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Ch.6 - Electronic Structure of Atoms
Chapter 6, Problem 108

(c) Consider the metal oxides whose enthalpies of formation (in kJ mol⁻¹) are listed here: Oxide K₂O₍s₂₎, CaO₍s₂₎, TiO₂₍s₂₎, V₂O₅₍s₂₎, ΔHf° -363.2, -635.1, -938.7, -1550.6. Calculate the enthalpy changes in the following general reaction for each case: MnOm₍s₂₎ + H₂(g) → nM₍s₂₎ + mH₂O(g). (You will need to write the balanced equation for each case and then compute ΔH°.)

Verified step by step guidance
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Step 1: Identify the balanced chemical equation for each metal oxide reacting with hydrogen gas. For example, for K₂O, the balanced equation is K₂O(s) + H₂(g) → 2K(s) + H₂O(g). Repeat this for CaO, TiO₂, and V₂O₅.
Step 2: Use the enthalpy of formation values provided to calculate the enthalpy change (ΔH°) for each reaction. The general formula is ΔH° = [ΣΔHf°(products)] - [ΣΔHf°(reactants)].
Step 3: For each reaction, calculate the enthalpy of formation of the products. For example, for K₂O, the products are 2K(s) and H₂O(g). Use the standard enthalpy of formation values for these substances.
Step 4: Calculate the enthalpy of formation of the reactants. For example, for K₂O, the reactants are K₂O(s) and H₂(g). Use the given enthalpy of formation for K₂O and note that the enthalpy of formation for H₂(g) is zero.
Step 5: Subtract the total enthalpy of the reactants from the total enthalpy of the products to find the enthalpy change (ΔH°) for each reaction.

Key Concepts

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

Enthalpy of Formation (ΔHf°)

The enthalpy of formation (ΔHf°) is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It is a crucial value in thermodynamics, allowing chemists to calculate the energy changes associated with chemical reactions. The values provided for metal oxides indicate how much energy is released or absorbed during their formation, which is essential for determining the overall enthalpy change in a reaction.
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Enthalpy of Formation

Balanced Chemical Equation

A balanced chemical equation represents a chemical reaction with equal numbers of each type of atom on both sides of the equation. Balancing is essential to obey the law of conservation of mass, ensuring that matter is neither created nor destroyed. In the context of the given reaction, writing a balanced equation for MnOm + H₂ → nM + mH₂O is necessary to accurately calculate the enthalpy change (ΔH°) for the reaction based on the stoichiometry of the reactants and products.
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Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps of the reaction, regardless of the pathway taken. This principle allows chemists to calculate the enthalpy change for complex reactions by using known enthalpy values of formation for the reactants and products. In this question, Hess's Law will be applied to compute the ΔH° for the reaction involving MnOm and H₂ by utilizing the enthalpy of formation values of the products and reactants.
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Related Practice
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?

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.

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). (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.

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?

Textbook Question

The two most common isotopes of uranium are 235U and 238U. (b) Using the periodic table in the frontinside cover, write the electron configuration for a U atom.