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Chapter 3: Problem 24

Consider the equation \(3 \mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}+\mathrm{D} .\) You react 4 moles of A with 2 moles of \(\mathrm{B}\) . Which of the following is true? a. The limiting reactant is the one with the higher molar mass. b. A is the limiting reactant because you need 6 moles of A and have 4 moles. c. B is the limiting reactant because you have fewer moles of B than A. d. B is the limiting reactant because three A molecules react with each B molecule. e. Neither reactant is limiting. Justify your choice. For those you did not choose, explain why they are incorrect.

Short Answer

Expert verified
The correct choice is (b). A is the limiting reactant because the stoichiometric ratio of A to B is 3:1, and there are not enough moles of A (only 4 moles) to react with all the moles of B present.

Step by step solution

01

Identify the balanced equation and the initial amounts of reactants.

The balanced equation is given as: \(3A + B \rightarrow C + D\) We are given 4 moles of A and 2 moles of B.
02

Calculate the stoichiometric ratio.

In this balanced equation, the stoichiometric ratio of A to B is 3:1, meaning that for each mole of B, there must be 3 moles of A present for the reaction to go to completion.
03

Determine the actual ratio of the reactants.

The actual ratio of A:B is given by the moles of A divided by the moles of B. In this case, it is given as: \(\frac{4\,\text{moles of A}}{2\,\text{moles of B}} = 2:1\)
04

Compare the stoichiometric ratio and actual ratio.

We can see that the stoichiometric ratio (3:1) is greater than the actual ratio (2:1). This indicates that there is not enough A available to react with all the B present. Therefore, A is the limiting reactant. B is not the limiting reactant since there are enough moles of B to react with all the moles of A present.
05

Evaluate and justify the answer choices.

a. The limiting reactant is the one with the higher molar mass. This statement is incorrect because the limiting reactant is determined by comparing the stoichiometric ratio and the actual ratio, not by comparing molar masses. b. A is the limiting reactant because you need 6 moles of A and have 4 moles. This statement is correct because the stoichiometric ratio of A to B is 3:1, and there are not enough moles of A to react with all the moles of B present. c. B is the limiting reactant because you have fewer moles of B than A. This statement is incorrect because the limiting reactant is determined by comparing the stoichiometric ratio and the actual ratio, not by the amounts of moles present. d. B is the limiting reactant because three A molecules react with each B molecule. This statement is incorrect because although the stoichiometric ratio is 3:1, the actual ratio favors A and there is not enough A present to react with all the B present. e. Neither reactant is limiting. This statement is incorrect because the actual ratio (2:1) does not match the stoichiometric ratio (3:1), indicating that one of the reactants is limiting. Thus, the correct choice is (b). A is the limiting reactant because you need 6 moles of A and have 4 moles.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Stoichiometric Ratio
In any chemical reaction, the stoichiometric ratio is crucial. It tells you how many moles of each reactant are needed to produce a particular product without any leftovers. This ratio is derived from the coefficients of the balanced chemical equation. For example, in the equation \(3A + B \rightarrow C + D\), the stoichiometric ratio of \(A\) to \(B\) is 3:1. This means three moles of \(A\) are required for every mole of \(B\).
If these proportional relationships aren't met, the reaction can't proceed to completion as expected. Understanding and calculating this ratio is a key step in finding the limiting reactant in a chemical reaction.
Balanced Chemical Equation
A balanced chemical equation is fundamental in stoichiometry. It ensures that the number of atoms for each element is the same on both sides of the equation. This balance adheres to the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction.
The equation \(3A + B \rightarrow C + D\) is balanced because it reflects the stable exchange where molecules of reactants transform into molecules of products without any net gain or loss of matter. Balancing these equations allows scientists and students to predict the amounts of products formed, identify reactants, and recognize limiting factors in a reaction.
Reaction Completion
For a reaction to reach completion, all reactants must be available in the stoichiometric ratios necessary for the reaction. If the reactants are not present in these required amounts, one will run out before the other can fully react, which halts the process.
In the scenario where \(4\) moles of \(A\) and \(2\) moles of \(B\) are available, the stoichiometric requirement of the reaction \(3A + B \rightarrow C + D\) isn't met as per the given conditions. This means the expected stoichiometry is not achieved because more \(A\) is needed to react with the \(B\), leading to incomplete reaction.
Reactant Comparison
One of the steps in finding the limiting reactant involves comparing the actual ratio of reactants available with the stoichiometric requirements of the balanced chemical equation. It requires evaluating which reactant will be exhausted first, thus preventing the reaction from proceeding.
In our example, even though more moles of \(B\) are present, it's not about the sheer number of moles but about meeting the stoichiometric needs. With a given actual ratio of \(2:1\), compared to the required \(3:1\), \(A\) is the limiting reactant since it's insufficient to sustain the reaction with the available \(B\). This comparison ensures efficiency and accuracy in chemical processing and lab experiments.

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Most popular questions from this chapter

One of the components that make up common table sugar is fructose, a compound that contains only carbon, hydrogen, and oxygen. Complete combustion of 1.50 \(\mathrm{g}\) of fructose produced 2.20 \(\mathrm{g}\) of carbon dioxide and 0.900 \(\mathrm{g}\) of water. What is the empirical formula of fructose?

A compound contains only \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{N}\) . Combustion of 35.0 \(\mathrm{mg}\) of the compound produces 33.5 \(\mathrm{mg} \mathrm{CO}_{2}\) and 41.1 \(\mathrm{mg}\) \(\mathrm{H}_{2} \mathrm{O}\) . What is the empirical formula of the compound?

Ammonia is produced from the reaction of nitrogen and hydrogen according to the following balanced equation: $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$ a. What is the maximum mass of ammonia that can be produced from a mixture of \(1.00 \times 10^{3} \mathrm{g} \mathrm{N}_{2}\) and \(5.00 \times 10^{2} \mathrm{g} \mathrm{H}_{2} ?\) b. What mass of which starting material would remain unreacted?

Zinc and magnesium metal each reacts with hydrochloric acid to make chloride salts of the respective metals, and hydrogen gas. A 10.00 -g mixture of zinc and magnesium produces 0.5171 g of hydrogen gas upon being mixed with an excess of hydrochloric acid. Determine the percent magnesium by mass in the original mixture.

Bornite \(\left(\mathrm{Cu}_{3} \mathrm{Fe} \mathrm{S}_{3}\right)\) is a copper ore used in the production of copper. When heated, the following reaction occurs: $$ 2 \mathrm{Cu}_{3} \mathrm{FeS}_{3}(s)+7 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{Cu}(s)+2 \mathrm{FeO}(s)+6 \mathrm{SO}_{2}(g) $$ If 2.50 metric tons of bornite is reacted with excess \(\mathrm{O}_{2}\) and the process has an 86.3\(\%\) yield of copper, what mass of copper is produced?
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