Problem 165 - Introductory Chemistry Atoms First

Question

Arrange in order of increasing valence-shell size: \(\mathrm{Sr}, \mathrm{Mg}, \mathrm{Ba}, \mathrm{Ca}, \mathrm{Be}\).

Step-by-Step Solution

Answer

The elements from Group 2 in the periodic table increase in valence-shell size as we go down the group. Their positions within the group are as follows: Be (2nd period), Mg (3rd period), Ca (4th period), Sr (5th period), and Ba (6th period). Therefore, the order of increasing valence-shell size for the given elements is: \(\mathrm{Be} < \mathrm{Mg} < \mathrm{Ca} < \mathrm{Sr} < \mathrm{Ba}\).

Step 1: Find the placement of each element in the periodic table

Locate the positions of each of the given elements from Group 2 in the periodic table. This will aid in determining which ones are placed higher and which ones are lower within the group.

Step 2: Compare the elements within the group

Remember that as we go down a group, the valence-shell size increases. Compare the elements within Group 2 based on their placement and order them accordingly.

Step 3: Arrange the elements in order of increasing valence-shell size

Organize the given elements in ascending order based on their valence-shell size, as gathered from observing their positions within Group 2 in the periodic table. From our analysis, we know that as we go down Group 2, the valence-shell size will increase. The placement of each element within Group 2 is as follows: - Be (Beryllium): 2nd period - Mg (Magnesium): 3rd period - Ca (Calcium): 4th period - Sr (Strontium): 5th period - Ba (Barium): 6th period Considering this information, we can now arrange the given elements in order of increasing valence-shell size: \(\mathrm{Be} < \mathrm{Mg} < \mathrm{Ca} < \mathrm{Sr} < \mathrm{Ba}\)

Key Concepts

Group 2 elements

Group 2 elements, also known as alkaline earth metals, are a fascinating collection of elements on the periodic table. These metals include beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), and barium (Ba), among others. Group 2 elements are located in the second column of the periodic table. This group is characterized by having two electrons in their outermost shell.

• They are metals that are typically shiny, silvery-white, and somewhat reactive.
• Due to their two valence electrons, they commonly form +2 ions.
• They have higher melting points than alkali metals in Group 1 but are still soft metals.

The small number of valence electrons means that these elements readily lose them to achieve a stable electron configuration. Each subsequent element in the group has a higher atomic number and is more massive. Alkaline earth metals are vital in many biological and industrial processes.

periodic table trends

The periodic table is organized in such a way that allows us to observe and understand patterns among the elements. One of these patterns or trends is seen in how valence-shell size changes as we move down a group. This is crucial for understanding the order of elements based on valence-shell size.
As you move from top to bottom in a group:

• The atomic number increases, introducing additional electron shells.
• The valence-shell size grows larger due to the addition of these shells, even though the number of valence electrons remains the same.

This trend helps in predicting the chemical behavior of elements as well as their physical properties like atomic radius. Understanding these patterns aids in organizing elements based on the increase or decrease of specific attributes such as valence-shell size.

electron configuration

The electron configuration of an element describes the arrangement of electrons within its atomic structure. For the elements in Group 2, electron configuration plays a fundamental role in understanding their reactivity and their place in periodic trends.
Each Group 2 element has an electron configuration ending in \( ns^2 \). This indicates that in their most outer shell, they have two electrons, crucial for the properties they exhibit:

• The outer shell for beryllium (Be) is 2s, so its configuration is \( 1s^2 2s^2 \).
• Magnesium (Mg) has its outer shell as 3s, yielding the configuration of \( 1s^2 2s^2 2p^6 3s^2 \).
• Similarly, each subsequent Group 2 element, like calcium (Ca), strontium (Sr), and barium (Ba), builds upon this basic configuration as they each add a new electron shell.

This configuration is the reason all Group 2 elements tend to lose two electrons and form +2 ions. It explains why they are bond-friendly metals readily participating in diverse chemical reactions.

atomic radius

The atomic radius is a way to describe the size of an atom from its nucleus to its outermost electron shell. It's an important trend to consider, especially when discussing periodic table trends and the properties of elements in Group 2.
As you move down Group 2:

• The atomic radius increases as the number of electron shells increases.
• This enlargement occurs even though there are the same two valence electrons orbiting further away from the nucleus.

The increased atomic radius impacts material properties such as density and melting points. For instance, although adding layers of electrons can shield the positive nucleus charge, making it weaker, this brings along a larger size. Group 2 elements demonstrate this well, with beryllium being the smallest in size and barium much larger, displaying this progressive enlargement when moving from the top to the bottom of the group.