Question

A unit cell of an ionic crystal (a) shares some ions with other unit cells; (b) is the same as the formula unit; (c) is any portion of the crystal that has a cubic shape; (d) must contain the same number of cations and anions.

Short answer

The statements are True, False, Partially true, and False respectively

Step-by-step solution

Understand the definition of a unit cell

A unit cell in a crystal structure is the smallest component that, reproduced in three dimensions, represents the whole crystal.

Analyze each statement

(a) A unit cell of an ionic crystal shares some ions with other unit cells: This statement is true. In a unit cell, each corner atom is shared by eight unit cells and each atom on the face center is shared by two unit cells. Therefore, a unit cell shares some of its ions with its neighboring unit cells. (b) A unit cell is the same as the formula unit: This statement is false. A formula unit is the lowest whole number ratio of ions in an ionic compound and does not necessarily represent the actual number of ions in the unit cell of that compound. (c) A unit cell is any portion of the crystal that has a cubic shape: This statement is partly false and true. A unit cell can be in any shape like cubic, tetragonal, orthorhombic, rhombohedral, etc. However, when we refer to a 'unit cell' in general terms, we are often referring to a 'cubic unit cell'. (d) A unit cell must contain the same number of cations and anions: This statement is false. The number of cations and anions in a unit cell depends on the formula of the ionic compound. For example, if the formula of the ionic compound is AB2, the unit cell will contain twice as many B ions (anions) as A ions (cations).

Summarize the findings

To summarize: (a) is true as unit cells do share ions with each other, (b) is false as unit cells and formula units are different, (c) can be considered generally true specifically for cubic unit cells but false for unit cells of other shapes, and (d) is also false as the number of cations and anions depends on the chemical formula of the ionic compound. So, the correct judgement of the provided statements is True, False, Partially true, and False respectively.

Key concepts

Ionic Crystal

The term 'ionic crystal' refers to a type of crystal structure formed by ions. These ions are arranged in a repeating pattern, where positive ions (cations) and negative ions (anions) are bonded together through ionic bonds. This arrangement leads to the formation of a solid lattice that extends in all three dimensions.
Ionic crystals are characterized by high melting points due to the strong attraction between cations and anions. They are also typically brittle and have low electrical conductivity in their solid state, because the ions are locked into position and cannot move freely. However, when dissolved in water or melted, ionic crystals become good conductors of electricity because the ions are free to move.
Examples of ionic crystals include common table salt (NaCl) and potassium bromide (KBr). Each of these compounds forms a specific crystal structure based on the sizes of the ions involved and the necessity to maintain electrical neutrality within the crystal structure.

Cubic Unit Cell

A cubic unit cell is a basic structural component of a crystal that has a cubic shape. It is one of the simplest and most symmetrical types of unit cells. In a cubic unit cell, atoms, ions, or molecules are positioned at the corners and sometimes at the centers of the cube's faces or body.
There are three main types of cubic unit cells:

• Simple cubic (SC), where atoms are only at the corners of the cube.
• Body-centered cubic (BCC), where there is an additional atom at the center of the cube.
• Face-centered cubic (FCC), where there are additional atoms at the center of each face of the cube.

The choice of a cubic unit cell helps in simplifying the description of the symmetry and the repetitive pattern of the atomic arrangement in a crystal. It is important to note that while cubic unit cells are common, crystals can have unit cells of various other shapes, depending on the crystal system involved.

Formula Unit

A formula unit is the simplest integer ratio of the ions involved in an ionic compound. It provides the necessary proportions of each ion that define the composition of the compound, essentially reflecting its chemical formula. For example, in magnesium chloride (MgCl extsubscript{2}), the formula unit consists of one magnesium ion and two chloride ions.
This terminology becomes especially useful when contrasting it with molecular compounds. Unlike molecules, which describe exact numbers of atoms bonded together, formula units indicate the smallest ratio of ions that repeats in the substance structure.
Keep in mind that a formula unit doesn’t represent actual numbers of ions within a structural unit like a unit cell, as it simplifies the abundance ratios while maintaining the compound's neutrality. This makes it a key concept when discussing ionic compounds in chemistry.

Cation and Anion Balance

Cation and anion balance is a crucial concept in understanding the neutrality of ionic compounds. In any ionic compound, the total positive charge must equal the total negative charge to maintain electrical neutrality. This balance is achieved through the arrangement and proportion of cations and anions within the structure.
For instance, if an ionic compound has the formula AB extsubscript{2}, it indicates that one cation from the 'A' group combines with two anions from the 'B' group to balance the charges. It is the formula unit that defines this ratio and balances out to form a neutral compound.
Within a unit cell, you won’t necessarily find an equal number of cations and anions. Instead, their ratio, as given by the chemical formula, determines the overall number, ensuring the entire crystal maintains that crucial charge balance. This concept is foundational and helps in predicting the properties and behaviors of ionic compounds.