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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?
$\mathrm{TiO}_{2}$60$\%$4
01:51
Aadit S.
Chemistry 102
Chapter 10
Liquids and Solids
Liquids
Solids
Carleton College
University of Central Florida
Rice University
Brown University
Lectures
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so continuing on with the work surrounding the lattice structures. So we have to touch behavioral holes for each an ion, and either are hexagonal, close packed or cubic close packed structure. For I announce, that is the ratio of the octahedron holds toe alliance in either off these structures, that is a 1 to 1. So, for example, are oxide conform A close pack of right whilst titanium will occupy one half of the holes where these holes Octa hydro. So, for example, we let n you the number of oxide irons, What two and tetra hydro halls and octahedron halls. So one half of the octahedron holes are occupied by titanium. So we take one half multiplied by end. We get on over to for titanium. And so the ratio for our titanium two oxide islands we have on over to for titanium to and, well, oxygen that gives us a 1 to 2 ratio is therefore we have t i 02 So next we can calculate the percent by mass of titanium. So the first thing we take is the molar mass of them both. And then we calculate the Mollema off t i 02 that is 79.86 g per mole just to sign post you there. So then we can calculate the mass off titanium, where we take 47 0.86 g per mall. Divided by the 79.86 g from all multiplied by 100. We get percentage that approximately 60%. Well, at this number on the top here is titanium molecular mass. So, lastly, total oxidation state for a neutral compound is zero on the oxidation state of the island's minus two. So we can assume that the oxidation state of titanium is there is X. So we have X on, uh minus two multiplied by two is equal to zero. So therefore we sold X for four to the oxidation State of titanium is plus four
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