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Chapter 3: Problem 92

When heated, lithium reacts with nitrogen to form lithium nitride: $$ 6 \mathrm{Li}(s)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{Li}_{3} \mathrm{~N}(s) $$ What is the theoretical yield of \(\mathrm{Li}_{3} \mathrm{~N}\) in grams when \(12.3 \mathrm{~g}\) of \(\mathrm{Li}\) are heated with \(33.6 \mathrm{~g}\) of \(\mathrm{N}_{2} ?\) If the actual yield of \(\mathrm{Li}_{3} \mathrm{~N}\) is \(5.89 \mathrm{~g}\), what is the percent yield of the reaction?

Short Answer

Expert verified
To get the correct theoretical yield of \(Li_{3}N\), first determine the limiting reactant by using stoichiometry. Then, use this information to calculate the theoretical yield from the given reaction equation. The percent yield is then computed by comparing this theoretical yield to the actual yield provided in the problem. Detailed mathematical calculations depend on the results from each individual steps.

Step by step solution

01

Calculate number of moles of reactants

First, calculate the number of moles of Lithium (\(Li\)) and Nitrogen (\(N_{2}\)). From the periodic table, the molar masses of Lithium and Nitrogen are approximately \(6.94 g/mol\) and \(28.01 g/mol\) respectively. Since Nitrogen in this reaction is \(N_{2}\), its molar mass is \(2*28.01 g/mol = 56.02 g/mol\). The number of moles of a substance is calculated as its mass divided by its molar mass. So, the number of moles of \(Li\) and \(N_2\) are \(12.3/6.94 mol\) and \(33.6/56.02 mol\) respectively.
02

Determine the limiting reactant

The stoichiometry of the reaction shows that 6 moles of \(Li\) react with 1 mole of \(N_{2}\) to produce 2 moles of \(Li_{3}N\). By dividing the number of moles of each reactant by the stoichiometric coefficients, we find which reactant is completely used up (or the limiting reactant). The reactant that uses up first is the limiting reactant.
03

Calculate theoretical yield

The theoretical yield is the amount of product formed when the limiting reactant is completely used up. It's calculated by multiplying the number of moles of the limiting reactant by the stoichiometric coefficient ratio (2/6 for \(Li\) and 2/1 for \(N_{2}\)), and then by the molar mass of \(Li_{3}N\) (approximately \(34.83 g/mol\)).
04

Calculate percent yield

The percent yield is the ratio of the actual yield to the theoretical yield, multiplied by 100. It's given by the formula: \[ \% yield = \frac{hyield}{theoretical yield} \times 100 \] In this problem, \(yield = 5.89g\).

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Most popular questions from this chapter

A sample of iron weighing \(15.0 \mathrm{~g}\) was heated with potassium chlorate \(\left(\mathrm{K} \mathrm{ClO}_{3}\right)\) in an evacuated container. The oxygen generated from the decomposition of \(\mathrm{KClO}_{3}\) converted some of the Fe to \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). If the combined mass of Fe and \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) was \(17.9 \mathrm{~g},\) calculate the mass of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) formed and the mass of \(\mathrm{KClO}_{3}\) decomposed.

Define the term "mole." What is the unit for mole in calculations? What does the mole have in common with the pair, the dozen, and the gross? What does Avogadro's number represent?

Describe how the knowledge of the percent composition by mass of an unknown compound can help us identify the compound.

A certain metal oxide has the formula MO, where \(\mathrm{M}\) denotes the metal. A 39.46-g sample of the compound is strongly heated in an atmosphere of hydrogen to remove oxygen as water molecules. At the end, \(31.70 \mathrm{~g}\) of the metal is left over. If \(\mathrm{O}\) has an atomic mass of 16.00 amu, calculate the atomic mass of \(\mathrm{M}\) and identify the element.

Give an everyday example that illustrates the limiting reagent concept.
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