The discovery of hafnium, element number 72, provided a controversial episode in chemistry. G. Urbain, a French chemist, claimed in 1911 to have isolated an element number 72 from a sample of rare earth (elements 58–71) compounds. However, Niels Bohr believed that hafnium was more likely to be found along with zirconium than with the rare earths. D. Coster and G. von Hevesy, working in Bohr’s laboratory in Copenhagen, showed in 1922 that element 72 was present in a sample of Norwegian zircon, an ore of zirconium. (The name hafnium comes from the Latin name for Copenhagen, Hafnia). (c) Solid zirconium dioxide, ZrO₂, reacts with chlorine gas in the presence of carbon. Starting with a 55.4-g sample of ZrO₂, calculate the mass of ZrCl₄ formed, assuming that ZrO₂ is the limiting reagent and assuming 100% yield.

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Write the balanced chemical equation for the reaction: ZrO2 + 2Cl2 + 2C -> ZrCl4 + 2CO.

Calculate the molar mass of ZrO2 by adding the atomic masses of zirconium (Zr) and oxygen (O).

Determine the number of moles of ZrO2 in the 55.4 g sample by dividing the mass of ZrO2 by its molar mass.

Using the stoichiometry of the balanced equation, find the number of moles of ZrCl4 produced from the moles of ZrO2, noting that the molar ratio of ZrO2 to ZrCl4 is 1:1.

Calculate the mass of ZrCl4 formed by multiplying the number of moles of ZrCl4 by its molar mass, which is the sum of the atomic masses of zirconium (Zr) and chlorine (Cl).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a reaction based on balanced chemical equations. Understanding stoichiometry is essential for calculating the mass of products formed from given reactants, as it involves mole ratios derived from the coefficients in the balanced equation.

Limiting Reagent

The limiting reagent is the reactant that is completely consumed first in a chemical reaction, thus determining the maximum amount of product that can be formed. Identifying the limiting reagent is crucial for stoichiometric calculations, as it dictates the extent of the reaction. In the context of the question, ZrO2 is specified as the limiting reagent, meaning that its amount will limit the formation of ZrCl4.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in a chemical formula. In the given problem, calculating the molar mass of ZrO2 and ZrCl4 is necessary to convert between grams and moles, enabling the determination of how much ZrCl4 can be produced from the available ZrO2.

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Textbook Question

The discovery of hafnium, element number 72, provided a controversial episode in chemistry. G. Urbain, a French chemist, claimed in 1911 to have isolated an element number 72 from a sample of rare earth (elements 58–71) compounds. However, Niels Bohr believed that hafnium was more likely to be found along with zirconium than with the rare earths. D. Coster and G. von Hevesy, working in Bohr's laboratory in Copenhagen, showed in 1922 that element 72 was present in a sample of Norwegian zircon, an ore of zirconium. (The name hafnium comes from the Latin name for Copenhagen, Hafnia). (a) How would you use electron configuration arguments to justify Bohr's prediction?

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Textbook Question

The discovery of hafnium, element number 72, provided a controversial episode in chemistry. G. Urbain, a French chemist, claimed in 1911 to have isolated an element number 72 from a sample of rare earth (elements 58–71) compounds. However, Niels Bohr believed that hafnium was more likely to be found along with zirconium than with the rare earths. D. Coster and G. von Hevesy, working in Bohr's laboratory in Copenhagen, showed in 1922 that element 72 was present in a sample of Norwegian zircon, an ore of zirconium. (The name hafnium comes from the Latin name for Copenhagen, Hafnia). (d) Using their electron configurations, account for the fact that Zr and Hf form chlorides MCl₄ and oxides MO₂.

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Textbook Question

The first 25 years of the twentieth century were momentous for the rapid pace of change in scientists' understanding of the nature of matter. (b) In what ways is de Broglie's hypothesis, as it applies to electrons, consistent with J. J. Thomson's conclusion that the electron has mass? In what sense is it consistent with proposals preceding Thomson's work that the cathode rays are a wave phenomenon?

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