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Chapter 3: Problem 16

Consider the equation \(2 A+B \longrightarrow A_{2} B .\) If you mix \(1.0 \mathrm{~mole}\) of \(A\) with \(1.0\) mole of \(B\), what amount (moles) of \(A_{2} B\) can be produced?

Short Answer

Expert verified
In the chemical reaction \(2A + B \longrightarrow A_{2}B\), when 1.0 mole of A and 1.0 mole of B are mixed, 0.5 moles of \(A_{2}B\) can be produced.

Step by step solution

01

Write the balanced chemical equation

\ First, let's write out the balanced chemical equation for the given reaction: \(2A + B \longrightarrow A_{2}B\) Since the equation is already balanced, we do not need to balance it.
02

Calculate the initial moles of reactants

\ The initial amounts of reactants A and B are given as: Moles of A = 1.0 mole Moles of B = 1.0 mole
03

Determine the limiting reactant

\ To find the limiting reactant, we must compare the mole ratio of A to B in the reaction. According to the balanced equation, 2 moles of A are required to react with 1 mole of B to produce A₂B. Divide the moles of each reactant by their respective coefficients from the balanced equation to find the reaction ratio. Reaction ratio A = Moles of A / 2 = 1.0 / 2 = 0.5 Reaction ratio B = Moles of B / 1 = 1.0 / 1 = 1.0 Since the reaction ratio of A is less than that of B, A is the limiting reactant in this reaction.
04

Calculate the moles of product A₂B produced

\ Now that we know A is the limiting reactant, we can use stoichiometry to determine the amount of product A₂B that can be formed. From the balanced equation, 2 moles of A will react with 1 mole of B to produce 1 mole of A₂B. Using the stoichiometric coefficients, we can set up the following proportion: (1 mole of A₂B / 2 moles of A) = (x moles of A₂B / 1.0 mole of A) Now, we can solve for x, which is the amount of product A₂B produced: x moles of A₂B = (1 mole of A₂B / 2 moles of A) * 1.0 mole of A x moles of A₂B = 0.5 mole of A₂B So, 0.5 moles of A₂B can be produced when 1.0 mole of A is mixed with 1.0 mole of B.

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Most popular questions from this chapter

Methane \(\left(\mathrm{CH}_{4}\right)\) is the main component of marsh gas. Heating methane in the presence of sulfur produces carbon disulfide and hydrogen sulfide as the only products. a. Write the balanced chemical equation for the reaction of methane and sulfur. b. Calculate the theoretical yield of carbon disulfide when 120\. g of methane is reacted with an equal mass of sulfur.

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