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Chapter 3: Problem 91

Titanium(IV) oxide \(\left(\mathrm{TiO}_{2}\right)\) is a white substance produced by the action of sulfuric acid on the mineral ilmenite \(\left(\mathrm{FeTiO}_{3}\right)\) $$ \mathrm{FeTiO}_{3}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{TiO}_{2}+\mathrm{FeSO}_{4}+\mathrm{H}_{2} \mathrm{O} $$ Its opaque and nontoxic properties make it suitable as a pigment in plastics and paints. In one process \(8.00 \times 10^{3} \mathrm{~kg}\) of \(\mathrm{FeTiO}_{3}\) yielded \(3.67 \times\) \(10^{3} \mathrm{~kg}\) of \(\mathrm{TiO}_{2}\). What is the percent yield of the reaction?

Short Answer

Expert verified
The percent yield of the reaction is \(\frac{3.67 \times 10^{3} \mathrm{~kg}}{8.00 \times 10^{3} \mathrm{~kg}} \times 100\% \approx 45.9\% \.

Step by step solution

01

Understand the reaction stoichiometry

We are given the chemical reaction: \(\mathrm{FeTiO}_{3}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{TiO}_{2}+\mathrm{FeSO}_{4}+\mathrm{H}_{2} \mathrm{O}\). This is a one-to-one reaction, which means one mole of \(\mathrm{FeTiO}_{3}\) produces one mole of \(\mathrm{TiO}_{2}\).
02

Calculate the theoretical yield

The theoretical yield is the maximum amount of product that can be formed from the given amount of reactant. In this case, the process used \(8.00 \times 10^{3} \mathrm{~kg}\) of \(\mathrm{FeTiO}_{3}\), which according to the reaction stoichiometry would yield the same amount of \(\mathrm{TiO}_{2}\) if the reaction go to completion. Therefore, the theoretical yield is \(8.00 \times 10^{3} \mathrm{~kg}\).
03

Calculate the percent yield

The percent yield is the ratio of the actual yield to the theoretical yield, multiplied by 100. In this case, the actual yield is \(3.67 \times 10^{3} \mathrm{~kg}\). The formula for percent yield is: \(\frac{actual~yield}{theoretical~yield} \times 100\%\). Substitute the given values into the equation to find the percent yield.

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Most popular questions from this chapter

An iron bar weighed 664 g. After the bar had been standing in moist air for a month, exactly one-eighth of the iron turned to rust \(\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)\). Calculate the final mass of the iron bar and rust.

The molar mass of caffeine is \(194.19 \mathrm{~g}\). Is the molecular formula of caffeine \(\mathrm{C}_{4} \mathrm{H}_{5} \mathrm{~N}_{2} \mathrm{O}\) or \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2} ?\)

Describe the steps involved in the mole method.

What are the empirical formulas of the compounds with the following compositions? (a) 2.1 percent \(\mathrm{H}\), 65.3 percent \(\mathrm{O}, 32.6\) percent \(\mathrm{S}\) (b) 20.2 percent \(\mathrm{Al}\), 79.8 percent \(\mathrm{Cl}\)

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?
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