Question

Predict the missing value (?) for each property listed below. The atomic radius, density, and boiling point are given for elements in Group VIIA/17. $$\begin{array}{cccc}\hline \text { Element } & \text { Atomic Radius } & \text { Density at } 20^{\circ} \mathrm{C} & \text { Boiling Point } \\ \hline \mathrm{Cl} & (?) \mathrm{nm} & 1.56 \mathrm{~g} / \mathrm{mL} & -34.6^{\circ} \mathrm{C} \\\\\mathrm{Br} & 0.115 \mathrm{nm} & (?) \mathrm{g} / \mathrm{mL} & 58.8^{\circ} \mathrm{C} \\\\\mathrm{I} & 0.133 \mathrm{nm} & 4.97 \mathrm{~g} / \mathrm{mL} & (?)^{\circ} \mathrm{C} \\\\\hline\end{array}$$

Short answer

Cl's atomic radius is ~0.1 nm, Br's density is ~3.12 g/mL, and I's boiling point is ~184.4°C.

Step-by-step solution

Understand the Periodic Trend

The elements Cl, Br, and I belong to Group VIIA/17 or the halogens in the periodic table. A general trend in this group is that as we move down the group, the atomic radius increases. Hence, Cl, being above Br and I in the group, will have the smallest atomic radius, while I will have the largest.

Predict Chlorine's (Cl) Atomic Radius

Given the atomic radius of Br is 0.115 nm and I is 0.133 nm, and noting the trend that the atomic radius increases down the group, Cl should have a smaller atomic radius than Br. A reasonable estimation for Cl is around 0.1 nm, based on typical values for halogens.

Estimate Bromine's (Br) Density

The density of halogens typically increases down the group. Given Cl has a density of 1.56 g/mL and I has a density of 4.97 g/mL, Br's density should be between these two values. A reasonable estimation would be around 3.12 g/mL, calculated as a midpoint.

Determine Iodine's (I) Boiling Point

Boiling points generally increase down the group as atomic weight and dispersion forces increase. Cl's boiling point is -34.6°C and Br's is 58.8°C. Given the trend, I should have a higher boiling point. A typical value for Iodine's boiling point is approximately 184.4°C.

Key concepts

Halogens

Halogens are a fascinating group of elements found in Group VIIA/17 of the periodic table. These elements include fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (At). They are known for being highly reactive, especially with alkali metals and alkaline earth metals, forming a wide range of salts.
One of the most interesting properties of halogens is their gradual change of characteristics as you move down the group. For instance, fluorine is a gas under normal conditions, while iodine is a solid. This variation in state is due to differences in intermolecular forces and molecular weight. Halogens play crucial roles in both biology and industry. For example, iodine is essential for thyroid function, while chlorine is widely used in water purification and the production of PVC.
Understanding halogens and their properties helps us appreciate their role in nature's delicate balance and their various applications across different fields.

Atomic Radius

The atomic radius is a critical concept when studying elements like halogens. Essentially, it is the distance from the nucleus of an atom to the outer boundary of its electron cloud. As you move down the group of halogens in the periodic table, the atomic radius increases. This happens because each successive element has an additional electron shell compared to the one above it.
For instance, chlorine (with an estimated atomic radius of 0.1 nm) has fewer electron shells than iodine, making iodine's atomic radius larger at 0.133 nm. These increasing sizes affect how halogens interact with other substances, explaining some of their unique reactivity patterns. This trend in atomic size is important for predicting how these elements will behave in chemical reactions.

Boiling Point

The boiling point of an element is the temperature at which it changes from a liquid to a gas. Among the halogens, the boiling point increases as you go down the group. This increase is due to the fact that atoms of heavier halogens have more electrons, leading to stronger London dispersion forces. These forces require more energy (heat) to overcome, thus raising the boiling point.
For example, chlorine has a boiling point of -34.6°C, while bromine boils at 58.8°C, and iodine at an impressive 184.4°C. Understanding boiling points is crucial, especially in industrial processes where precise temperature control is necessary, such as in the distillation of bromine.

Density

Density is a measure of how much mass is contained within a given volume and is a useful physical property to understand elements like halogens. As you descend the Group VIIA in the periodic table, the density of these elements increases. This trend is because the atomic mass increases with additional electron shells and a larger nucleus, despite the increase in atomic size.

• Chlorine, which is typically a gas at room temperature, has a relatively low density of 1.56 g/mL.
• Bromine, with a density of about 3.12 g/mL, is a liquid.
• Iodine, being a solid, has a much higher density of 4.97 g/mL.

Understanding density trends helps in anticipating how these elements will behave in different environments and applications, which is vital in fields like chemistry and materials science.