Problem 78 - Chemistry: The Central Science

Question

Little is known about the properties of astatine, \(\mathrm{At}\), because of its rarity and high radioactivity. Nevertheless, it is possible for us to make many predictions about its properties. (a) Do you expect the element to be a gas, liquid, or solid at room temperature? Explain. (b) What is the chemical formula of the compound it forms with Na?

Step-by-Step Solution

Answer

(a) Astatine is likely to be a solid at room temperature, as it belongs to the halogen group and has a higher atomic mass than iodine, which is a solid. (b) The chemical formula for the compound astatine forms with sodium is NaAt, as astatine has a valence of -1 and sodium has a valence of +1.

Step 1: Locate Astatine on Periodic Table

Firstly locate astatine (At) on the periodic table. Astatine is found in group 17, which is also known as the halogen group. Therefore, knowing its position helps us to gain insights into predicting its properties.

Step 2: Compare Astatine with Other Group 17 Elements

Since astatine belongs to the halogen group, it shares some properties with other elements in the group like fluorine (F), chlorine (Cl), bromine (Br), and iodine (I). Following the periodic trend, the elements undergo a phase change from gas at the top of the group (F and Cl) to liquid in the middle with increasing atomic mass (like Br), and to solid in iodine (I). So, we can predict that astatine will be a solid at room temperature, as it is heavier (higher atomic mass) than iodine. (a) Based on our analysis, we can conclude that astatine is likely to be a solid at room temperature.

Step 3: Determine the Valence of Astatine

In general, the valence of an element refers to the number of electrons it can either gain, lose or share in a chemical bond. Halogens, including astatine, typically have a valence of -1. They tend to gain one electron to complete their outer shell and obtain a stable noble gas configuration.

Step 4: Determine the Valence of Sodium

Sodium (Na) is an alkali metal that belongs to group 1 of the periodic table. Alkali metals have a valence of +1, as they tend to lose one electron to achieve a stable noble gas configuration.

Step 5: Write the Chemical Formula for the Compound with Astatine and Sodium

Now that we have determined the valences of astatine and sodium, we can use them to write the chemical formula for the compound. A compound is neutral, so it is necessary to balance the charges. The valence of astatine is -1, and the valence of sodium is +1. To balance the charges, we need one sodium atom to react with one astatine atom. (b) Therefore, the chemical formula for the compound astatine forms with sodium is NaAt.

Key Concepts

Periodic Table

The Periodic Table is a comprehensive chart that organizes the chemical elements in a systematic way. Each element is placed in a specific location based on its atomic number, which is the number of protons in the nucleus of an atom. The table is divided into rows called periods and columns known as groups, with each group having elements with similar properties.

For example, the halogen group, where astatine (At) resides, is group 17. The periodic trends like atomic size, electronegativity, and state of matter at room temperature can be predicted based on an element's position in the table. As elements move down a group, their atomic size increases, and there is a general progression from gases to liquids to solids. This predictive power of the Periodic Table helps us to estimate that astatine, being below iodine in the halogen group, is likely a solid at room temperature.

Halogens

The halogens are a group of elements on the Periodic Table that include fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (At). They form group 17 and possess distinctive characteristics: they are highly reactive, particularly with alkali and alkaline earth metals.

Halogens typically have seven electrons in their outermost shell, which explains their reactivity as they strive to gain the one additional electron needed to achieve a full valence shell, a state that is energetically favorable. Consequently, their general valence is -1. Understanding the behavior of halogens allows us to make educated guesses about astatine's properties, even though it is rare and highly radioactive. Like its lighter counterparts, astatine is expected to participate in one-to-one reactions with metals, exemplified by the reaction with sodium (Na) to produce the compound NaAt.

Chemical Formula

A chemical formula represents the types and numbers of atoms in a molecule or compound. It serves as the shorthand that conveys the precise chemical composition. Deriving the chemical formula involves understanding the valence of each element and how they combine to achieve chemical stability.

For instance, to determine the chemical formula for the compound that astatine forms with sodium, it is essential to know their respective valences. Astatine, being a halogen, has a valence of -1, indicating it tends to gain one electron. Sodium, an alkali metal, has a valence of +1, as it typically loses one electron.When combining these two elements, their charges must balance to create a neutral compound, which results in the chemical formula NaAt. This formula indicates a one-to-one ratio of sodium to astatine atoms, adhering to the most straightforward stoichiometric relationship for the elements with valences of +1 and -1 respectively.