g/mol = 85.22 g
Final Answer Therefore, the theoretical yield of methanol is 85.22 grams. The closest answer is D. 85.12 grams.
Conclusion The theoretical yield of methanol ( C H 3 O H ) is approximately 85.12 grams.
Examples
In the chemical industry, determining the theoretical yield of a reaction is crucial for optimizing production processes. For example, when producing methanol from carbon monoxide and hydrogen, knowing the theoretical yield helps chemical engineers to estimate the maximum amount of methanol that can be obtained from given amounts of reactants. This information is essential for cost analysis, process design, and ensuring efficient use of resources. By accurately calculating the theoretical yield, companies can make informed decisions about reactant quantities, reaction conditions, and overall process feasibility, leading to more sustainable and economically viable chemical production.
The theoretical yield of methanol produced from 12.0 grams of hydrogen and 74.5 grams of carbon monoxide is approximately 85.12 grams, making the correct choice D. This yield is determined by calculating the moles of the reactants, finding the limiting reactant, and then using that to calculate the mass of methanol produced.
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