Question

The ionization energies of sodium (in \(\mathrm{kJ} / \mathrm{mol}\) ), starting with the first and ending with the eleventh, are 496 , 4562,6910,9543,13,354,16,613,20,117,25,496 \(28,932,141,362,159,075 .\) Plot the log of ionization energy \((y\) axis \()\) versus the number of ionization \((x\) axis); for example, \(\log 496\) is plotted versus 1 (labeled \(I E_{1}\), the first ionization energy), \(\log 4562\) is plotted versus 2 (labeled \(I E_{2},\) the second ionization energy \(),\) and so on. (a) Label \(I E_{1}\) through \(I E_{11}\) with the electrons in orbitals such as \(1 s, 2 s, 2 p,\) and \(3 s\) (b) What can you deduce about electron shells from the breaks in the curve?

Short answer

Sharp breaks in ionization energy indicate the transition between filling electron shells, correlating to removing core versus valence electrons.

Step-by-step solution

Record Ionization Energies

List the given ionization energies in order: \[496, 4562, 6910, 9543, 13354, 16613, 20117, 25496, 28932, 141362, 159075\] in \(\text{kJ/mol}\).

Calculate Logarithms

Calculate the logarithm (base 10) of each ionization energy. For example, \( \log 496 \approx 2.696 \), \( \log 4562 \approx 3.659 \), and continuing this for all energies.

Create a Plot for Log Values

Create a plot with the x-axis representing the ionization number (1 to 11) and the y-axis representing the logarithm of the ionization energy calculated previously. Label each point corresponding to \( IE_1 \), \( IE_2 \), up to \( IE_{11} \).

Label Electrons in Orbitals

Assign the electrons to orbitals based on common knowledge of electron configurations: \( IE_1 \) (1s), \( IE_2 \) (2s), \( IE_3 \) (2p), \( IE_4 \) (2p), continuing to \( IE_{11} \), recognizing breaks in energy due to moving to the next shell.

Analyze Breaks in the Curve

Identify significant increases in ionization energies between certain points, indicative of moving to inner electron shells, e.g., notable breaks between \( IE_1 \) to \( IE_2 \) and \( IE_9 \) to \( IE_{10} \), imply significant energy when removing core electrons compared to valence electrons.

Conclude Observations on Electron Shells

The plotted curve should visually represent lower energies for removing valence electrons and sharp increases for removing core electrons, highlighting electron shell structure.

Key concepts

Logarithmic Plot

A logarithmic plot helps in understanding how ionization energy changes, making it easier to analyze trends. When plotting the log of ionization energy on the y-axis against the number of ionizations on the x-axis, the steepness in the curve can reveal shifts in electron shells.
Since ionization energies can vary greatly in magnitude, using a logarithmic scale compresses these large differences, providing a clearer visualization.

• This type of plot transforms exponential behavior into linear, making patterns easier to spot.
• It is especially useful for observing rapid changes in data values.

For sodium, plotting the logarithm of the ionization energies illuminates the difference between valence and core electrons, as the slope changes at specific points.

Electron Configuration

Electron configuration describes how electrons are distributed in an atom's orbitals. Understanding it is crucial for predicting chemical behavior. Electrons populate orbitals starting from the lowest energy level available (1s, 2s, 2p, etc.).

• Electrons fill in a specific order, known as the Aufbau principle, which prioritizes minimizing energy.
• Each orbital can hold a set number of electrons: s (2), p (6), d (10), f (14).

For sodium, its electron configuration can be expressed as \(1s^2, 2s^2, 2p^6, 3s^1\). This simple pattern aids in explaining variations in ionization energy, especially observed as one moves from valence to core electrons.

Core Electrons

Core electrons reside closer to the nucleus and are not involved in bonding. These inner electrons are shielded by valence electrons and experience a higher effective nuclear charge.

• They are much harder to remove, which reflects in the high ionization energies associated with them.
• Removing a core electron often requires several times the energy needed to remove a valence electron due to their proximity to the nucleus and shielding effect.

In sodium, once the valence electron is removed, higher ionization energies correspond to the removal of 1s and 2s/2p electrons, where significant increases in energy demands are evident on a logarithmic plot.

Valence Electrons

Valence electrons are the electrons located in an atom's outermost shell. These electrons are involved in chemical reactions and play a pivotal role in determining an element’s chemical properties.

• In sodium, the single 3s electron is the valence electron.
• Valence electrons are relatively easy to remove compared to core electrons, hence lower ionization energy values are observed.

Observing sodium's ionization energies, the first energy required (associated with removing the valence electron) is notably less than subsequent energies, depicting how valence electrons are less tightly held than core electrons.