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Sagot :
To determine which statement about crystal lattice energy is best supported by the information in the table, let's analyze the given lattice energies in relation to cation size:
### Given Lattice Energies:
- LiF: -1036 kJ/mol
- LiCl: -853 kJ/mol
- NaF: -923 kJ/mol
- KF: -821 kJ/mol
- NaCl: -786 kJ/mol
### Analysis of Relationships:
1. LiF vs. KF:
- Cations: Li[tex]\(^+\)[/tex] vs. K[tex]\(^+\)[/tex]
- Lattice Energies: LiF (-1036 kJ/mol) vs. KF (-821 kJ/mol)
- Observation: Li[tex]\(^+\)[/tex] is smaller than K[tex]\(^+\)[/tex], and LiF has a more negative (higher) lattice energy than KF.
2. LiF vs. LiCl:
- Anions: F[tex]\(^-\)[/tex] vs. Cl[tex]\(^-\)[/tex]
- Cations: Li[tex]\(^+\)[/tex]
- Lattice Energies: LiF (-1036 kJ/mol) vs. LiCl (-853 kJ/mol)
- Observation: Since F[tex]\(^-\)[/tex] is smaller than Cl[tex]\(^-\)[/tex], comparing these does not directly relate to cation size changes.
3. NaCl vs. NaF:
- Anions: Cl[tex]\(^-\)[/tex] vs. F[tex]\(^-\)[/tex]
- Cations: Na[tex]\(^+\)[/tex]
- Lattice Energies: NaCl (-786 kJ/mol) vs. NaF (-923 kJ/mol)
- Observation: Since F[tex]\(^-\)[/tex] is smaller than Cl[tex]\(^-\)[/tex], comparing these does not directly relate to cation size changes.
4. NaF vs. KF:
- Cations: Na[tex]\(^+\)[/tex] vs. K[tex]\(^+\)[/tex]
- Anions: F[tex]\(^-\)[/tex]
- Lattice Energies: NaF (-923 kJ/mol) vs. KF (-821 kJ/mol)
- Observation: Na[tex]\(^+\)[/tex] is smaller than K[tex]\(^+\)[/tex], and NaF has a more negative (higher) lattice energy than KF.
### Conclusion:
From the comparisons:
- LiF vs. KF:
- Li[tex]\(^+\)[/tex] is smaller than K[tex]\(^+\)[/tex].
- LiF with Li[tex]\(^+\)[/tex] has a higher lattice energy (-1036 kJ/mol) than KF with K[tex]\(^+\)[/tex] (-821 kJ/mol).
- NaF vs. KF:
- Na[tex]\(^+\)[/tex] is smaller than K[tex]\(^+\)[/tex].
- NaF with Na[tex]\(^+\)[/tex] has a higher lattice energy (-923 kJ/mol) than KF with K[tex]\(^+\)[/tex] (-821 kJ/mol).
Both sets of comparisons clearly support the statement: "The lattice energy increases as cations get smaller."
Thus, the statement best supported by the data is:
"The lattice energy increases as cations get smaller, as shown by LiF and KF."
### Given Lattice Energies:
- LiF: -1036 kJ/mol
- LiCl: -853 kJ/mol
- NaF: -923 kJ/mol
- KF: -821 kJ/mol
- NaCl: -786 kJ/mol
### Analysis of Relationships:
1. LiF vs. KF:
- Cations: Li[tex]\(^+\)[/tex] vs. K[tex]\(^+\)[/tex]
- Lattice Energies: LiF (-1036 kJ/mol) vs. KF (-821 kJ/mol)
- Observation: Li[tex]\(^+\)[/tex] is smaller than K[tex]\(^+\)[/tex], and LiF has a more negative (higher) lattice energy than KF.
2. LiF vs. LiCl:
- Anions: F[tex]\(^-\)[/tex] vs. Cl[tex]\(^-\)[/tex]
- Cations: Li[tex]\(^+\)[/tex]
- Lattice Energies: LiF (-1036 kJ/mol) vs. LiCl (-853 kJ/mol)
- Observation: Since F[tex]\(^-\)[/tex] is smaller than Cl[tex]\(^-\)[/tex], comparing these does not directly relate to cation size changes.
3. NaCl vs. NaF:
- Anions: Cl[tex]\(^-\)[/tex] vs. F[tex]\(^-\)[/tex]
- Cations: Na[tex]\(^+\)[/tex]
- Lattice Energies: NaCl (-786 kJ/mol) vs. NaF (-923 kJ/mol)
- Observation: Since F[tex]\(^-\)[/tex] is smaller than Cl[tex]\(^-\)[/tex], comparing these does not directly relate to cation size changes.
4. NaF vs. KF:
- Cations: Na[tex]\(^+\)[/tex] vs. K[tex]\(^+\)[/tex]
- Anions: F[tex]\(^-\)[/tex]
- Lattice Energies: NaF (-923 kJ/mol) vs. KF (-821 kJ/mol)
- Observation: Na[tex]\(^+\)[/tex] is smaller than K[tex]\(^+\)[/tex], and NaF has a more negative (higher) lattice energy than KF.
### Conclusion:
From the comparisons:
- LiF vs. KF:
- Li[tex]\(^+\)[/tex] is smaller than K[tex]\(^+\)[/tex].
- LiF with Li[tex]\(^+\)[/tex] has a higher lattice energy (-1036 kJ/mol) than KF with K[tex]\(^+\)[/tex] (-821 kJ/mol).
- NaF vs. KF:
- Na[tex]\(^+\)[/tex] is smaller than K[tex]\(^+\)[/tex].
- NaF with Na[tex]\(^+\)[/tex] has a higher lattice energy (-923 kJ/mol) than KF with K[tex]\(^+\)[/tex] (-821 kJ/mol).
Both sets of comparisons clearly support the statement: "The lattice energy increases as cations get smaller."
Thus, the statement best supported by the data is:
"The lattice energy increases as cations get smaller, as shown by LiF and KF."
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