Ionization Energy Formula: Definition, Solved Examples

Lonization Energy Formula refers to the amount of energy required to remove an electron from either a gaseous atom (denoted as A) or a gaseous molecule (denoted as AB). This energy is also sometimes referred to as the "threshold" or "appearance" energy or potential. It can be determined using a mass spectrometer, as illustrated in the following equations:

Energy + A → A + e-

Energy + AB → AB + e-

The ionization energy is a critical measure of how tightly an atom retains its electrons. A higher ionization energy indicates a stronger electron binding. This relationship is inversely related to atomic radii; usually, as atomic radii increase, ionization energies decrease, and vice versa.

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Ionization Energy Formula Solved Example

Example 1: Comparing Copper and Potassium Ionization Energies

In both copper and potassium, the outer electron is located in the 4s-orbital. However, the first ionization energy for copper (745 kJ mol-1) is higher than that of potassium (418 kJ mol-1). This disparity can be explained as follows:

Potassium (K): Atomic number 19, electronic configuration [Ar] 4s¹.

Copper (Cu): Atomic number 29, electronic configuration [Ar] 3d¹⁰4s¹.

Both elements have their outermost electron in the 4s level. However, copper has ten additional electrons in the 3d level. The diffuse and strongly directional nature of the d-electrons in copper provides less shielding to the 4s electron from the nuclear charge. Consequently, the 4s electron in copper experiences a more effective nuclear charge, resulting in a significantly higher ionization energy compared to potassium.

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Example 2: Calculating the Energy Required for Converting Aluminum to Al3+ Ions

To determine the energy needed to convert all aluminum (Al) atoms to Al³⁺ ions in 0.720 grams of Al vapor, you can use the first, second, and third ionization energies of Al, which are 578, 1817, and 2745 kJ mol-1, respectively. Here's the calculation:

Total energy required for the conversion Al → Al³⁺

= IE₁ + IE₂ + IE₃

= (578 + 1817 + 2745) kJ mol-1

= 5140 kJ mol-1

The number of moles in 0.720 grams of Al can be calculated as:

Number of moles in 0.720 g of Al = (0.720/27) = 0.03 moles or 3 × 10⁻² moles

Therefore, the ionization energy required for 3 moles of aluminum is 5140 kJ. For 3 × 10⁻² moles of Al, the energy required can be determined using the proportion:

3 moles — 5140 kJ

3 × 10⁻² moles — X

X = (5140 × 3 × 10⁻²) / 3 = 5140 × 10⁻² kJ = 51.4 kJ

Hence, 3 × 10⁻² moles of Al requires 51.4 kJ of ionization energy for the conversion to Al³⁺ ions.

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Ionization Energy for An Element

Ionization energy, also recognized as ionization potential, represents a fundamental characteristic of elements found within the periodic table. It signifies the energy quantity needed to eliminate one mole of electrons from one mole of atoms existing in the gaseous state, which leads to the generation of one mole of cations (positively charged ions). Ionization energy usually exhibits an ascending pattern as you traverse a period (a horizontal row) from left to right, whereas it shows a declining trend when moving down a group (a vertical column) within the periodic table.

Here are some key trends and patterns in ionization energy within the periodic table:

Ionization Energy Across a Period (Left to Right): As you move from left to right across a period, the ionization energy generally increases. This trend is primarily due to the increasing effective nuclear charge (the positive charge experienced by the outermost electrons). The outermost electrons are held more tightly by the nucleus, making it more difficult to remove them. As a result, elements on the right side of a period have higher ionization energies than those on the left.

Ionization Energy Down a Group (Top to Bottom): The trend observed when descending a group is a general decrease in ionization energy. This reduction occurs because elements within the same group possess an identical count of valence electrons (the outermost electrons), and as you progress down the group, the number of electron shells (energy levels) increases. Consequently, the outermost electrons are positioned farther from the nucleus and enjoy shielding from inner electron shells, rendering them more readily removable.

Exceptions: While the general trends hold, there are some exceptions. For example, elements in Group 2 (alkaline earth metals) have higher ionization energies than elements in Group 13 (boron group) in the same period due to the full and stable electron configuration in Group 2.

Half-filled and Fully Filled Subshells: Elements characterized by half-filled or completely filled electron subshells, such as helium with its fully occupied 1s² subshell, usually possess lower ionization energies. This phenomenon arises from the exceptional stability associated with these specific electron configurations.

Transition Metals: Transition metals, found in the middle of the periodic table, have variable ionization energies. This is because the removal of electrons can occur from different subshells, and the shielding effect plays a significant role in determining ionization energies in these elements.

Noble Gases: Noble gases, which are found in Group 18 of the periodic table, exhibit the highest ionization energies within their respective periods due to their possession of complete valence electron shells, resulting in exceptional stability. Removing an electron from a noble gas requires a substantial amount of energy.

Ionization energy is a property that reflects an element's ability to hold onto its electrons. It follows specific trends and patterns across the periodic table, with increasing ionization energy across periods and decreasing ionization energy down groups, but there are exceptions based on electron configurations and other factors.