A metal burns in air at 600^∘ C under high pressure to form an oxide with formula MO2. This comp

step 1 The easiest way to start this question is by assuming that you have 100 grams total. From there,

A metal burns in air at 600^∘ C under high pressure to form...

A metal burns in air at $600^{\circ} \mathrm{C}$ under high pressure to form an oxide with formula $\mathrm{MO}_{2}$. This compound is $23.72 \%$ oxygen by mass. The distance between touching atoms in a cubic closest packed crystal of this metal is $269.0 \mathrm{pm} .$ What is this metal? What is its density?

Key Concepts

Percent Composition Analysis

This concept involves using the mass percentages of elements in a compound to determine the ratio of the constituent elements. In problems like this, the percentage of oxygen in the oxide can be used with the known atomic mass of oxygen to work back to the atomic mass of the metal, which is a critical step in identifying the metal from its oxide composition.

Stoichiometric Determination of Molar Mass

This concept is about applying stoichiometry to relate the masses of reactants and products in a chemical formula. With the mass percentage and the stoichiometric coefficients provided in the compound's formula, one can set up an equation that relates the atomic mass of the metal to the given percent composition, allowing for the determination of the metal’s molar mass.

Cubic Close?Packed Crystal Structure

The cubic close?packed (ccp) crystal structure, often equivalent to the face?centered cubic (FCC) structure, is a fundamental arrangement of atoms in a solid. This concept includes understanding how atoms are packed in such lattices, the number of atoms per unit cell, and the high packing efficiency, all of which are used when calculating properties like density.

Atomic Radius and Lattice Parameter Relationship

In a closely packed structure, the distance between the centers of touching atoms is directly related to the atomic radius. Specifically, for an FCC lattice, this distance helps determine the unit cell edge length. Understanding this geometric relationship is crucial for converting between interatomic distances and lattice dimensions used in further calculations.

Density Calculation from Crystalline Structure

This concept relates the microscopic structural parameters of a crystal, such as the number of atoms per unit cell, the unit cell volume, and the atomic mass, to the macroscopic property of density. Using the relation density = (number of atoms per cell × atomic mass)/(Avogadro's number × cell volume), one can compute the density of the metal from its crystallographic and atomic data.

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