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Sagot :
To determine which statement about crystal lattice energy is best supported by the information in the table, we need to understand the trend in lattice energy with respect to the size of cations.
Step-by-Step Analysis:
1. List the Lattice Energies:
- LiF: -1036 kJ/mol
- LiCl: -853 kJ/mol
- NaF: -923 kJ/mol
- KF: -821 kJ/mol
- NaCl: -786 kJ/mol
2. Cation Sizes:
- Lithium ion (Li⁺) is the smallest cation.
- Sodium ion (Na⁺) is larger than Li⁺.
- Potassium ion (K⁺) is larger than Na⁺.
3. Comparing Lattice Energies Based on Cation Size:
- LiF vs KF:
- Li⁺ is smaller than K⁺.
- LiF: -1036 kJ/mol
- KF: -821 kJ/mol
- Lattice energy of LiF is more negative than that of KF.
- Conclusion: Smaller cations (Li⁺) result in higher (more negative) lattice energy compared to larger cations (K⁺).
- LiF vs LiCl:
- Li⁺ is common in both.
- F⁻ is smaller than Cl⁻.
- LiF: -1036 kJ/mol
- LiCl: -853 kJ/mol
- Lattice energy of LiF is more negative than that of LiCl.
- Conclusion: Smaller anions (F⁻) result in higher (more negative) lattice energy compared to larger anions (Cl⁻).
- NaCl vs NaF:
- Na⁺ is common in both.
- F⁻ is smaller than Cl⁻.
- NaCl: -786 kJ/mol
- NaF: -923 kJ/mol
- Lattice energy of NaF is more negative than that of NaCl.
- Conclusion: Smaller anions (F⁻) result in higher (more negative) lattice energy compared to larger anions (Cl⁻).
4. Eliminate the Incorrect Statements:
- Statement 2: "The lattice energy increases as the cations get larger, as shown by LiF and LiCl."
- This is incorrect because the lattice energy of LiF (-1036 kJ/mol) is more negative than that of LiCl (-853 kJ/mol), indicating that smaller cations (Li⁺) increase lattice energy.
- Statement 3: "The lattice energy decreases as cations get smaller, as shown by NaCl and NaF."
- This is incorrect because NaF has a more negative lattice energy (-923 kJ/mol) compared to NaCl (-786 kJ/mol), indicating that smaller cations actually increase lattice energy.
- Statement 4: "The lattice energy decreases as the cations get smaller, as shown by NaF and KF."
- This is incorrect because NaF has a more negative lattice energy (-923 kJ/mol) compared to KF (-821 kJ/mol), indicating that smaller cations actually increase lattice energy.
5. Verify the Correct Statement:
- Statement 1: "The lattice energy increases as cations get smaller, as shown by LiF and KF."
- This is correct because Li⁺ (in LiF) is smaller than K⁺ (in KF), and LiF has a more negative lattice energy (-1036 kJ/mol) compared to KF (-821 kJ/mol).
Final Answer:
The statement about crystal lattice energy that is best supported by the information in the table is:
"The lattice energy increases as cations get smaller, as shown by LiF and KF."
Step-by-Step Analysis:
1. List the Lattice Energies:
- LiF: -1036 kJ/mol
- LiCl: -853 kJ/mol
- NaF: -923 kJ/mol
- KF: -821 kJ/mol
- NaCl: -786 kJ/mol
2. Cation Sizes:
- Lithium ion (Li⁺) is the smallest cation.
- Sodium ion (Na⁺) is larger than Li⁺.
- Potassium ion (K⁺) is larger than Na⁺.
3. Comparing Lattice Energies Based on Cation Size:
- LiF vs KF:
- Li⁺ is smaller than K⁺.
- LiF: -1036 kJ/mol
- KF: -821 kJ/mol
- Lattice energy of LiF is more negative than that of KF.
- Conclusion: Smaller cations (Li⁺) result in higher (more negative) lattice energy compared to larger cations (K⁺).
- LiF vs LiCl:
- Li⁺ is common in both.
- F⁻ is smaller than Cl⁻.
- LiF: -1036 kJ/mol
- LiCl: -853 kJ/mol
- Lattice energy of LiF is more negative than that of LiCl.
- Conclusion: Smaller anions (F⁻) result in higher (more negative) lattice energy compared to larger anions (Cl⁻).
- NaCl vs NaF:
- Na⁺ is common in both.
- F⁻ is smaller than Cl⁻.
- NaCl: -786 kJ/mol
- NaF: -923 kJ/mol
- Lattice energy of NaF is more negative than that of NaCl.
- Conclusion: Smaller anions (F⁻) result in higher (more negative) lattice energy compared to larger anions (Cl⁻).
4. Eliminate the Incorrect Statements:
- Statement 2: "The lattice energy increases as the cations get larger, as shown by LiF and LiCl."
- This is incorrect because the lattice energy of LiF (-1036 kJ/mol) is more negative than that of LiCl (-853 kJ/mol), indicating that smaller cations (Li⁺) increase lattice energy.
- Statement 3: "The lattice energy decreases as cations get smaller, as shown by NaCl and NaF."
- This is incorrect because NaF has a more negative lattice energy (-923 kJ/mol) compared to NaCl (-786 kJ/mol), indicating that smaller cations actually increase lattice energy.
- Statement 4: "The lattice energy decreases as the cations get smaller, as shown by NaF and KF."
- This is incorrect because NaF has a more negative lattice energy (-923 kJ/mol) compared to KF (-821 kJ/mol), indicating that smaller cations actually increase lattice energy.
5. Verify the Correct Statement:
- Statement 1: "The lattice energy increases as cations get smaller, as shown by LiF and KF."
- This is correct because Li⁺ (in LiF) is smaller than K⁺ (in KF), and LiF has a more negative lattice energy (-1036 kJ/mol) compared to KF (-821 kJ/mol).
Final Answer:
The statement about crystal lattice energy that is best supported by the information in the table is:
"The lattice energy increases as cations get smaller, as shown by LiF and KF."
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