Calculate the theoretical yield of product (in moles) for each initial amount of reactants.
3 Mn(s) + 2 O₂(g) → Mn₃O₄(s)
a. 3 mol Mn, 2 mol O₂
b. 4 mol Mn, 7 mol O₂
c. 27.5 mol Mn, 43.8 mol O₂

검증된 단계별 안내

Identify the balanced chemical equation: 3 \(\text{ Mn}\)(s) + 2 \(\text{ O}\)_2(g) \(\rightarrow\) \(\text{ Mn}\)_3\(\text{O}\)_4(s)

Determine the molar ratio between reactants and product from the balanced equation: 3 \(\text{ mol Mn}\) : 2 \(\text{ mol O}\)_2 : 1 \(\text{ mol Mn}\)_3\(\text{O}\)_4

Calculate the theoretical yield of Mn_3O_4 based on the amount of Mn: \(\frac{4 \text{ mol Mn}\)}{3 \(\text{ mol Mn}\)} \(\times\) 1 \(\text{ mol Mn}\)_3\(\text{O}\)_4

Calculate the theoretical yield of Mn_3O_4 based on the amount of O_2: \(\frac{7 \text{ mol O}\)_2}{2 \(\text{ mol O}\)_2} \(\times\) 1 \(\text{ mol Mn}\)_3\(\text{O}\)_4

Identify the limiting reactant by comparing the theoretical yields from Mn and O_2, and use the smaller yield as the theoretical yield of Mn_3O_4.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a given reaction based on balanced chemical equations. Understanding stoichiometry is essential for calculating theoretical yields, as it provides the mole ratios needed to determine how much product can be formed from specific amounts of reactants.

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. Identifying the limiting reactant is crucial for yield calculations, as it dictates the extent of the reaction. In the given question, one must compare the mole ratios of the reactants to find which one limits the formation of Mn3O4.

Theoretical Yield

Theoretical yield is the maximum amount of product that can be generated from a given amount of reactants, assuming complete conversion and no losses. It is calculated using stoichiometric relationships derived from the balanced chemical equation. The theoretical yield is important for evaluating the efficiency of a reaction and is often compared to the actual yield obtained in practice to determine the reaction's success.

Calculate the theoretical yield of product (in moles) for each initial amount of reactants. 3 Mn(s) + 2 O2(g) → Mn3O4(s) a. 3 mol Mn, 2 mol O2b. 4 mol Mn, 7 mol O2c. 27.5 mol Mn, 43.8 mol O2