AP Chemistry
2.3 Structure of Ionic Solids
2.1 Types of Chemical Bonds
1.8 Valence Electrons and Ionic Compounds
Multi-Unit
A student models the magnitude of the Coulombic attractive force between adjacent oppositely charged ions in two crystalline solids, \(\text{X}\) and \(\text{Y}\), using Coulomb's law:
\[ F \propto \dfrac{|q_1 q_2|}{d^2} \]
where \(q_1\) and \(q_2\) represent the ion charges and \(d\) represents the equilibrium internuclear distance between the cation and anion. The parameters for each solid are shown in the table below.
Based on the model and the data provided, what is the ratio of the Coulombic attractive force in solid \(\text{Y}\) to that in solid \(\text{X}\), \(\dfrac{F_{\text{Y}}}{F_{\text{X}}}\)?
\[ F \propto \dfrac{|q_1 q_2|}{d^2} \]
where \(q_1\) and \(q_2\) represent the ion charges and \(d\) represents the equilibrium internuclear distance between the cation and anion. The parameters for each solid are shown in the table below.
| Solid | Cation charge | Anion charge | Internuclear distance |
|---|---|---|---|
| \(\text{X}\) | \(+2\) | \(-2\) | \(d_0\) |
| \(\text{Y}\) | \(+1\) | \(-1\) | \(1.5\,d_0\) |
Based on the model and the data provided, what is the ratio of the Coulombic attractive force in solid \(\text{Y}\) to that in solid \(\text{X}\), \(\dfrac{F_{\text{Y}}}{F_{\text{X}}}\)?
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