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Chapter 7: Problem 26

Using only the periodic table, arrange each set of atoms in order of increasing radius: (a) Ba, Ca, Na; (b) In, Sn, As; (c) Al, Be, Si.

Short Answer

Expert verified
In order of increasing atomic radius: 1. (a) Na < Ca < Ba 2. (b) As < Sn < In 3. (c) Be < Si < Al

Step by step solution

01

Identify Group and Period of Each Element

Using the periodic table, we can identify the group and period of each element: - Ba (Barium): Group 2, Period 6 - Ca (Calcium): Group 2, Period 4 - Na (Sodium): Group 1, Period 3
02

Apply Group and Period Trends

Now, we will apply the group and period trends to determine the order of atomic radii. In this case, Na is in Group 1, and Ba and Ca are in Group 2. Remember that atomic radius increases as we go down a group. Therefore, Na will have the smallest atomic radius. The atomic radius of Ca is larger than Na as its in the following period, and Ba has a larger atomic radius than Ca as it is further down the group.
03

Final Order

In order of increasing atomic radius: Na < Ca < Ba 2. (b) Arrange In, Sn, As in order of increasing atomic radius
04

Identify Group and Period of Each Element

Using the periodic table, we can identify the group and period of each element: - In (Indium): Group 13, Period 5 - Sn (Tin): Group 14, Period 5 - As (Arsenic): Group 15, Period 4
05

Apply Group and Period Trends

In this case, In and Sn are in the same period (Period 5) but different groups. Remember that atomic radius decreases as we go from left to right across a period, so In will have a larger atomic radius than Sn. As for As, it is in Group 15 and Period 4, while In is in Group 13 and Period 5. Since the atomic radius increases as we go down a group, As will have a smaller atomic radius than In.
06

Final Order

In order of increasing atomic radius: As < Sn < In 3. (c) Arrange Al, Be, Si in order of increasing atomic radius
07

Identify Group and Period of Each Element

Using the periodic table, we can identify the group and period of each element: - Al (Aluminum): Group 13, Period 3 - Be (Beryllium): Group 2, Period 2 - Si (Silicon): Group 14, Period 3
08

Apply Group and Period Trends

Both Al and Si belong to Period 3, but they are in different groups. Remember that atomic radius decreases as we go from left to right across a period, so Al will have a larger atomic radius than Si. Furthermore, both Be and Al are in Group 2 and Group 13 respectively, but they are in different periods (Period 2 and Period 3). As we go down a group, atomic radius increases, so Be will have a smaller atomic radius compared to Al.
09

Final Order

In order of increasing atomic radius: Be < Si < Al

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Periodic Table
The periodic table is an organized chart of all known elements, arranged by increasing atomic number – the number of protons in an atom's nucleus. Elements are positioned from left to right and top to bottom in order of increasing atomic number, forming rows called periods and columns known as groups or families.

Each element’s placement in the table reveals important information about its properties. For instance, elements in the same group share similar chemical characteristics. This is because they have the same number of valence electrons, which are involved in chemical reactions. Moreover, the periodic table is structured so that elements with similar properties fall into the same vertical columns, allowing us to predict the behaviour of an element based on its position.
Group and Period Trends in Atomic Radius
Atomic radius refers to the size of an atom, typically the distance from the nucleus to the boundary of the surrounding cloud of electrons. Understanding the trends in atomic radius across the periodic table is crucial for predicting and explaining chemical behaviour.

The atomic radius tends to increase as you move down a group because new electron shells are added, making the atom larger. Conversely, as you move from left to right across a period, atomic radius generally decreases. This is because atoms gaining more protons in their nuclei pull the electron cloud closer, due to an increase in positive charge, which reduces the size of the atom.

This general pattern can sometimes have exceptions due to atomic structure complexities. However, remembering these group and period trends will help students determine the relative sizes of atoms.
Order of Atomic Radius
In exercises requiring the arrangement of elements by atomic radius, understanding the periodic table's trends is key. To solve such exercises, first, locate each element on the periodic table to determine its group and period. Then, apply your knowledge of increases down a group and decreases across a period to determine the order.

For example, Ba, Ca, and Na are located in Group 2, Group 2, and Group 1 respectively. Since Ba and Ca are in the same group but different periods, with Ba being lower, it has the larger radius. Na, however, is in a different group and period but being the highest in the table, it has the smallest radius. So, the order is Na < Ca < Ba, which represents increasing atomic radius.

Remember, there's always an elegant synergy between an element's position on the table and its properties. With practice, students can harness this relationship to effortlessly solve chemistry problems involving atomic radii.

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Most popular questions from this chapter

(a) If the core electrons were totally effective at screening the valence electrons and the valence electrons provided no screening for each other, what would be the effective nuclear charge acting on the 3\(s\) and 3p valence electrons in P? (b) Repeat these calculations using Slater's rules. (c) Detailed calculations indicate that the effective nuclear charge is \(5.6+\) for the 3\(s\) electrons and \(4.9+\) for the 3\(p\) electrons. Why are the values for the 3\(s\) and 3\(p\) electrons different? (d) If you remove a single electron from a Patom,which orbital will it come from?

[7.113]When magnesium metal is burned in air (Figure 3.6), two products are produced. One is magnesium oxide, MgO. The other is the product of the reaction of Mg with molecular nitrogen, magnesium nitride. When water is added to magnesium nitride, it reacts to form magnesium oxide and ammonia gas. (a) Based on the charge of the nitride ion (Table 2.5), predict the formula of magnesium nitride. (b) Write a balanced equation for the reaction of magnesium nitride with water. What is the driving force for this reaction? (c) In an experiment, a piece of magnesium ribbon is burned in air in a crucible. The mass of the mixture of MgO and magnesium nitride after burning is 0.470 g. Water is added to the crucible, further reaction occurs, and the crucible is heated to dryness until the final product is 0.486 g of MgO. What was the mass percentage of magnesium nitride in the mixture obtained after the initial burning? (d) Magnesium nitride can also be formed by reaction of the metal with ammonia at high temperature. Write a balanced equation for this reaction. If a \(6.3-\mathrm{g}\) Mg ribbon reacts with 2.57 \(\mathrm{g} \mathrm{NH}_{3}(g)\) and the reaction goes to completion, which component is the limiting reactant? What mass of \(\mathrm{H}_{2}(g)\) is formed in the reaction? (e) The standard enthalpy of formation of solid magnesium nitride is \(-461.08 \mathrm{kJ} / \mathrm{mol} .\) Calculate the standard enthalpy change for the reaction between magnesium metal and ammonia gas.

(a) What is the trend in first ionization energies as one proceeds down the group 7 A elements? Explain how this trend relates to the variation in atomic radii. (b) What is the trend in first ionization energies as one moves across the fourthperiod from \(\mathrm{K}\) to \(\mathrm{Kr}\) ? How does this trend compare with the trend in atomic radii?

Detailed calculations show that the value of \(Z_{\text { eff }}\) for the outermost electrons in Na and \(K\) 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 Na and 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 Rb atom based on the calculations for Na and K.

(a) Use orbital diagrams to illustrate what happens when an oxygen atom gains two electrons. (b) Why does \(\mathrm{O}^{3-}\) not exist?
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