Question

An ionic substance of formula MX has a lattice energy of \(6 \times 10^{3} \mathrm{~kJ} / \mathrm{mol}\). Is the charge on the ion M likely to be \(1+, 2+\), or \(3+\) ? Explain.

Short answer

Based on the given lattice energy of \(6 \times 10^3 \mathrm{kJ/mol}\) for the ionic substance MX, the charge on ion M is likely to be \(3+\). This is because the lattice energy is dependent on the product of the charges \(q_1\) and \(q_2\), and the largest magnitude product (-3) occurs when the charge on ion M is \(3+\), producing a larger lattice energy.

Step-by-step solution

We are given that the lattice energy of an ionic substance MX is \(6 \times 10^3 \mathrm{kJ/mol}\). We are asked to determine if the charge on ion M is likely to be \(1+\), \(2+\), or \(3+\). #Step 2: Review the formula for lattice energy#

The lattice energy of an ionic substance is given by the following formula, which is based on Coulomb's Law: $$E_\text{lattice} = K \frac{q_1 q_2}{r}$$ where \(E_\text{lattice}\) is the lattice energy, \(q_1\) and \(q_2\) are the charges of the ions, \(r\) is the distance separating the ions, and \(K\) is a proportionality constant. #Step 3: Analyze the relationship between charge and lattice energy#

From the formula mentioned in step 2, we can see that the lattice energy depends on the product \(q_1 q_2\). This means that as the charges increase, the lattice energy generally becomes larger as well. Since we are dealing with an ionic substance of formula MX, it means that the charges should be equal and opposite. Therefore, if we assume the charge on ion X to be \(1-\), then the product \(q_1 q_2\) would be as follows for the different possible values of the charge on ion M: 1. If the charge on ion M is \(1+\), the product \(q_1 q_2 = (-1)(1) = -1\). 2. If the charge on ion M is \(2+\), the product \(q_1 q_2 = (-1)(2) = -2\). 3. If the charge on ion M is \(3+\), the product \(q_1 q_2 = (-1)(3) = -3\). #Step 4: Estimate the likely charge on ion M#

Given that the lattice energy of MX is \(6 \times 10^3 \mathrm{kJ/mol}\), we can assume that the charge on ion M has an effect on the magnitude of the lattice energy. Comparing the products \(q_1 q_2\) from step 3, we can see that the product (-3) has the largest magnitude, which would be produced when the charge on ion M is \(3+\). Therefore, the charge on the ion M is likely to be \(3+\).

Key concepts

Ionic Bonding

Ionic bonding is the type of chemical bond where an electrostatic attraction occurs between two oppositely charged ions. In simpler terms, it's like the strong pull an opposite pair of magnets feel towards each other. This bond forms typically between metals and nonmetals where the metal atom loses electrons to become a positively charged cation, and the nonmetal atom gains electrons to become a negatively charged anion.

During the formation of an ionic bond, atoms achieve a more stable electron configuration, often resembling that of noble gases. For instance, in table salt (sodium chloride), sodium (Na) donates one electron to chlorine (Cl), leading to Na+ and Cl- ions. These ions then stick together because of the attractive forces between their opposite charges, creating a solid network or lattice that we recognize as salt.

Understanding ionic bonding is crucial for predicting the physical properties of compounds, including their melting points, boiling points, and solubility in water. Additionally, ionic compounds typically conduct electricity when dissolved in water, due to the mobility of their ions in solution.

Coulomb's Law in Chemistry

Coulomb's Law in chemistry explains how strongly two charges attract or repel each other. Named after French physicist Charles-Augustin de Coulomb, this principle can be expressed in a simple formula: \( F = k \frac{{q_1q_2}}{{r^2}} \), where:\(F\) stands for force,\( q_1 \) and \( q_2\)represent the magnitudes of the charges,\( r\)is the distance between the centers of the two charges, and\( k\) is a constant that depends on the medium between the charges.

For chemistry students, this law is vital when studying ionic compounds as it helps to understand the factors affecting lattice energy—a measure of the strength of the bonds in an ionic crystal. Generally, larger charges or smaller distances result in stronger attractions and thus higher lattice energies. However, remember that Coulomb's Law only applies to point charges and ideal spherical charges, but it's a useful approximation for ions.

Ionic Compound Properties

Ionic compounds have distinctive physical and chemical properties owing to their unique bonding patterns. They typically form a crystalline lattice structure, which contributes to their high melting and boiling points. These compounds are also usually solid at room temperature. Here are some characteristic properties of ionic compounds:

• Electrical Conductivity: Ionic compounds can conduct electricity when dissolved in water (aqueous solution) or molten because the ions are free to move and carry charge.
• Solubility: Many ionic compounds are soluble in polar solvents, such as water, due to the ability of solvent molecules to stabilize the ions.
• Hardness: The strong ionic bonds in the crystal lattice make these compounds quite hard and brittle.
• High Melting and Boiling Points: The strong attractions between ions require a lot of energy to overcome, which results in ionic compounds having high melting and boiling points.

When considering the exercise, the significant lattice energy suggests a strong force of attraction within the ionic lattice, likely due to ions with higher charges. The properties of ionic compounds give us a clue as to why the substance MX has such a high lattice energy—ultimately connecting the macroscopic properties we can observe with the microscopic interactions explained by Coulomb's Law.