Problem 64 - Chemistry and Chemical Reactivity

Question

Explain why the first ionization energy of Ca is greater than that of K, whereas the second ionization energy of Ca is lower than the second ionization energy of \(\mathrm{K}\).

Step-by-Step Solution

Answer

Ca's nuclear charge makes its first ionization energy higher than K's, but losing two electrons leaves Ca with a stable configuration more easily than K.

Step 1: Understanding Ionization Energy

Ionization energy is the energy required to remove an electron from an atom, and it increases across a period and decreases down a group in the periodic table. This is because atoms become smaller with more protons as you move across a period, making it harder to remove an electron.

Step 2: Difference in Atomic Structure

Calcium (Ca) has an atomic number of 20 and a configuration of [Ar] 4s², while Potassium (K), with an atomic number of 19, has a configuration of [Ar] 4s¹. Since Ca has more protons, its nucleus has a stronger pull on its electrons compared to K, which contributes to a higher first ionization energy.

Step 3: Analyzing First Ionization Energy

The first ionization energy involves removing the outermost electron. For Ca, this means removing one of the 4s electrons, whereas for K, it means removing its only 4s electron. The stronger nuclear charge in Ca makes it harder to remove this electron compared to K, which explains why Ca has a higher first ionization energy.

Step 4: Examining Second Ionization Energy

The second ionization energy involves removing another electron after the first has been removed. After losing one electron, potassium is left with a stable electron configuration of [Ar], similar to noble gases, making it very difficult to remove a second electron. Conversely, Ca loses an electron to become [Ar]4s¹, which still allows the removal of an electron with relatively less energy compared to K, resulting in a lower second ionization energy for Ca.

Key Concepts

Periodic Trends

Ionization energy is closely related to periodic trends, which refer to how certain properties of elements change across periods and down groups on the periodic table. As you move from left to right across a period,

• Atoms generally become smaller.
• Nuclear charge increases due to more protons.
• Ionization energy tends to increase because the increased nuclear charge holds electrons more tightly.

Conversely, as you go down a group,

• Atoms become larger because additional electron shells are added.
• The outer electrons are further from the nucleus and more shielded by inner electrons.
• Ionization energy decreases since the outermost electrons are less tightly held.

For instance, calcium (Ca) has a higher first ionization energy than potassium (K) because, even though they are in the same period (Period 4), calcium is further to the right, benefiting more from these periodic trends. This results in a stronger nuclear attraction on the outer electrons.

Atomic Structure

Understanding atomic structure is crucial for explaining ionization energy differences between elements. Each element's atomic structure is defined by its

• Number of protons, which determines its positive nuclear charge.
• Electron configuration, which dictates how electrons are arranged around the nucleus.

Calcium (Ca) has an atomic number of 20, indicating it has 20 protons, resulting in a powerful nuclear attraction. Its electron configuration is [Ar] 4s², meaning it has two electrons in its outermost shell. Potassium (K), with an atomic number of 19, has one less proton and an electron configuration of [Ar] 4s¹.

The extra proton in calcium compared to potassium results in a stronger nucleus, exerting a greater pull on the outer electrons. This is why more energy is required to remove an electron from calcium compared to potassium in their first ionization energies.

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom and is essential for predicting chemical properties like ionization energy. Calcium (Ca) and Potassium (K) both have electron configurations that start with [Ar], the configuration of Argon, due to their position in Period 4.

• Calcium's configuration is [Ar] 4s², indicating two electrons in the outer 4s orbital.
• Potassium's configuration is [Ar] 4s¹, with just one outer electron.

These configurations reveal that removing the first electron (first ionization) is easier for potassium than for calcium due to its fewer outer electrons. Furthermore, after losing one electron, potassium achieves a stable noble gas-like electron configuration [Ar], meaning its remaining electrons are extremely stable, hence why its second ionization energy is significantly higher than that of calcium.

Calcium still has another outer electron after the first loss and therefore can release this second electron with relatively lower energy. This illustrates how electron configuration affects the ease with which electrons are removed, influencing both first and second ionization energies.