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Chapter 12: Problem 63

Enthalpy change in the following process is \(\mathrm{M}+\mathrm{e}^{-} \longrightarrow \mathrm{M}^{-}, \Delta \mathrm{H}=\mathrm{X} \mathrm{kJ} \mathrm{mole}^{-1}\) Which of the following process have enthalpy change \(=\mathrm{X} \mathrm{kJ} \mathrm{mole}^{-1} ?\) (a) \(\mathrm{M}^{-} \longrightarrow \mathrm{M}+\mathrm{e}^{-}\) (b) \(\mathrm{M}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{M}\) (c) \(\mathrm{M}^{2+}+\mathrm{e}^{2} \longrightarrow \mathrm{M}^{+}\) (d) \(\mathrm{M}+\mathrm{e}^{-} \longrightarrow \mathrm{M}^{-}\)

Short Answer

Expert verified
The correct process is (d): \( \mathrm{M} + \mathrm{e}^{-} \longrightarrow \mathrm{M}^{-} \).

Step by step solution

01

Identify the given reaction

The enthalpy change given in the problem is for the reaction: \( \mathrm{M} + \mathrm{e}^{-} \longrightarrow \mathrm{M}^{-} \) with \( \Delta \mathrm{H} = \mathrm{X} \mathrm{kJ} \text{ mole}^{-1} \). Here, a neutral atom \( \mathrm{M} \) gains an electron to become an anion \( \mathrm{M}^{-} \).
02

Analyze each option's reaction

Let's analyze each option:(a) \( \mathrm{M}^{-} \longrightarrow \mathrm{M} + \mathrm{e}^{-} \): This is the reverse reaction of the given process, where an anion loses an electron to form a neutral atom. The enthalpy change for this reaction would be \( -X \mathrm{kJ} \text{ mole}^{-1} \) (opposite in sign because it's the reverse).
03

Determine pairs for Option (b)

(b) \( \mathrm{M}^{+} + \mathrm{e}^{-} \longrightarrow \mathrm{M} \): In this process, a cation gains an electron to form a neutral atom. Typically, this process does not have the same enthalpy change as forming an anion from a neutral atom as described in the given reaction.
04

Examine Option (c)

(c) \( \mathrm{M}^{2+} + \mathrm{e}^{2-} \longrightarrow \mathrm{M}^{+} \): This would involve a doubly charged cation gaining one electron to become a singly charged cation. The stoichiometry does not match, nor does the nature of enthalpy change align with the given reaction \( \Delta \mathrm{H} = X \mathrm{kJ} \text{ mole}^{-1} \).
05

Confirmation of given process (Option (d))

(d) \( \mathrm{M} + \mathrm{e}^{-} \longrightarrow \mathrm{M}^{-} \): This is the same as the original reaction given in the problem. Hence, the enthalpy change for this process is clearly \( X \mathrm{kJ} \text{ mole}^{-1} \), matching the description provided.

