2.4.5: Calculating Reaction Yields (Problems)

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PROBLEM $\PageIndex{1}$

The following quantities are placed in a container: 1.5 × 10²⁴ molecules of diatomic hydrogen, 1.0 mol of sulfur, and 88.0 g of diatomic oxygen.

What is the total mass in grams for the collection of all three elements?
What is the total number of moles of atoms for the three elements?
If the mixture of the three elements formed a compound with molecules that contain two hydrogen atoms, one sulfur atom, and four oxygen atoms, which substance is consumed first?
How many atoms or molecules of each remaining element would remain unreacted in the change described above ?

Answer a: 4.98 g H₂, 32 g S; 124.98 g total

Answer b: 2.49 mol H₂, 2.75 mol O₂; 6.24 mol total

Answer c: S is the limiting reactant (what would be consumed first)

Answer d: 8.978 × 10²³molecules of H₂ and 4.6 × 10²³molecules of O₂ remain

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PROBLEM $\PageIndex{2}$

What is the limiting reactant in a reaction that produces sodium chloride from 8 g of sodium and 8 g of diatomic chlorine?

Answer: The limiting reactant is Cl₂

PROBLEM $\PageIndex{3}$

Which of the postulates of Dalton's atomic theory explains why we can calculate a theoretical yield for a chemical reaction?

Answer: Postulate 4 (A compound consists of atoms of two or more elements combined in a small, whole-number ratio. In a given compound, the numbers of atoms of each of its elements are always present in the same ratio).

PROBLEM $\PageIndex{4}$

A student isolated 25 g of a compound following a procedure that would theoretically yield 81 g. What was his percent yield?

Answer: $\mathrm{Percent\: yield = 31\%}$

PROBLEM $\PageIndex{5}$

A sample of 0.53 g of carbon dioxide was obtained by heating 1.31 g of calcium carbonate. What is the percent yield for this reaction?

\[\ce{CaCO3}(s)\rightarrow \ce{CaO}(s)+\ce{CO2}(s)\]

Answer: $\mathrm{Percent\: yield = 91.9\%}$

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PROBLEM $\PageIndex{6}$

Freon-12, CCl₂F₂, is prepared from CCl₄ by reaction with HF. The other product of this reaction is HCl. Outline the steps needed to determine the percent yield of a reaction that produces 12.5 g of CCl₂F₂ from 32.9 g of CCl₄. Freon-12 has been banned and is no longer used as a refrigerant because it catalyzes the decomposition of ozone and has a very long lifetime in the atmosphere. Determine the percent yield.

Answer

$\ce{g\: CCl4\rightarrow mol\: CCl4\rightarrow mol\: CCl2F2 \rightarrow g\: CCl2F2}$

$\mathrm{\:percent\: yield=48.3\%}$

PROBLEM $\PageIndex{7}$

Citric acid, C₆H₈O₇, a component of jams, jellies, and fruity soft drinks, is prepared industrially via fermentation of sucrose by the mold Aspergillus niger. The equation representing this reaction is

\[\ce{C12H22O11 + H2O + 3O2 \rightarrow 2C6H8O7 + 4H2O}\]

What mass of citric acid is produced from exactly 1 metric ton (1.000 × 10³ kg) of sucrose (C₁₂H₂₂O₁₁) if the yield is 92.30%?

Answer: 1036 kg citric acid

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PROBLEM $\PageIndex{8}$

Toluene, C₆H₅CH₃, is oxidized by air under carefully controlled conditions to benzoic acid, C₆H₅CO₂H, which is used to prepare the food preservative sodium benzoate, C₆H₅CO₂Na. What is the percent yield of a reaction that converts 1.000 kg of toluene to 1.21 kg of benzoic acid?

\[\ce{2C6H5CH3 + 3O2 \rightarrow 2C6H5CO2H + 2H2O}\]

Answer: $\mathrm{percent\: yield=91.3\%}$

PROBLEM $\PageIndex{9}$

In a laboratory experiment, the reaction of 3.0 mol of H₂ with 2.0 mol of I₂ produced 1.0 mol of HI. Determine the theoretical yield in grams and the percent yield for this reaction.

Answer: 512 g (theoretical yield); $\mathrm{percent\: yield=25\%}$

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PROBLEM $\PageIndex{10}$

What is the limiting reactant when 1.50 g of lithium and 1.50 g of nitrogen combine to form lithium nitride, a component of advanced batteries, according to the following unbalanced equation?

\[\ce{Li + N2 \rightarrow Li3N}\]

Answer

\[\ce{6Li} + \ce{N2} \rightarrow \: \ce{2Li3N}\]

\[1.50g\: \ce{Li} \times \dfrac{1\: mole\: \ce{Li}}{6.94g\: \ce{Li}} \times\dfrac{2\: mole\: \ce{Li3N}}{6\:mole\: \ce{Li}} = 0.0720\: moles\: \ce{Li3N}\]

\[1.50g\: \ce{N2} \times \dfrac{1\: mole\: \ce{N2}}{28.02g\: \ce{N2}} \times\dfrac{2\: mole\: \ce{Li3N}}{1\:mole\: \ce{N2}} = 0.107\: moles\: \ce{Li3N}\]

$\ce{Li}$ is the limiting reactant

PROBLEM $\PageIndex{11}$

Uranium can be isolated from its ores by dissolving it as UO₂(NO₃)₂, then separating it as solid UO₂(C₂O₄)·3H₂O. Addition of 0.4031 g of sodium oxalate, Na₂C₂O₄, to a solution containing 1.481 g of uranyl nitrate, UO₂(NO₂)₂, yields 1.073 g of solid UO₂(C₂O₄)·3H₂O.

\[\ce{Na2C2O4 + UO2(NO3)2 + 3H2O ⟶ UO2(C2O4)·3H2O + 2NaNO3}\]

Determine the limiting reactant and the percent yield of this reaction.

Answer: Na₂C₂O₄ is the limiting reactant. percent yield = 86.6%

PROBLEM $\PageIndex{12}$

How many molecules of C₂H₄Cl₂ can be prepared from 15 C₂H₄ molecules and 8 Cl₂ molecules?

Answer: Only 8 molecules can be formed

PROBLEM $\PageIndex{13}$

How many molecules of the sweetener saccharin can be prepared from 30 C atoms, 25 H atoms, 12 O atoms, 8 S atoms, and 14 N atoms?

Answer: Only four molecules can be made.

PROBLEM $\PageIndex{14}$

The phosphorus pentoxide used to produce phosphoric acid for cola soft drinks is prepared by burning phosphorus in oxygen.

What is the limiting reactant when 0.200 mol of P₄ and 0.200 mol of O₂ react according to \[\ce{P4 + 5O2 \rightarrow P4O10}\]
Calculate the percent yield if 10.0 g of P₄O₁₀ is isolated from the reaction.

Answer a: O₂ is the limiting reactant

Answer b: $\mathrm{percent\: yield=88\%}$

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PROBLEM $\PageIndex{15}$

Would you agree to buy 1 trillion (1,000,000,000,000) gold atoms for $5? Explain why or why not. Find the current price of gold at http://money.cnn.com/data/commodities/ $\mathrm{(1\: troy\: ounce=31.1\: g)}$

Answer: This amount cannot be weighted by ordinary balances and is worthless.

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Contributors and Attributions

Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/85abf193-2bd...a7ac8df6@9.110).
Adelaide Clark, Oregon Institute of Technology

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