Titanium(IV) oxide (TiO) is a white substance produced by...

Titanium(IV) oxide (TiO_) is a white substance produced by the action of sulfuric acid on the mineral ilmenite (FeTiO $_{3}$ ): $$\mathrm{FeTiO}_{3}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{TiO}_{2}+\mathrm{FeSO}_{4}+\mathrm{H}_{2} \mathrm{O}$$ 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?

Titanium(IV) oxide (TiO_) is a white substance produced by the action of sulfuric acid on the mineral ilmenite (FeTiO $_{3}$ ):
$$\mathrm{FeTiO}_{3}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{TiO}_{2}+\mathrm{FeSO}_{4}+\mathrm{H}_{2} \mathrm{O}$$
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?

Key Concepts

Percent Yield

Percent yield is a measure of the efficiency of a chemical reaction, expressed as the ratio of the actual yield obtained from the reaction to the theoretical yield, multiplied by 100. It provides insight into how practical or loss-prone the reaction process is, taking into account real-world conditions such as incomplete reactions or side reactions.

Mole Concept and Molar Mass

The mole concept is a fundamental principle in chemistry that links the atomic scale of elements to measurable quantities. Molar mass allows conversion between the mass of substances and the number of moles, enabling the use of stoichiometric ratios from the balanced equation in yield calculations.

Theoretical Yield

The theoretical yield is the maximum amount of product that can be formed in a chemical reaction based on the stoichiometric relationships in the balanced equation. It is calculated by converting the given amount of a reactant to moles, using the mole ratio from the balanced equation to determine the number of moles of product expected, and then converting that back to mass.

Stoichiometry

Stoichiometry is the quantitative study of reactants and products in a chemical reaction. It uses the balanced chemical equation to relate the moles (or masses) of reactants consumed and products formed, serving as the foundation for calculating theoretical yields and establishing the proportions in which substances react.

Transcript

00:01 So for this problem, we have a reaction involving titanium oxide.

00:05 And we want to find the percent yield of this reaction given this chemical reaction as a whole.

00:12 So we have f .e.

00:16 T .i .o .3 plus h2 s .4 yields t .i .o .2 plus f .e.

00:28 S .4 plus h2o.

00:29 So we know that our initial quantity of f -e -t -i -o -3 is 8 times 10 to 3 kilograms, and we know that our yield of titanium oxide was 3 .67 times 10 to 3 kilograms.

00:53 So the first step in solving this problem is we're going to have to find the molar masses of both of these substances so we can find, or we can find, or we can find, can do relevant calculations regarding them.

01:04 So for f -e -t -i -o -3, we have one iron atom, which is 55 .85 grams per mole.

01:17 We then have titanium, which is 47 .87 grams per mole.

01:27 And finally, we have three oxygians, which are each 16 .0 grams per mole.

01:31 We multiply this through, we get 151 .71 grams per mole is our molar mass.

01:41 Now we want to find the molar mass of titanium oxide.

01:45 Well, one titanium atom, which is 74 .87 grams from all, and two oxygen atoms, which are each 16 .0 grams per mole.

01:57 We multiply this through.

01:58 You get 79 .87 grams per mole.

02:03 So now that we found, the molar mass of both the substances, we want to then convert kilograms of feti -o -3 into kilograms of titanium oxide so we can then find the theoretical yield.

02:19 In other words, how much titanium oxide we expect to produce if all of the f -e -ti -o -3 reacts properly...

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