Problem 54 - Chemistry: The Central Science

Question

Consider the following equation: $$ \mathrm{Ca}^{+}(g)+\mathrm{e}^{-} \longrightarrow \mathrm{Ca}(g) $$ Which of the following statements are true? (i) The energy change for this process is the electron affinity of the \(\mathrm{Ca}^{+}\)ion. (ii) The energy change for this process is the negative of the first ionization energy of the Ca atom. (iii) The energy change for this process is the negative of the electron affinity of the \(\mathrm{Ca}\) atom.

Step-by-Step Solution

Answer

Only statement (i) is true for the given process, as it corresponds to the electron affinity of the Ca+ ion. Statements (ii) and (iii) are false because they refer to ionization energy and the electron affinity of a neutral Ca atom, respectively, which are not relevant to the process in question.

Step 1: Statement (i) Analysis

The given process is defined as the electron affinity of the Ca+ ion. Electron affinity refers to the energy change that occurs when an electron is added to a neutral atom or a positive ion to form a negative ion or a neutral atom, respectively. In this case, an electron is added to the Ca+ ion to form a neutral Ca atom, so statement (i) is true.

Step 2: Statement (ii) Analysis

Statement (ii) is about ionization energy, which is the energy required to remove an electron from a neutral atom or a negative ion to form a positive ion or a neutral atom, respectively. This process is the opposite of ionization energy because it involves adding an electron to the Ca+ ion to form a neutral Ca atom. Therefore, statement (ii) is false.

Step 3: Statement (iii) Analysis

Similar to statement (i), statement (iii) is about electron affinity. However, it refers to the electron affinity of a neutral Ca atom rather than the Ca+ ion. Given the process involves adding an electron to the Ca+ ion to form a neutral Ca atom, statement (iii) is not describing the energy change for this specific process. Thus, statement (iii) is false. In summary, only statement (i) is true for the given process.

Key Concepts

Ionization Energy

Ionization energy is a crucial concept in chemistry. It refers to the amount of energy needed to remove an electron from a gaseous atom or ion. This process results in the formation of a cation, or a positively charged ion.

Here are some important points about ionization energy:

• It is measured in kilojoules per mole (kJ/mol).
• Higher ionization energy means it is more difficult to remove an electron.
• Ionization energy generally increases across a period on the periodic table and decreases down a group.

In the context of the exercise, the energy change described is the opposite of ionization energy. Instead of removing an electron to form an ion, an electron is being added, which typically involves a different energy concept known as electron affinity.

Ca+ Ion

The \(Ca^{+}\) ion is calcium in a gaseous state missing one electron, making it a positively charged ion or cation. Cations are usually formed when atoms lose electrons.

Some interesting facts about the \(Ca\^{+}\) ion include:

• It plays a role in various chemical reactions involving calcium.
• As a cation, it can attract electrons, leading to electron affinity interactions.
• The removal of one electron gives it a stable electronic configuration similar to the element Argon.

In the exercise, an electron is added to this ion to transform it back into a neutral calcium atom. This process is linked to electron affinity, highlighting how ions can revert to their atomic states under certain conditions.

Energy Change Analysis

Energy change analysis is a vital part of understanding reactions and processes in chemistry. It helps in determining whether a reaction releases or absorbs energy.

Here are some key points about energy change analysis:

• Energy release is typically associated with processes like electron affinity.
• Energy absorption is generally related to ionization energy.
• Understanding these changes helps in predicting the likelihood of chemical reactions.

For the given problem, the focus is on energy change when an electron is added to \(Ca^{+}\). This scenario involves using the concept of electron affinity, where energy is typically released as the ion gains an electron. Hence, accurate analysis of energy change helps simplify and clarify these processes in chemistry.