AP Chem lattice energy and Coulomb law cheat sheet

Lattice energy definition

The energy released when gaseous ions form an ionic solid. It reflects the strength of the ionic bonds.

True or False: Lattice energy is always negative.

True. It indicates energy release during ionic bond formation.

Factors affecting lattice energy

- Charge of ions - Size of ions - Arrangement of ions

Fill in the blank: Lattice energy increases with ______ charges and ______ ionic sizes.

increasing, decreasing

What does higher lattice energy imply?

Stronger ionic bonds, higher melting points, and greater stability of the ionic compound.

Relationship between ionic size and lattice energy

As ionic size increases, lattice energy decreases due to reduced electrostatic attraction.

Equation for lattice energy using Coulomb's Law

$\displaystyle U = k \\frac{Q_1 Q_2}{r}$, where $\displaystyle U$ is lattice energy, $\displaystyle Q_1$ and $\displaystyle Q_2$ are ion charges, $\displaystyle r$ is distance.

Cation vs. Anion size effect

Cations are typically smaller than anions, leading to stronger attractions and greater lattice energies.

Worked example: Lattice energy of NaCl

For NaCl, $\displaystyle Q_1 = +1, Q_2 = -1$ and $\displaystyle r$ approx. 2.81 Å. Calculate $\displaystyle U$.

What is Born-Haber cycle?

A thermodynamic cycle that relates lattice energy to other thermodynamic quantities like ionization energy and electron affinity.

Higher charge effects on lattice energy

A +2 charge ion has significantly greater lattice energy than a +1 charge ion, ceteris paribus.

True or False: Lattice energy can be measured directly.

False. It's calculated indirectly using other thermodynamic data.

Comparison: NaCl vs. MgO

MgO has higher lattice energy due to +2 and -2 charges versus +1 and -1 in NaCl.

Effect of ionic radius on melting point

Smaller ionic radius leads to higher lattice energy and thus higher melting point.

Lattice energy and solubility relationship

Higher lattice energy often results in lower solubility in water.

What happens to lattice energy with increased distance?

Increased distance between ions reduces lattice energy due to weaker electrostatic forces.

Coulomb's Law formula?

$\displaystyle F = k \\frac{|q_1 q_2|}{r^2}$; Defines force between two charges.

True or False: Lattice energy is inversely proportional to distance.

False; Lattice energy is directly proportional to the charges and inversely proportional to distance.

Calculate force between charges +2 and -3 at 5 cm.

$\displaystyle F = k \\frac{|2 \times -3|}{(0.05)^2} \Rightarrow F = 240 k$ N.

Coulomb's Law application?

Used to calculate ionic interaction strength in ionic compounds.

What does increasing charge do to force?

Increases the electrostatic force between the charges.

Fill in the blank: The force decreases as ______ increases.

distance (r) increases.

Compare ionic interactions in NaCl vs MgCl2.

MgCl2 has higher lattice energy due to greater charge of Mg²⁺.

Effect of distance on ionic bonding strength?

Increased distance weakens the ionic bond strength.

Coulomb's Law constant (k)?

k = 8.99 × 10^9 N m²/C²; used in calculations.

True or False: Lattice energy increases with larger ionic radii.

False; Lattice energy decreases with larger ionic radii.

What role does lattice energy play?

Indicates stability of ionic compounds; higher energy = more stable.

Coulomb's Law units for force?

Newtons (N); derived from electrostatic interactions.

What factors affect lattice energy?

1. Ionic charge 2. Ionic radius - Higher charge = stronger attraction - Smaller radius = stronger attraction

True or False: Lattice energy decreases with increasing ionic size.

True. Larger ions have increased distance between charges, resulting in weaker electrostatic attraction.

Comparing NaCl and KCl, which has higher lattice energy?

NaCl. Na+ is smaller than K+, leading to stronger attraction and higher lattice energy.

Fill in the blank: Lattice energy is inversely proportional to the ______.

Distance between ions. Greater distance decreases the electrostatic force.

Cause → Effect: Increasing ionic charge results in ______.

Increased lattice energy. Higher charge means stronger electrostatic forces.

Calculate the relative lattice energy: MgO vs NaCl.

MgO has higher lattice energy due to +2 charge on Mg vs +1 on Na.

What is the effect of ionic charge on lattice energy?

Higher ionic charges result in significantly higher lattice energies due to enhanced electrostatic forces.

True or False: Lattice energy is solely dependent on ionic radius.

False. It depends on both ionic charge and radius.

Which compound has the lowest lattice energy: NaBr or NaI?

NaI. I- is larger than Br-, resulting in a weaker attraction.

Comparative lattice energy: LiF vs NaF.

LiF has higher lattice energy due to Li+ being smaller than Na+, leading to stronger attraction.

What happens to lattice energy as ionic size increases?

Lattice energy decreases. Increased size reduces the electrostatic attraction between ions.

Fill in the blank: Lattice energy can be calculated using ______.

The Born-Lande equation or through Born-Haber cycles.