NaCl and KF have the same crystal structure. The only difference between the two is the distance that separates cations and anions. (a) The lattice energies of NaCl and KF are given in Table 8.1. Based on the lattice energies, would you expect the Na─Cl or the K─F distance to be longer?

검증된 단계별 안내

Identify the relationship between lattice energy and ionic distance. Lattice energy is inversely proportional to the distance between ions; the greater the distance, the lower the lattice energy.

Look up the lattice energies for NaCl and KF in Table 8.1. Compare the values to determine which compound has the higher lattice energy.

Based on the comparison, determine which compound has the shorter ionic distance. The compound with the higher lattice energy will have the shorter distance between ions.

Conclude which ionic distance is longer based on the inverse relationship between lattice energy and ionic distance. If NaCl has a higher lattice energy than KF, then the Na─Cl distance is shorter, making the K─F distance longer, and vice versa.

Summarize the findings: The compound with the lower lattice energy will have the longer distance between its cations and anions.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Lattice Energy

Lattice energy is the amount of energy released when gaseous ions combine to form an ionic solid. It is a measure of the strength of the forces between the ions in an ionic compound. Higher lattice energy indicates stronger ionic bonds, which typically results in shorter distances between cations and anions.

Ionic Radius

Ionic radius refers to the size of an ion in a crystal lattice. Cations are smaller than their parent atoms due to the loss of electrons, while anions are larger due to the gain of electrons. The size of the ions affects the distance between them in the lattice structure, influencing the overall lattice energy.

Coulomb's Law

Coulomb's Law describes the electrostatic interaction between charged particles. It states that the force between two charged ions is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This principle helps explain how the distance between ions affects lattice energy and stability.