Problem 55 - Chemistry and Chemical Reactivity

Question

Sodium ions, Na \(^{+}\), form ionic compounds with fluoride ions, \(\mathrm{F}^{-},\) and iodide ions, \(\mathrm{I}^{-}\). The radii of these ions are as follows: \(\mathrm{Na}^{+}=116 \mathrm{pm} ; \mathrm{F}^{-}=119 \mathrm{pm} ;\) and \(\mathrm{I}^{-}=206 \mathrm{pm} .\) In which ionic compound, \(\mathrm{NaF}\) or \(\mathrm{NaI}\) are the forces of attraction between cation and anion stronger? Explain your answer.

Step-by-Step Solution

Answer

The forces of attraction are stronger in \( \mathrm{NaF} \) than in \( \mathrm{NaI} \) due to the smaller distance between ions.

Step 1: Understanding Coulomb's Law

Coulomb's Law describes the electric force between charged objects. The formula is given by \( F = k \frac{|q_1 \cdot q_2|}{r^2} \), where \( F \) is the force of attraction, \( q_1 \) and \( q_2 \) are the charges of the ions, \( r \) is the distance between the ions, and \( k \) is Coulomb's constant.

Step 2: Identifying Ionic Charges

The charges of the sodium ion \( \mathrm{Na}^+ \) and the fluoride ion \( \mathrm{F}^- \) and iodide ion \( \mathrm{I}^- \) are each one unit of positive or negative charge. Therefore, \( q_1 \cdot q_2 = 1 \cdot (-1) = -1 \) for both \( \mathrm{NaF} \) and \( \mathrm{NaI} \).

Step 3: Calculating the Distance Between Ions

The effective distance \( r \) between the charged ions is the sum of their ionic radii: \( r = \text{radius of } \mathrm{Na}^+ + \text{radius of anion} \). For \( \mathrm{NaF} \), the distance is \( 116 \mathrm{pm} + 119 \mathrm{pm} = 235 \mathrm{pm} \). For \( \mathrm{NaI} \), the distance is \( 116 \mathrm{pm} + 206 \mathrm{pm} = 322 \mathrm{pm} \).

Step 4: Comparing Forces of Attraction

According to Coulomb's Law, as the distance \( r \) increases, the force \( F \) decreases because of the \( r^2 \) relationship. Thus, the smaller the distance, the stronger the force of attraction. \( 235 \mathrm{pm} < 322 \mathrm{pm} \), so \( \mathrm{NaF} \) has the stronger force.

Key Concepts

Coulomb's Law and Ionic Compounds

Coulomb's Law explains how charged particles interact with each other through electrical forces. This is particularly useful in understanding ionic compounds, where positive and negative ions come together to form stable structures. The formula, \( F = k \frac{|q_1 \cdot q_2|}{r^2} \), shows that the force of attraction \( F \) between two charges \( q_1 \) and \( q_2 \) depends on their magnitude and distance \( r \) apart, with \( k \) being Coulomb's constant.

Let's break this down:

• \( |q_1 \cdot q_2| \) represents the product of the charges' magnitudes.
• \( r \) is the separation distance between the ions.
• The force \( F \) increases as the magnitude of the charges increases or the distance decreases.

For ionic compounds like \( \text{NaF} \) and \( \text{NaI} \), this means the force of ion attraction depends heavily on how far apart the ions are.

The Significance of Ionic Radii

Ionic radii indicate the size of an ion, impacting how closely ions can approach each other in a compound. This dimension is crucial in determining the effective distance \( r \) between ions in a structure. For example, in \( \text{NaF} \), the sodium ion \( \text{Na}^+ \) with a radius of 116 pm pairs with a fluoride ion \( \text{F}^- \) having a radius of 119 pm, leading to a total distance of 235 pm.

In \( \text{NaI} \), however, the iodide ion \( \text{I}^- \) has a considerably larger radius of 206 pm, making the distance between \( \text{Na}^+ \) and \( \text{I}^- \) equal to 322 pm.

How do these radii values affect the overall ionic bond strength?

• The smaller the sum of the radii, the closer the ions can get.
• Closer ions have stronger electrostatic forces holding them together.
• Thus, \( \text{NaF} \) exhibits stronger ionic attraction than \( \text{NaI} \) due to the closer proximity.

Forces of Attraction in Ionic Compounds

Forces of attraction in ionic compounds are primarily the electrostatic forces between the positively and negatively charged ions. These forces are responsible for the high melting and boiling points, and the solidity of ionic compounds. The strength of these forces can be directly understood through the Coulomb's Law.

When analyzing compounds like \( \text{NaF} \) versus \( \text{NaI} \), the ionic attractions become clearer:

• In \( \text{NaF} \), the smaller distance (235 pm) results in stronger attraction.
• In \( \text{NaI} \), the larger distance (322 pm) weakens the force of attraction.
• Thus, \( \text{NaF} \), with stronger ionic forces, tends to be more robust.

By ensuring the ions are as close as possible, the ionic compound can achieve maximum stability and strength. This principle is key when evaluating the properties and behaviors of different ionic compounds.