Question

Recall that the IE of \(\mathrm{H}\) is \(1.31 \mathrm{MJ} / \mathrm{mole}\). If all three electrons in Li were in the first shell at a distance equal to that of hydrogen, which of the following values would be the better estimate of the IE of Li: 3.6 MJ/mole or 0.6 MJ/mole? Explain.

Short answer

The better estimate for the ionization energy of Li is 3.6 MJ/mole.

Step-by-step solution

Understand the relationship between number of electrons and IE

Notice that the more electrons an atom has in its outer shell, the higher its ionization energy will be. This is because you need more energy to remove additional electrons. Since the ionization energy of hydrogen, which has one electron, is 1.31 MJ/mole, the ionization energy of Li, which has three electrons, should logically just be three times greater than that of H, assuming their distance from the nucleus is equivalent.

Calculate the expected IE for Li

Multiply the ionization energy of hydrogen by the number of electrons in Li (which is 3): IE(Li) = 3 * 1.31 MJ/mole = 3.93 MJ/mole.

Compare the calculated value with the given options

Comparing the calculated Li IE of 3.93 MJ/mole with the two provided values (3.6 MJ/mole and 0.6 MJ/mole), it is evident that 3.6 MJ/mole is closer to our computed value than 0.6 MJ/mole.

Make final assertions

The value of 3.6 MJ/mole would, thus, be a better estimate than 0.6 MJ/mole for the ionization energy of Lithium.

Key concepts

Atomic Structure

Atoms are the fundamental building blocks of matter. They consist of three main components: protons, neutrons, and electrons.
The nucleus, at the atom's core, houses protons and neutrons, carrying a positive charge due to protons. Surrounding the nucleus are electrons, negatively charged subatomic particles that exist in regions known as electron shells or orbitals.

• Protons and neutrons have similar masses, but electrons weigh significantly less.
• The number of protons in an atom's nucleus is called the atomic number, which determines the element's identity.
• Electrons inhabit energy levels at varying distances from the nucleus, influenced by their energy states.

Understanding atomic structure is crucial for predicting chemical behavior and the bonding properties of elements, such as ionization energy.

Electron Configuration

Electron configuration describes the arrangement of electrons around an atom's nucleus. These configurations follow specific rules based on quantum mechanics, which provide the groundwork for understanding chemical properties.

• Electrons fill orbitals starting from the lowest energy level to higher levels, in order of increasing energy.
• Each orbital can hold a maximum of two electrons, with opposite spins.
• Configurations are denoted using notations that indicate the filled orbitals (e.g., 1s² 2s² 2p⁶).

For lithium (Li), the electron configuration is 1s² 2s¹, showing that two electrons fill the first shell (1s) and one electron occupies the second shell (2s). This influences how much energy is required to remove an electron, known as ionization energy.

Periodic Trends

Periodic trends explain how certain properties change across different elements in the periodic table. These trends arise from their electron configurations and help predict various chemical and physical properties, including ionization energy.

• Across a period from left to right, ionization energy generally increases due to more effective nuclear charge, pulling electrons closer and more tightly.
• Descending a group in the periodic table typically results in a decrease in ionization energy due to electrons being more distant from the nucleus and experiencing more electron shielding.
• Elements in the same column share similar properties due to equivalent valence electron configurations.

These trends allow chemists to make informed predictions about an element's reactivity and ability to form compounds.

Ionization Energy Calculation

Ionization energy (IE) is the energy needed to remove an electron from an atom in its gaseous state. Different factors, including the number of electrons and their distribution, affect ionization energy calculations.
For hydrogen (H), with one electron, IE is gauged as 1.31 MJ/mole. Lithium (Li), with three electrons, should conceivably show a higher ionization energy since it also includes influence from electron configuration, which determines how tightly atoms hold their electrons.

• IE increases with higher nuclear charge, i.e., more protons in the nucleus.
• Electrons in closer shells experience higher attraction and thus require more energy for removal.
• Calculating IE may involve estimating the contribution of each electron based on their position and electron shielding effect.

From the provided exercise solution, multiplying the IE of hydrogen by three (considering similar conditions), an estimation of lithium’s ionization energy closer to 3.6 MJ/mole was considered accurate.