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Chapter 7: Problem 40

Identify each statement as true or false: (a) lonization energies are always endothermic. (b) Potassium has a larger first ionization energy than lithium. (c) The second ionization energy of the sodium atom is larger than the second ionization energy of the magnesium atom. (d) The third ionization energy is three times the first ionization energy of an atom.

Short Answer

Expert verified
(a) True: Ionization energies are always endothermic since they require energy input to remove an electron from a gaseous atom or ion. (b) False: Potassium has a lower first ionization energy than lithium because it is located below lithium in the same group in the periodic table. (c) False: The second ionization energy of the sodium atom is smaller than the second ionization energy of the magnesium atom due to the higher effective nuclear charge in magnesium. (d) False: There is no fixed relationship between the third ionization energy and the first ionization energy of an element. The difference is specific to each element and its electron configuration.

Step by step solution

01

Statement a: Ionization energies are always endothermic.

Ionization energy is the energy required to remove an electron from a gaseous atom or ion. The process of ionization requires energy input to overcome the attractive forces between the negatively charged electron and the positively charged nucleus. Since energy is being absorbed to remove the electron, the process is endothermic. Thus, the statement is true.
02

Statement b: Potassium has a larger first ionization energy than lithium.

When moving across a period in the periodic table, ionization energy generally increases due to a greater effective nuclear charge. Lithium is in the second period, while potassium is in the fourth period. When moving down a group, ionization energy typically decreases because of an increase in atomic size and shielding effect. Since potassium is located below lithium in the same group, its first ionization energy is lower than that of lithium. Therefore, the statement is false.
03

Statement c: The second ionization energy of the sodium atom is larger than the second ionization energy of the magnesium atom.

Sodium and magnesium are both in the third period, with magnesium being to the right of sodium. The second ionization energy of an element corresponds to the energy required to remove the second electron. In the case of sodium, the second electron is being removed from a complete \(2p^6\) subshell, while in magnesium, it is being removed from an almost filled \(3s^2\) subshell. The effective nuclear charge of magnesium is greater than that of sodium, making it more difficult to remove the second electron. Therefore, the second ionization energy of magnesium is larger than that of sodium, and the statement is false.
04

Statement d: The third ionization energy is three times the first ionization energy of an atom.

Ionization energy generally increases with the removal of each subsequent electron due to a smaller atomic size and a higher effective nuclear charge. However, there is no fixed relationship between the third ionization energy and the first ionization energy of an element. The difference is specific to each element and its electron configuration. As a result, the statement is false.

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Most popular questions from this chapter

Detailed calculations show that the value of \(Z_{\text {eff }}\) for the outermost electrons in \(\mathrm{Na}\) and \(\mathrm{K}\) atoms is \(2.51+\) and \(3.49+\), respectively. (a) What value do you estimate for \(Z_{\text {eff }}\) experienced by the outermost electron in both \(\mathrm{Na}\) and \(\mathrm{K}\) by assuming core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant? (b) What values do you estimate for \(Z_{\text {eff }}\) using Slater's rules? (c) Which approach gives a more accurate estimate of \(Z_{\text {eff }}\) ? (d) Does either method of approximation account for the gradual increase in \(Z_{\text {eff }}\) that occurs upon moving down a group? (e) Predict \(Z_{\text {eff }}\) for the outermost electrons in the \(\mathrm{Rb}\) atom based on the calculations for \(\mathrm{Na}\) and \(\mathrm{K}\).

Chlorine reacts with oxygen to form \(\mathrm{Cl}_{2} \mathrm{O}_{7} .\) (a) What is the name of this product (see Table 2.6)? (b) Write a balanced equation for the formation of \(\mathrm{Cl}_{2} \mathrm{O}_{7}(l)\) from the elements. (c) Would you expect \(\mathrm{Cl}_{2} \mathrm{O}_{7}\) to be more reactive toward \(\mathrm{H}^{+}(a q)\) or \(\mathrm{OH}^{-}(a q) ?(\mathbf{d})\) If the oxygen in \(\mathrm{Cl}_{2} \mathrm{O}_{7}\) is considered to have the -2 oxidation state, what is the oxidation state of the \(\mathrm{Cl}\) ? What is the electron configuration of \(\mathrm{Cl}\) in this oxidation state?

Write balanced equations for the following reactions: (a) boron trichloride with water, (b) cobalt (II) oxide with nitric acid, (c) phosphorus pentoxide with water, (d) carbon dioxide with aqueous barium hydroxide.

The following observations are made about two hypothetical elements \(\mathrm{A}\) and \(\mathrm{B}:\) The \(\mathrm{A}-\mathrm{A}\) and \(\mathrm{B}-\mathrm{B}\) bond lengths in the elemental forms of \(\mathrm{A}\) and \(\mathrm{B}\) are 236 and \(194 \mathrm{pm}\), respectively. A and \(B\) react to form the binary compound \(A B_{2}\), which has a linear structure (that is \(\left.\angle \mathrm{B}-\mathrm{A}-\mathrm{B}=180^{\circ}\right) .\) Based on these statements, predict the separation between the two B nuclei in a molecule of \(\mathrm{AB}_{2}\).

Consider the stable elements through lead \((Z=82) .\) In how many instances are the atomic weights of the elements out of order relative to the atomic numbers of the elements?
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