Question

Which is the larger ion, \(\mathrm{K}^{+}\)or \(\mathrm{Ca}^{2+}\) ? Explain.

Short answer

The \(\mathrm{K}^{+}\) ion is larger than the \(\mathrm{Ca}^{2+}\) ion. This is because the two ions have the same number of electrons, but \(\mathrm{Ca}^{2+}\) has more protons in the nucleus which means the electrons are drawn more closely to it, resulting in a smaller ion size.

Step-by-step solution

Understand the elements

Before beginning, familiarize yourself with Potassium (K) and Calcium (Ca) on the periodic table. Potassium is found in period 4, group 1 of the periodic table, and Calcium is in period 4, group 2.

Determine the number of electrons

Since \(\mathrm{K}^{+}\) represents a Potassium ion with a charge of +1, this means it has lost one electron. The atomic number of Potassium (K) is 19, so normally it would have 19 electrons. But because it lost one electron to become an ion, it now has 18 electrons. For \(\mathrm{Ca}^{2+}\), since Calcium normally has 20 electrons (given its atomic number of 20), losing 2 electrons leaves it with 18 electrons.

Compare the size of the ions

When atoms lose electrons and become positive ions, the result is often a decrease in atomic size. This is due to the loss of electron-electron repulsion in the outermost shell and the closer draw of the remaining electrons towards the nucleus. Given that both \(\mathrm{K}^{+}\) and \(\mathrm{Ca}^{2+}\) have the same number of electrons, the ion with the higher nuclear charge (more protons in the nucleus) will draw the electrons closer and be smaller. Since \(\mathrm{Ca}^{2+}\) has more protons (20) than \(\mathrm{K}^{+}\) (19), it will be smaller.

Key concepts

Potassium Ion

Potassium ions are derived from the element potassium, which is denoted by the symbol K on the periodic table. It belongs to group 1, which consists of alkali metals. These elements are known for readily losing one electron to form a positive ion, or cation. Potassium has an atomic number of 19, meaning it typically has 19 protons and 19 electrons.

When potassium forms a \(\mathrm{K}^{+}\\) ion, it loses one electron. This results in a reduction from 19 to 18 electrons, leading to a positively charged ion. Despite having the same number of electrons as calcium ions in their ionized states, potassium ions have fewer protons. This affects their overall size and the attractive forces within the atom.

Potassium ions play a crucial role in biological processes, especially in cell function and nerve transmission. Understanding potassium ions is essential not only for chemistry students but also for those in biology and medicine fields.

Calcium Ion

Calcium ions arise from the element calcium, located in group 2 of the periodic table, also known as the alkaline earth metals. This group has a tendency to lose two electrons and form a \(\mathrm{Ca}^{2+}\\) ion. Calcium’s atomic number is 20, meaning it normally has 20 protons and 20 electrons.

In forming a \(\mathrm{Ca}^{2+}\\) ion, calcium loses two electrons, leaving it with 18 electrons, similar to the potassium ion. However, calcium has 20 protons in its nucleus, creating a strong positive charge that pulls electrons closer. This results in a smaller ion size compared to potassium ions, which have only 19 protons.

Calcium ions are vital for many physiological processes, such as muscle contraction and bone formation. Learning about calcium's characteristics is crucial for students in both chemistry and the life sciences.

Periodic Table Trends

The periodic table is a powerful tool for understanding elemental properties and predicting behaviors of ions. When analyzing periodic table trends, it's essential to consider both the periods (horizontal rows) and groups (vertical columns). Potassium and calcium are located in the same period (period 4), indicating they have the same number of energy levels for their electrons.

However, these elements belong to different groups. Group 1 elements, like potassium, have one electron in their outer shell, while group 2 elements, such as calcium, have two. This difference greatly influences their ionization processes and the size of the resulting ions. As you move across a period, the number of protons increases, strengthening the nuclear pull and often resulting in smaller ionic and atomic sizes.

Understanding periodic table trends helps explain why \(\mathrm{Ca}^{2+}\\) ions are smaller than \(\mathrm{K}^{+}\\) ions. The higher nuclear charge of calcium compared to potassium means a stronger attraction toward electrons, shrinking the overall ionic size. This knowledge is crucial for mastering chemistry concepts related to ion size and behavior.