Sublimation energy of \(\mathrm{Ca}\) is \(121 \mathrm{~kJ} / \mathrm{mol}\). Dissociation energy of \(\mathrm{Cl}_{2}\) is \(242.8 \mathrm{~kJ} / \mathrm{mol}\), the total ionization energy of \(\mathrm{Ca}(\mathrm{g})\) \(\rightarrow \mathrm{Ca}^{2+}(\mathrm{g})\) is \(2422 \mathrm{~kJ} / \mathrm{mol}\) and electron affinity of \(\mathrm{Cl}\) is \(-355 \mathrm{~kJ} / \mathrm{mol}\). Lattice energy of \(\mathrm{CaCl}_{2}\) is \(-2430.8 \mathrm{~kJ} / \mathrm{mol}\). What is \(\Delta H\) for the process \(\mathrm{Ca}(\mathrm{s})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \mathrm{CaCl}_{2}(\mathrm{~s})\) ? (a) \(-355 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(+3550 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(-35.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(-1720 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Step by step solution

01

Analyze the Formation of CaCl2

The formation of CaCl2 from its elements involves several steps: sublimation of Ca(s), dissociation of Cl2(g), ionization of Ca(g), electron affinity of Cl, and the formation of the lattice structure of CaCl2. Each of these steps has an associated enthalpy change.

02

Sublimation of Ca

The sublimation of Ca(s) to Ca(g) requires energy and the enthalpy change for this process is given as +121 kJ/mol.

03

Dissociation of Cl2

The dissociation of Cl2 into 2 Cl atoms requires energy and the enthalpy change for this process is given as +242.8 kJ/mol. This energy is required to break the Cl-Cl bond.

04

Ionization of Ca

The ionization of Ca(g) to Ca^2+(g) releases energy and the enthalpy change for this process is given as +2422 kJ/mol.

05

Electron Affinity

The addition of an electron to a Cl atom to form Cl- releases energy and this electron affinity is given as -355 kJ/mol. However, two Cl atoms are required per molecule of CaCl2, so the total electron affinity change is -710 kJ/mol (2 * -355 kJ/mol).

06

Lattice Energy

The formation of the lattice structure from ions releases energy and the lattice energy of CaCl2 is given as -2430.8 kJ/mol.

07

Calculate the Overall Enthalpy Change

Sum the enthalpy changes for all the steps involved in the formation of CaCl2: total enthalpy change = sublimation energy + dissociation energy/2 + ionization energy + electron affinities + lattice energy = 121 kJ + (242.8 kJ / 2) + 2422 kJ + (-710 kJ) + (-2430.8 kJ)

08

Simplify the Enthalpy Calculation

Simplify the equation by combining the values: total enthalpy change = 121 kJ + 121.4 kJ + 2422 kJ - 710 kJ - 2430.8 kJ = -476.4 kJ/mol.So, the overall enthalpy change for the reaction is -476.4 kJ/mol. This value is not listed among the provided options, indicating that there may have been a mistake in the arithmetic or in the interpretation of the question.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Thermochemistry

Thermochemistry is the study of the heat energy involved in chemical reactions and changes of state. It plays a fundamental role in understanding how energy is transformed during chemical processes. One of the key concepts in thermochemistry is the enthalpy change (\r\text{\(\Delta H\)}), which represents the heat absorbed or released at constant pressure. Calculating enthalpy changes allows us to predict whether a reaction is endothermic (absorbing heat) or exothermic (releasing heat) and to estimate the strength of chemical bonds. This knowledge is crucial for a vast range of applications, from industrial synthesis to environmental science.

Lattice Energy

Lattice energy is a measure of the binding forces holding ionic solids together. It's the energy released when gaseous ions combine to form an ionic solid, or the energy required to fully separate an ionic solid into its gaseous ions. When calcium chloride forms from calcium and chlorine, the negative lattice energy \r\text{\(-2430.8 \mathrm{~kJ} / \mathrm{mol}\)} indicates that the formation is exothermic, with a significant release of energy due to the strong electrostatic attractions between \r\text{\(\mathrm{Ca}^{2+}\)} and \r\text{\(\mathrm{Cl}^{-}\)} ions.

Sublimation Energy

Sublimation energy refers to the amount of energy needed to transform a substance from a solid directly into a gas without passing through a liquid phase. For calcium \r\text{\(\mathrm{Ca(s)}\)}, the sublimation energy is \r\text{\(+121 \mathrm{~kJ} / \mathrm{mol}\)}. This endothermic process requires energy input to overcome the forces holding the solid in its structured form.

Dissociation Energy

Dissociation energy is the amount of energy required to break a specific chemical bond. In this context, we deal with the energy to dissociate a chlorine molecule \r\text{\(\mathrm{Cl}_{2}\)} into two chlorine atoms, which is \r\text{\(+242.8 \mathrm{~kJ} / \mathrm{mol}\)}. This positive value signifies that energy must be supplied to overcome the bond between the two chlorine atoms in a \r\text{\(\mathrm{Cl}_{2}\)} molecule.

Ionization Energy

Ionization energy is defined as the energy required to remove an electron from a gaseous atom or ion. The first ionization energy refers to the removal of the first electron, with successive ionization energies increasing for further electrons. The total ionization energy for calcium to go from \r\text{\(\mathrm{Ca(g)}\)} to \r\text{\(\mathrm{Ca}^{2+}(g)\)} is significant, at \r\text{\(+2422 \mathrm{~kJ} / \mathrm{mol}\)}, reflecting the substantial energy needed to completely remove two electrons and form a \r\text{\(\mathrm{Ca}^{2+}\)} ion.

Electron Affinity

Electron affinity is the energy change that occurs when an electron is added to a neutral atom in the gaseous state, to form an anion. It is often exothermic, as seen with chlorine, where energy is released (\r\text{\(-355 \mathrm{~kJ} / \mathrm{mol}\)} per chlorine atom). For the formation of \r\text{\(\mathrm{CaCl}_{2}\)}, two atoms of chlorine take up electrons, doubling the energy change due to electron affinity.

Chemical Thermodynamics

Chemical thermodynamics involves the study of energy transformations in chemical reactions and the direction in which a chemical reaction will proceed. It combines the concepts of thermochemistry and thermodynamics to predict the spontaneous direction of processes and to determine the position of equilibrium. The enthalpy changes in the formation of calcium chloride illustrate the principles of chemical thermodynamics, where the total enthalpy change gives insight into the favorability of the reaction. The negative signs of lattice energy and electron affinity, for instance, demonstrate the spontaneous nature of those steps.

Physical Chemistry Problems

Physical chemistry problems often involve a combination of theoretical concepts and quantitative calculations to solve complex problems. An example is the problem of calculating the overall enthalpy change for the formation of calcium chloride from elemental calcium and chlorine gas. Such problems require understanding of concepts like sublimation energy, dissociation energy, ionization energy, and lattice energy, all of which contribute to the final \r\text{\(\Delta H\)} of the reaction. By ensuring each step is understood and each energy change is accurately accounted for, students can master not only the calculation but also the underlying chemical principles.