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Key Concepts

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

Thermochemistry
Thermochemistry focuses on the heat changes that occur during chemical reactions. It deals with the relationship between chemical reactions and energy changes involving heat. The enthalpy change is a crucial concept in thermochemistry. It's the amount of heat absorbed or released in a reaction at constant pressure. Understanding how different reactions absorb or release energy helps us manipulate reactions for desired results. For example, knowing the enthalpy change helps predict reaction feasibility under given conditions. Key to understanding enthalpy changes is realizing that they can be positive or negative:
  • A positive enthalpy change (9H > 0) indicates an endothermic process, where heat is absorbed.
  • A negative enthalpy change (9H < 0) indicates an exothermic process, where heat is released.
Ionization Energy
Ionization energy is the energy required to remove an electron from a gaseous atom or ion. It's a fundamental property that measures the tendency of an atom to resist losing an electron. For instance, turning a neutral atom into a cation involves overcoming the attraction between the negatively charged electron and the positively charged nucleus:
  • First ionization energy refers to the removal of the first electron.
  • Successive ionization energies refer to removing additional electrons, each requiring more energy.
Ionization energies are crucial for understanding the stability of ions and help predict the reactivity of elements. Generally, ionization energy increases across a period and decreases down a group in the periodic table.
Chemical Reactions
Chemical reactions are processes that lead to the transformation of one set of chemical substances to another. They involve breaking and forming bonds between atoms, leading to changes in the composition and energy of substances involved. In reactions:
  • Reactants are the starting substances.
  • Products are the substances formed as a result.
Each reaction involves changes in energy, usually measured as enthalpy. The nature of these energy changes can dictate whether a reaction is feasible. Reactions where products are at a lower energy state than reactants tend to be spontaneous.
Electron Affinity
Electron affinity measures an atom's tendency to gain an electron, forming a negative ion. It's the energy change when an electron is added to a gaseous atom. Electron affinities vary across the periodic table and provide insights into the chemical properties of elements. A higher electron affinity indicates a greater tendency to accept an electron:
  • Most nonmetals have high electron affinities, making them more likely to form anions.
  • Typically, electron affinity becomes more negative across a period and less negative down a group.
This property is central to the process of forming anions during chemical reactions, where energy changes are described by the enthalpy of the process.

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Most popular questions from this chapter

According to Modern Periodic Law, the physical and chemical properties of elements are a periodic function of their atomic number. When the elements are arranged according to this law, a table is obtained in which the elements with similar properties are placed together. The properties of elements are gradually changing but repeated at regular intervals. An element has exceptional outer electronic configuration as \(4 \mathrm{~d}^{10} 5 \mathrm{~s}^{0}\). It belongs to (a) 5 th period, group 10 (b) 4th period, group 11 (c) 5 th period, group 11 (d) 4th period, group 10

The values of \(\mathrm{IE}_{1}, \mathrm{IE}_{2}, \mathrm{IE}_{3}, \mathrm{IE}_{4}\) and \(\mathrm{IE}_{5}\) are \(7.1,14.3\), \(34.5,46.8\) and \(162.2 \mathrm{eV}\) respectively. Number of valence electrons in that element is __ .

The correct order of decreasing first ionization potential is (a) \(\mathrm{Ca}>\mathrm{K}>\mathrm{Rb}>\mathrm{Cs}\) (b) \(\mathrm{Cs}>\mathrm{Rb}>\mathrm{K}>\mathrm{Ca}\) (c) \(\mathrm{Ca}>\mathrm{Cs}>\mathrm{Rb}>\mathrm{K}\) (d) \(\mathrm{K}>\mathrm{Rb}>\mathrm{Cs}>\mathrm{Ca}\)

The formation of the oxide ion \(\mathrm{O}^{2-}(\mathrm{g})\) require first an exothermic and then an endothermic step as shown below \(\mathrm{O}(\mathrm{g})+\mathrm{e}^{-} \longrightarrow \mathrm{O}^{-}(\mathrm{g}) ; \Delta \mathrm{H}^{0}=-142 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(\mathrm{O}^{-}(\mathrm{g})+\mathrm{e}^{-} \longrightarrow \mathrm{O}^{2-}(\mathrm{g}) ; \Delta \mathrm{H}^{0}=844 \mathrm{~kJ} \mathrm{~mol}^{-1}\) This is because (a) oxygen is more electronegative (b) oxygen has high electron affinity (c) \(\mathrm{O}^{-}\)ion has comparatively larger size than oxygen atom (d) \(\mathrm{O}^{-}\)ion will tend to resist the addition of another electron

Which of the following ion has the highest value of ionic radius? (a) \(\mathrm{F}^{-}\) (b) \(\mathrm{O}^{2-}\) (c) \(\mathrm{B}^{3+}\) (d) \(\mathrm{Li}^{+}\)
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