Question

Which titanium-containing mineral, rutile $\left({\mathrm{TiO}}_2\right)$ or ilmenite (FeTiO ${}_3),$ has the larger percentage of titanium?

Short answer

Rutile $\left({\mathrm{TiO}}_2\right)$ has a percentage of titanium of 59.93%, while ilmenite (FeTiO${}_3$) has a percentage of titanium of 31.56%. Therefore, rutile has the larger percentage of titanium.

Step-by-step solution

Find the molar mass of each compound

To find the molar mass of each compound, we will add up the atomic masses of each element present in each compound. The molar mass of rutile (TiO2) = (1 * Molar mass of Ti) + (2 * Molar mass of O) Molar masses: Ti = 47.87 g/mol, O = 16.00 g/mol The molar mass of ilmenite (FeTiO3) = (1 * Molar mass of Fe) + (1 * Molar mass of Ti) + (3 * Molar mass of O) Molar masses: Fe = 55.85 g/mol, Ti = 47.87 g/mol, O = 16.00 g/mol

Calculate the percent composition of titanium in both compounds

For percent composition, we divide the molar mass of the element (titanium) by the total molar mass of the compound, and multiply the result by 100 to get percent. Percentage of titanium in rutile (TiO2) = (Molar mass of Ti / Molar mass of TiO2) x 100 Percentage of titanium in ilmenite (FeTiO3) = (Molar mass of Ti / Molar mass of FeTiO3) x 100

Find out which mineral has the larger percentage of titanium

Compare the percentages obtained to determine which mineral has the larger percentage of titanium.

Calculate the molar mass of rutile and ilmenite and the percent composition of titanium in each compound

Molar mass of rutile (TiO2) = (1 * 47.87) + (2 * 16.00) = 47.87 + 32 = 79.87 g/mol Percentage of titanium in rutile (TiO2) = (47.87 / 79.87) x 100 = 59.93 % Molar mass of ilmenite (FeTiO3) = (1 * 55.85) + (1 * 47.87) + (3 * 16.00) = 55.85 + 47.87 + 48 = 151.72 g/mol Percentage of titanium in ilmenite (FeTiO3) = (47.87 / 151.72) x 100 = 31.56 %

Compare results and conclude

By comparing the percentage of titanium in both minerals, we can conclude the following: Percentage of titanium in rutile (TiO2) = 59.93 % Percentage of titanium in ilmenite (FeTiO3) = 31.56 % Rutile (TiO2) has the larger percentage of titanium when compared to ilmenite (FeTiO3).

Key concepts

Molar Mass

Understanding the molar mass of a compound is critical for various calculations in chemistry, including finding percent compositions. Molar mass is defined as the mass of one mole of a substance, and is typically expressed in grams per mole (g/mol). One mole of any substance contains Avogadro's number ($6.022\times {10}^{23}$ particles) of those substances.

For compounds like rutile (\text{TiO}_2) and ilmenite (\text{FeTiO}_3), the molar mass is calculated by adding the molar masses of each individual element within the compound. For example, to calculate the molar mass of rutile, you would add the molar mass of titanium (\text{Ti}) once and the molar mass of oxygen (\text{O}) twice since there are two oxygen atoms in rutile.

\text{Molar Mass of TiO}_2 = 1 \times \text{Molar Mass of Ti} + 2 \times \text{Molar Mass of O}
The concept of molar mass serves as a bridge between the microscopic world of atoms and molecules and the macroscopic world we interact with daily.

Chemical Composition

Chemical composition refers to the identity and proportion of elements in a chemical substance. Using the concept of molar mass, one can determine the percent composition of an element within a compound. This is the percentage by mass of each element in the overall compound. The calculation is a simple ratio of the molar mass of the specific element to the total molar mass of the compound, multiplied by 100%.

Understanding the chemical composition is important because it defines the properties of the substance and dictates how it will react with other substances. For instance, the percentage of titanium in rutile and ilmenite determines the value and applications of these minerals. The percent composition is not only essential in commercial valuations but is also fundamental in stoichiometric calculations as it describes the proportion of reactants and products in chemical reactions.

Stoichiometry

Stoichiometry is a section of chemistry that involves the calculation of the quantities of reactants and products in a chemical reaction. It's based on the law of conservation of mass where the mass of the reactants equals the mass of the products. A stoichiometric calculation often starts with a balanced chemical equation from which the ratios of moles involved are derived.

However, to perform stoichiometric calculations, a solid understanding of molar masses and chemical composition is needed. For example, being able to quickly identify the percentage of titanium in minerals like rutile and ilmenite through their percent compositions enables the calculation of how much pure titanium can be extracted from a given amount of the mineral. This is a practical application of stoichiometry in industrial chemistry and resource management. Stoichiometry is not only pivotal in academic exercises but also in real-life situations such as the manufacturing of various products where precise amounts of substances are required.