Problem 80 - Introductory Chemistry Atoms First

Question

Of the atoms \(\mathrm{Na}, \mathrm{Mg}\), and \(\mathrm{K}\), which should be the most difficult to ionize? Which has the smallest first ionization energy?

Step-by-Step Solution

Answer

The most difficult element to ionize is Mg, as it has a larger ionization energy compared to Na and K. The smallest first ionization energy belongs to K, as it is lower in the same group as Na.

Step 1: Identify the atomic numbers and positions of the elements in the periodic table

First, we need to find the atomic numbers for each element and locate their positions in the periodic table: Na (Sodium) - Atomic number 11 Mg (Magnesium) - Atomic number 12 K (Potassium) - Atomic number 19 Now, locate them in the periodic table. Na and K belong to group 1, and Mg belongs to group 2. Na is in period 3, Mg is in period 3, and K is in period 4.

Step 2: Compare the ionization energies based on position in the periodic table

As mentioned earlier, the ionization energy generally increases as we move from left to right across a period and decreases as we go down a group. Since Na and K belong to the same group (group 1), and K is below Na, the ionization energy of K is smaller than Na. Mg belongs to group 2 which is on the right side of Na and K, so its ionization energy should be larger.

Step 3: Determine the most difficult element to ionize and the element with smallest first ionization energy

Based on our comparison, Mg (group 2) should be the most difficult to ionize due to having a larger ionization energy compared to Na and K (group 1). Additionally, K has a smaller first ionization energy than Na because it is lower in the same group. So, the most difficult to ionize is Mg and the smallest first ionization energy belongs to K.

Key Concepts

Periodic Table

The periodic table is a systematic arrangement of elements in order of increasing atomic number. Each element is placed in a specific position based on its atomic structure and properties.
The vertical columns on the periodic table are known as "groups" and the horizontal rows are known as "periods."

• Groups contain elements with similar chemical properties and the same number of valence electrons.
• Periods show a gradual change in chemical and physical properties across the row.

Understanding the periodic table is essential for predicting the behavior of different elements, including their ionization energy, reactivity, and atomic structure.

Group Trends

Group trends refer to patterns of properties that can be observed within elements of the same group on the periodic table. These trends are largely due to the similar electron configurations found within a group.

• Elements in the same group often display similar chemical and physical characteristics.
• For instance, ionization energy generally decreases from top to bottom within a group.
• This is because the outer electrons are further from the nucleus and are shielded by inner electrons, making them easier to remove.

In the context of our exercise, both Sodium (Na) and Potassium (K) belong to group 1, yet K is easier to ionize because it sits below Na in the group.

Atomic Number

The atomic number of an element represents the number of protons found in the nucleus of its atoms. This number uniquely identifies an element and determines its position on the periodic table.
For example, in our given problem:

• Sodium (Na) has an atomic number of 11.
• Magnesium (Mg) has an atomic number of 12.
• Potassium (K) has an atomic number of 19.

The atomic number increases as we move from left to right across a period. It is fundamental in predicting an element’s properties, such as ionization energy and reactivity, allowing us to position elements correctly on the periodic table.

Ionization Energy Trends

Ionization energy is the energy required to remove an electron from an atom or ion in its gaseous state. The trend of ionization energy across the periodic table shows that it generally increases across a period and decreases down a group.

• Elements on the right side of the periodic table usually have higher ionization energies compared to those on the left.
• This increase is due to the greater effective nuclear charge that holds the electrons more tightly.
• In contrast, for elements within the same group, ionization energy decreases as you move down because the outer electrons are farther from the attractive pull of the nucleus.

In the given exercise, Mg is found in group 2, and Na and K in group 1, with Mg expected to have the highest ionization energy and K the lowest, demonstrating these periodic trends.