Urea (CH₄N₂O) is a common fertilizer that is synthesized by the reaction of ammonia (NH₃) with carbon dioxide: 2 NH₃(aq) + CO₂(aq) → CH₄N₂O(aq) + H₂O(l) In an industrial synthesis of urea, a chemist combines 149.4 kg of ammonia with 231.1 kg of carbon dioxide and obtains 172.3 kg of urea. Determine the limiting reactant, theoretical yield of urea, and percent yield for the reaction.

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Step 1: Convert the masses of ammonia (NH₃) and carbon dioxide (CO₂) to moles. Use the molar masses: NH₃ = 17.03 \text{ g/mol} and CO₂ = 44.01 \text{ g/mol}.

Step 2: Use the balanced chemical equation to determine the mole ratio between NH₃ and CO₂. The equation is 2 NH₃ + CO₂ → CH₄N₂O + H₂O, which shows a 2:1 ratio.

Step 3: Calculate the theoretical moles of urea (CH₄N₂O) that can be produced from each reactant. The limiting reactant will produce the fewer moles of urea.

Step 4: Convert the theoretical moles of urea to mass using its molar mass (CH₄N₂O = 60.06 \text{ g/mol}) to find the theoretical yield in kilograms.

Step 5: Calculate the percent yield using the formula: \text{Percent Yield} = \left(\frac{\text{Actual Yield}}{\text{Theoretical Yield}}\right) \times 100\%. Use the actual yield of 172.3 kg of urea.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Limiting Reactant

The limiting reactant is the substance that is completely consumed first in a chemical reaction, thus determining the maximum amount of product that can be formed. To identify the limiting reactant, one must compare the mole ratios of the reactants used in the reaction to the stoichiometric coefficients in the balanced equation. The reactant that produces the least amount of product is the limiting reactant.

Theoretical Yield

The theoretical yield is the maximum amount of product that can be generated from a given amount of reactants, based on the stoichiometry of the balanced chemical equation. It is calculated using the moles of the limiting reactant and the molar ratios from the balanced equation. This value represents an ideal scenario without any losses or inefficiencies during the reaction.

Percent Yield

Percent yield is a measure of the efficiency of a chemical reaction, calculated by taking the actual yield of the product obtained from the reaction and dividing it by the theoretical yield, then multiplying by 100. This metric helps chemists assess how well a reaction proceeds under given conditions and can indicate potential issues in the reaction process or product recovery.

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