Ch.4 - Chemical Reactions and Chemical Quantities

Problem 49

Chapter 4, Problem 49

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 136.4 kg of ammonia with 211.4 kg of carbon dioxide and obtains 168.4 kg of urea. Determine the limiting reactant, theoretical yield of urea, and percent yield for the reaction.

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Convert the masses of ammonia (NH_3) and carbon dioxide (CO_2) to moles using their molar masses. The molar mass of NH_3 is approximately 17.03 g/mol, and the molar mass of CO_2 is approximately 44.01 g/mol.

Use the balanced chemical equation to determine the mole ratio between NH_3 and CO_2. According to the equation, 2 moles of NH_3 react with 1 mole of CO_2 to produce 1 mole of urea (CH_4N_2O).

Calculate the theoretical moles of urea that can be produced from the moles of each reactant. The reactant that produces the lesser amount of urea is the limiting reactant.

Convert the theoretical moles of urea to mass using the molar mass of urea, which is approximately 60.06 g/mol, to find the theoretical yield in kilograms.

Calculate the percent yield using the formula: (actual yield / theoretical yield) * 100%, where the actual yield is given as 168.4 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 it, one must compare the mole ratios of the reactants based on the balanced chemical 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, calculated using stoichiometry based on the balanced chemical equation. It assumes complete conversion of the limiting reactant into the product without any losses. This value is essential for evaluating the efficiency of a reaction.

Percent Yield

Percent yield is a measure of the efficiency of a chemical reaction, calculated by dividing the actual yield (the amount of product obtained from the reaction) by the theoretical yield and multiplying by 100. It provides insight into how effectively the reactants were converted into products and can indicate potential losses or side reactions.

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