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 \(_{1}\) of Li: \(3.6 \mathrm{MJ} / \mathrm{mole}\) or \(0.6 \mathrm{MJ} / \mathrm{mole}\) ? Explain.

Short answer

The better estimate of the IE1 of Lithium (Li) would be 3.6 MJ/mole.

Step-by-step solution

Recap the Concept of Ionization Energy

Ionization Energy is the energy required to remove an electron from a neutral atom in its gaseous phase. Removal of each successive electron requires more energy, so 1st Ionization Energy would be the energy required to remove one electron, creating a 1+ ion; the 2nd Ionization Energy is the energy required to remove a second electron, creating a 2+ ion, and so on.

Understand Given Data and Parameters

From the given problem, we know that Hydrogen (H) has Ionization Energy of 1.31 MJ/mole and we need to predict the ionization energy of Lithium (Li) considering all three electrons in Li were in the first shell.

Relate the Given Data to Estimate Lithium's Ionization Energy

Since each atom of lithium has three electrons, if all were in the 1st shell (like Hydrogen), we'd expect the 1st ionization energy of lithium to be approximately three times that of Hydrogen. So, it should be around 3 x 1.31 MJ/mole = 3.93 MJ/mole.

Comparison with Provided Options

Comparing the estimated value (3.93 MJ/mole) with the given options (3.6 MJ/mole and 0.6 MJ/mole), we find that 3.6 MJ/mole is closer to our calculated value and thus, would be the better estimate of the IE1 of Lithium.

Key concepts

Ionization Energy of Hydrogen

Ionization energy, often abbreviated as IE, is a fundamental concept in chemistry, referring to the amount of energy needed to remove an electron from an atom in its gaseous state. In the specific case of hydrogen, the simplest and lightest of all elements, this value is critical for comparisons across the periodic table.

For hydrogen, the first (and only) ionization energy is relatively high due to its sole electron being close to the nucleus and experiencing a strong electrostatic attraction. Thus, the ionization energy of hydrogen is typically measured as 1.31 MJ/mole. This value serves as a reference point when evaluating or predicting the IE for other elements.

Whenever dealing with ionization energies, remember that they are indicative of how tightly an electron is bound to an atom. For hydrogen, with its electron in the 1s shell, it takes a considerable amount of energy to overcome the nuclear attraction and free the electron, thereby ionizing the atom.

1st Ionization Energy

The 1st ionization energy is a specific term that refers to the energy necessary to remove the first electron from a neutral atom. Since removing the first electron perturbs the electron-nuclear balance the least compared to subsequent removals, the 1st ionization energy is often the lowest for a given atom.

This energy is an essential indicator of an element's reactivity and its ability to form compounds. Atoms with lower 1st ionization energy are typically more reactive because their outermost electrons are more easily removed. Conversely, atoms with a high 1st ionization energy tend to be less reactive.

Understanding the first ionization energy helps in predicting how an atom will interact with other atoms and can give insights into the properties of elements, particularly their place on the periodic table. Trends in the periodic table, such as the increase in ionization energy from left to right across a period, or the decrease down a group, are based on the concept of 1st ionization energy.

Lithium Ionization Energy Estimation

Estimating the ionization energy for lithium can be complex, as it involves more than just the first ionization energy. Lithium has three electrons: two in its inner shell and one in its outermost shell.

When approximating the first ionization energy for lithium, if we assume all three electrons were in the same orbital distance as hydrogen's sole electron, we could anticipate that the IE to be three times that of Hydrogen. However, in reality, lithium's electrons reside in different shells with varying distances from the nucleus, affecting the required energy for ionization.

The correct estimation process, shown in the exercise, demonstrates that while a simple triplet multiplication might provide an initial approximation (3.93 MJ/mole), ionization energy calculations must consider the atomic structure and electron configuration, making the 3.6 MJ/mole a more contextually accurate approximation. This estimation still simplifies the complex quantum mechanical nature of atoms but is useful for understandings trends and comparisons among elements.