The table lists the lattice energies of some compounds. compoundlattice energy (kj/mol)lif            –1,036licl            –853naf            –923kf            –821nacl            –786which statement about crystal lattice energy is  best  supported by the information in the table? the lattice energy increases as cations get smaller, as shown by lif and kf. the lattice energy increases as the cations get larger, as shown by lif and licl. the lattice energy decreases as cations get smaller, as shown by nacl and naf. the lattice energy decreases as the cations get smaller, as shown by naf and kf.

Answer : Option A) The lattice energy increases as cations get smaller, as shown by LiF and KF.

Explanation : It is observed that lattice energy is mostly influenced by two main factors of an ionic solid which are;

i) The charge on the ions - As the charge of the ions increases, the lattice energy is observed to increase too.

and

ii) The radius, or size, of the ions - As the size of the ions increases, the lattice energy decreases with it.

So, here in this question the second reason is clearly observed. Hence, it is self-explained that the size of the cations are decreased in the ionic solids the lattice energy increases.

its A

The lattice energy increases as cations get smaller, as shown by LiF and KF.

OR

The lattice energy increases as the charge of anions increases, as shown by LiF and LiCl. The answer is B.

The lattice energy increases as cations get smaller, as shown by LiF and KF.

Explanation:

Lattice energy is the change in internal energy that accompanies the formation of one mole of the solid from its constituent gas phase ions at 0 K. In calculating the lattice energy, we assume an electrostatic model where the ions are regarded as point charges.

The size of the ions determines the magnitude of the lattice energy. If the anion is the same, then the magnitude of the lattice energy depends on the the size of the cation, the smaller the cation the greater the lattice energy.

Since Li^+ is smaller than K^+, it is expected that LiF will have a greater lattice energy than KF, hence the answer.

Among the choices the statement about crystal lattice energy is best supported by the information in the table is The lattice energy increases as the charge of anions increases, as shown by LiF and LiCl. The answer is B. 

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Cations from smallest to largest
Li⁺ ,Na⁺, K⁺ (from Periodic Table, the bigger number of period, the bigger size, of atom, so the bigger size of cation)

1) LiF smaller  cation then KF
1,036                                 853
The lattice energy increases as cations get smaller, as shown by LiF and KF.
I think this one should be correct answer, because the compared substances have also the same anion, and we can compare cations in them.

2) The same cation Li , so wrong statement.

3)The same cation Na , so wrong statement.

4) NaCl smaller cation then KF
  786                                   853

From the table the enthalpies are negative  meaning the reactions are exothermic where gaseous ions bind to form an ionic solid.Lattice Energy is a type of potential energy that may be referred to as the energy required to break apart an ionic solid and convert its component atoms into gaseous ions; where the lattice energy is always positive, since the will be an endothermic reactions. Lattice energy may be also be defined as the energy released when gaseous ions bind to form an ionic solid where the energy value will be negative since the reactions are exothermic. 

The best and the most correct answer among the choices provided by the question is the first choice. The statement the supports the information is "The lattice energy increases as cations get smaller, as shown by LiF and KF." I hope my answer has come to your help. God bless and have a nice day ahead!