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Chapter 4: Problem 7

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 your reasoning.

Short Answer

Expert verified
The better estimate for the IE of Lithium (Li), assuming all its three electrons are in the first shell at a distance equal to that of Hydrogen, would be \(3.6 MJ/mole\).

Step by step solution

01

Understand Ionization Energy

Firstly, it's crucial to understand what Ionization Energy is. Ionization Energy (IE) is the energy required to remove an electron from an atom or a positive ion. It generally increases across a period and decreases down a group in the Periodic Table. Hydrogen (H) has an IE of \(1.31 MJ/mole\). Hydrogen has only one electron located in its first shell.
02

Consider the question

The question asks to estimate the IE of Lithium (Li), given that all of its three electrons are in the first shell at a distance equal to that of Hydrogen. Lithium (Li) in its neutral, ground state has one electron in the second shell and two in the first shell. However, this exercise assumes all three electrons are in the first shell, like Hydrogen.
03

Compare the IE values

We are given two potential IE values for Li: \(3.6 MJ/mole\) or \(0.6 MJ/mole\). As we are assuming all three electrons are in the first shell like Hydrogen, a simple assumption could be that the IE of Li is three times that of H (since Li has three electrons while H has just one). This would give an approximate IE for Li of \(1.31 MJ/mole * 3 = 3.93 MJ/mole\).
04

Choose the closest estimate

Comparing our calculated estimate of \(3.93 MJ/mole\) with the two provided values, it can be observed that \(3.6 MJ/mole\) is closer. Therefore, \(3.6 MJ/mole\) would be the better estimate for the IE of Li.

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Most popular questions from this chapter

a) How much energy does it take to remove an electron from one \(\mathrm{H}\) atom? b) How much total energy would it take to remove the electrons from two H atoms? c) How much total energy would it take to remove the electrons from a mole of \(\mathrm{H}\) atoms? Express this energy in units of \(\mathrm{J}\) and in units of \(\mathrm{MJ} .\)

Based on what you have learned so far in this course, predict the relationship between \(\mathrm{IE}_{1}\) and atomic number by making a rough graph of \(\mathrm{IE}_{1}\) vs. atomic number. Discuss possible ideas with your team and decide which one you think makes the most sense. DO NOT PROCEED TO THE NEXT PAGE UNTIL YOU HAVE MADE YOUR PREDICTED GRAPH.

Using grammatically correct sentences: a) provide a possible explanation for why \(\mathrm{IE}_{1}\) for \(\mathrm{He}\) is greater than \(\mathrm{IE}_{1}\) for \(\mathrm{H}\). b) provide a possible explanation for why \(\mathrm{IE}_{1}\) for \(\mathrm{Li}\) is less than \(\mathrm{IE}_{1}\) for He.

For atoms with many electrons, not all electrons are at the same distance from the nucleus. In this case, which electron would have the lowest ionization energy: the electron that is closest to the nucleus or the electron that is farthest from the nucleus? Explain.

The value of the ionization energy of He given in Table 1 is described as being consistent with a model in which the two electrons in He are in a "shell" at approximately the same distance from the nucleus as the one electron in \(\mathrm{H}\). Use the Coulombic Potential Energy equation, \(V=\frac{\mathrm{kq}_{1} \mathrm{q}_{2}}{\mathrm{~d}}\) to explain how this conclusion can be reached. Hint: recall the relationship between \(V\) and \(\mathrm{IE}_{1}\).
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