What is the percent by mass of titanium in rutile, a mineral...

Name: Problem 93, Chapter 10: Chemistry
Uploaded: 2020-12-16T20:07:40-08:00
Duration: 2 min 51 s
Channel: Lottie Adams
Description: What is the percent by mass of titanium in rutile, a mineral that contains titanium and oxygen, if structure can be described as a closest packed array of oxide ions with titanium ions in one-half of the octahedral holes? What is the oxidation number of titanium?

What is the percent by mass of titanium in rutile, a mineral that contains titanium and oxygen, if structure can be described as a closest packed array of oxide ions with titanium ions in one-half of the octahedral holes? What is the oxidation number of titanium?

Key Concepts

Percentage Composition Calculation

Percentage composition is calculated by dividing the mass of a particular element in the formula unit by the total formula mass and expressing the result as a percentage. Once the empirical formula is established (here, TiO2), the molar masses of titanium and oxygen are used to compute the mass percentage of titanium in the mineral.

Empirical Formula Determination

Determining the empirical formula involves using the structural information provided by the crystal lattice. Given a closest packed array of oxide ions and the occupancy of half of the octahedral holes by titanium ions, the ratio of titanium to oxygen is derived, leading to the empirical formula. For rutile, this process confirms that the formula is TiO2.

Oxidation State Determination

Oxidation state determination involves assigning charges to the elements in a compound based on known charges, so as to balance the overall electrical neutrality of the compound. In the case of TiO2, where oxygen typically has an oxidation state of -2, the titanium ion must adopt an oxidation state of +4 in order to neutralize the -4 total from the two oxygen ions.

Closest Packed Structures

A closest packed structure refers to an arrangement of atoms or ions in which the constituent particles are packed together as closely as possible, minimizing empty space. In many minerals, including those with oxide ions, this arrangement provides the framework upon which other ions or atoms, such as metal cations, are incorporated in specific interstitial sites.

Octahedral Voids

Octahedral voids are the spaces found within a closest packed array where an ion or atom can fit. They are called octahedral because each void is surrounded by six neighboring ions at the vertices of an octahedron. In the context of rutile, the titanium ions are positioned in half of these octahedral holes, which directly influences the stoichiometry of the compound.

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