Question

The alkali metal ions are very important for the proper functioning of biologic systems, such as nerves and muscles, and \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\) ions are present in all body cells and fluids. In human blood plasma, the concentrations are $$ \left[\mathrm{Na}^{+}\right] \approx 0.15 M \text { and }\left[\mathrm{K}^{+}\right] \approx 0.005 M $$ For the fluids inside the cells, the concentrations are reversed: $$ \left[\mathrm{Na}^{+}\right] \approx 0.005 M \text { and }\left[\mathrm{K}^{+}\right] \approx 0.16 M $$ Since the concentrations are so different inside and outside the cells, an elaborate mechanism is needed to transport \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\) ions through the cell membranes. What are the ground-state electron configurations for \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\) ? Which ion is smaller in size? Counterions also must be present in blood plasma and inside intracellular fluid. Assume the counterion present to balance the positive charge of \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\) is \(\mathrm{Cl}^{-}\). What is the ground-state electron configuration for \(\mathrm{Cl}^{-}\) ? Rank these three ions in order of increasing size.

Short answer

The ground-state electron configurations for Na⁺, K⁺, and Cl⁻ ions are as follows: For Na⁺: \(1s^{2} 2s^{2} 2p^{6}\) For K⁺: \(1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6}\) For Cl⁻: \(1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6}\) The order of these ions in increasing size is: Na⁺ < K⁺ < Cl⁻.

Step-by-step solution

Determine the neutral atom electron configurations

According to the periodic table, the neutral atom electron configuration for sodium (Na), potassium (K), and chlorine (Cl) can be found as follows: For Sodium (Na, Z=11): 1s² 2s² 2p⁶ 3s¹ For Potassium (K, Z=19): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ For Chlorine (Cl, Z= 17): 1s² 2s² 2p⁶ 3s² 3p⁵

Determine the electron configurations for Na⁺, K⁺, and Cl⁻ ions

To find the electron configurations for Na⁺ and K⁺ ions, we will remove one electron each from their neutral atom configuration as they have lost one electron. For Na⁺: \[1s^{2} 2s^{2} 2p^{6}\] For K⁺: \[1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6}\] For Cl⁻, we will add one electron to its neutral atom configuration as it has gained an electron: For Cl⁻: \[1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6}\]

Compare the sizes of the ions

The size of ions depends on the effective nuclear charge, electron shielding, and the number of electron shells. In general, a cation (positively charged ion) is smaller than its neutral atom, while an anion (negatively charged ion) is larger than its neutral atom. Comparing Na⁺ and K⁺ ions, we can see that Na⁺ has fewer electron shells compared to the K⁺ ion. Therefore, Na⁺ will be smaller than K⁺ due to the effective nuclear charge acting on valence electrons more strongly. Comparing Na⁺ and Cl⁻ ions, Na⁺ ion has fewer electrons than Cl⁻ ion; hence there are fewer repulsive forces between electrons, making the Na⁺ ion smaller in size. Thus, the order of ions in increasing size is: Na⁺ < K⁺ < Cl⁻

Key concepts

Alkali Metal Ions

Alkali metal ions, such as \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\), are vital components in many biological processes, including the operation of nerves and muscles. These ions originate from alkali metals, which reside in group 1 of the periodic table and are renowned for their high reactivity, often forming +1 charged ions when they come into contact with nonmetals.

For instance, sodium (Na) becomes a \(\mathrm{Na}^{+}\) ion by losing its single valence electron, resulting in a full second energy level that is identical to the electron configuration of neon, an inert gas. This loss stabilizes the \(\mathrm{Na}^{+}\) ion, making it favorable for forming ionic bonds and participating in physiological functions. Potassium (K) follows a similar pattern, shedding its single valence electron to achieve the stable configuration of argon.

As ions, these alkali metals play indispensable roles in maintaining cellular function and overall homeostasis within the body, particularly in the transmission of nerve impulses and regulation of heart rhythms. Understanding their electron configurations and reactions aids students in grasping the foundational principles of chemistry associated with health sciences and physiology.

Cell Membrane Ion Transport

The cell membrane is a critical barrier that regulates the movement of ions in and out of the cell. A key function of this semi-permeable membrane is to maintain the concentration gradients of ions such as \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\). These gradients are crucial for physiological processes like transmitting nerve signals and muscle contraction.

Effective ion transport requires specific proteins embedded within the cell membrane. These are known as ion pumps and channels, which help maintain the resting membrane potential by actively or passively moving ions against or along their concentration gradients. One such example is the sodium-potassium pump (\(\mathrm{Na}^{+}/\mathrm{K}^{+}\) pump), which uses ATP to exchange three \(\mathrm{Na}^{+}\) ions from inside the cell with two \(\mathrm{K}^{+}\) ions from outside the cell.

The intricate balance and precise control of ion transport are integral to cell function, and disruptions can lead to significant health issues. Hence, the study of cell membrane ion transport is not only fundamental to biology and medicine but also to understanding the applications and significance of alkali metal ions in this context.

Ionic Size Comparison

The size of ions plays a significant role in their reactivity and how they interact with one another. When comparing ionic sizes, it's important to consider factors such as the number of protons in the nucleus, the number of electron shells, and the net charge of the ion.

When an atom loses an electron to form a cation, as in the case of \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\), the loss of the outermost electron reduces electron-electron repulsion and allows the remaining electrons to be pulled closer to the nucleus, resulting in a smaller ionic radius. On the other hand, when an atom gains an electron to become an anion, such as \(\mathrm{Cl}^{-}\), increased electron-electron repulsion causes the ion to expand, creating a larger ionic size. This leads to the following ranking in ionic size: \(\mathrm{Na}^{+}\) is smaller than \(\mathrm{K}^{+}\) because \(\mathrm{Na}^{+}\) has fewer electron shells. Conversely, \(\mathrm{K}^{+}\) is smaller than \(\mathrm{Cl}^{-}\) since cations are generally smaller than anions, particularly when comparing ions of nearby elements in the periodic table.

Understanding these ionic size comparisons is crucial for predicting the properties of substances and their interactions in both chemical reactions and biochemistry. This knowledge is foundational for students embarking on studies in chemistry, biology, and related fields.