Problem 74 - Chemistry

Question

Calculate the energy change in kilojoules per mole when lithium atoms lose an electron to bromine atoms to form isolated \(\mathrm{Li}^{+}\) and \(\mathrm{Br}^{-}\) ions. [The \(E_{\mathrm{i}}\) for \(\mathrm{Li}(g)\) is \(520 \mathrm{~kJ} / \mathrm{mol}\); the \(E_{\text {ea }}\) for \(\mathrm{Br}(\mathrm{g})\) is \(-325 \mathrm{~kJ} / \mathrm{mol} .]\)

Step-by-Step Solution

Answer

The energy change is 195 kJ/mol, which is endothermic.

Step 1: Identify the Given Values

We are given the ionization energy for lithium, which is the energy required to remove an electron from a lithium atom in gaseous state. This value is \( E_i = 520 \, \text{kJ/mol} \). For bromine, we are given the electron affinity, which is the energy change when a bromine atom in gaseous state gains an electron. This value is \( E_{ea} = -325 \, \text{kJ/mol} \).

Step 2: Understand the Concept

When lithium loses an electron, energy is consumed, equal to the ionization energy of lithium. When bromine gains an electron, energy is released, equal to the negative of its electron affinity. The total energy change in forming the ions is the sum of these two values.

Step 3: Set Up the Energy Change Equation

The total energy change \( \Delta E \) can be calculated by adding the ionization energy \( E_i \) of lithium and the electron affinity \( E_{ea} \) of bromine: \[ \Delta E = E_i + E_{ea} \] where \( E_i = 520 \, \text{kJ/mol} \) and \( E_{ea} = -325 \, \text{kJ/mol} \).

Step 4: Calculate the Energy Change

Substitute the given values into the equation: \[ \Delta E = 520 \, \text{kJ/mol} + (-325 \, \text{kJ/mol}) \] Calculate the result: \[ \Delta E = 520 \, \text{kJ/mol} - 325 \, \text{kJ/mol} = 195 \, \text{kJ/mol} \]

Step 5: Interpret the Result

The positive value of \( 195 \, \text{kJ/mol} \) indicates that the formation of \( \mathrm{Li}^+ \) and \( \mathrm{Br}^- \) ions is an endothermic process, required more energy than released.

Key Concepts

Understanding Electron Affinity

Electron affinity is an important concept in chemistry that describes the energy change when an electron is added to a neutral atom in the gaseous state. In simple terms, it tells us how much energy is released when an atom gains an electron. Think of it as the atom's attraction for an additional electron.
In the case of bromine, its electron affinity is given as \(-325 \, \text{kJ/mol}\). The negative sign indicates that energy is released when a bromine atom gains an electron.
This means bromine has a relatively high tendency to attract an extra electron, making it more stable in its anion form, denoted as \(\text{Br}^-\).

• Higher absolute values of electron affinity suggest a stronger attraction for additional electrons.
• The negative sign shows energy release, contributing to the stability of the ion formed.

Understanding this concept helps in analyzing chemical reactions, especially those involving electron transfer, such as the one between lithium and bromine.

Lithium Ion: Formation and Characteristics

The lithium ion \(\text{Li}^+\) forms when a lithium atom loses an electron. This process requires energy, known as ionization energy. For lithium, the ionization energy is \(520 \, \text{kJ/mol}\), which is the energy needed to remove one electron from \(\text{Li} (g)\).

Removing an electron from lithium involves energy input because it must overcome the attraction between the negatively charged electron and the positively charged nucleus.

• This makes the removal process endothermic, meaning it requires energy.
• Lithium, being in Group 1 of the periodic table, generally has a low ionization energy compared to elements in other groups, due to its single electron in the outer shell.

Once lithium loses its electron, it becomes a \(\text{Li}^+\) ion which is the cationic form, more stable in many reactions.

Bromine Ion: Formation and Impact

Bromine (\(\text{Br}\)) naturally tends to gain an electron to become more stable. Upon gaining an electron, it forms a bromine ion, \(\text{Br}^-\). The energy associated with this process is captured by the concept of electron affinity, with bromine having a notable energy release of \(-325 \, \text{kJ/mol}\).

This means bromine is eager to fill its valence electron shell, achieving a stable electronic configuration similar to noble gases.

• The \(\text{Br}^-\) ion is an anion, meaning it carries an extra negative charge due to the additional electron.
• This tendency to gain an electron makes bromine reactive, particularly with elements that have a low ionization energy, like lithium.

The formation of \(\text{Br}^-\) is exothermic, which complements the energy influx needed to form \(\text{Li}^+\), illustrating the electron transfer and bonding between differing electronegativities.