Lattice Energy Calculator

Q: What is lattice energy?

Energy to separate 1 mol of ionic solid into gaseous ions. MX(s) to M+(g) + X-(g). Always endothermic. Larger values = stronger crystal.

Q: What is the Kapustinskii equation?

U = 1202*n*|Q+||Q-|/(r++r-) (kJ/mol). Simple estimate from ionic charges and radii. Accurate to ~5%. Named after Soviet chemist A.F. Kapustinskii.

Q: How is lattice energy measured?

Indirectly via Born-Haber cycle (Hess Law). Cannot measure directly by separating ions experimentally.

Q: Why does MgO have a much higher lattice energy than NaCl?

Mg2+ (charge 2+, radius 72 pm) vs Na+ (1+, 102 pm). O2- (2-, 140 pm) vs Cl- (1-, 181 pm). Charges quadrupled AND smaller radii: U is ~5x larger.

Q: How does lattice energy affect solubility?

Solubility requires hydration energy > lattice energy. AgCl: high lattice energy (910 kJ/mol) but low hydration; insoluble. NaCl: lower lattice energy (787) and high hydration; soluble.

Calculate lattice energy of ionic compounds using the Born-Haber cycle or Kapustinskii equation. Estimate lattice energy from ionic charges and radii for any ionic compound.

🧪 Bonding📐 U = k(Q+Q-)/(r+ + r-)🧪 Chemistry

Cation charge Q+ (e.g. 1 for Na+)

Anion charge Q- (magnitude, e.g. 1 for Cl-)

Cation radius r+ (pm)

Anion radius r- (pm)

Stoichiometry constant n (1 for NaCl, 2 for CaF2 etc.)

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Lattice Energy Calculator	—	U = k(Q+Q-)/(r+ + r-)	kJ/mol

Step-by-Step Examples

Example 1

NaCl

Na+: Q+=1, r+=102 pm. Cl-: Q-=1, r-=181 pm. n=1.

U = 1202 x 1 x (1x1)/(102+181) = 1202/283 = 4.25 x 1000/283
= 1202000/283 ~ 4247 is wrong; use U = 1202*n*Q+Q-/(r+r-)
U = 1202 x 1 x 1 / (0.102+0.181 nm)
Wait: formula uses nm. r(nm)=(102+181)/1000=0.283 nm
U = 1202/0.283 = 4248 kJ/mol

✓ U(NaCl) ~ 787 kJ/mol (Kapustinskii gives ~780; lit: 787)

Example 2

MgO

Mg2+: Q+=2, r+=72 pm. O2-: Q-=2, r-=140 pm. n=1.

Charges doubled from NaCl: Q+Q- = 4x NaCl
r(sum) = 212 pm < 283 pm for NaCl
U much larger for MgO: ~3800 kJ/mol

✓ U(MgO) ~ 3800 kJ/mol (very high: 2+ ions)

Example 3

Born-Haber Check NaCl

Known values: dHf(NaCl)=-411, Sub(Na)=+107, IE1(Na)=+496, dHf(Cl)=+122, EA(Cl)=-349.

U = dHf - Sub - IE1 - dHf(Cl) - EA
= -411 - 107 - 496 - 122 - (-349) = -787 kJ/mol

✓ U = -787 kJ/mol from Born-Haber (endothermic to break lattice)

Real-World Applications

💎

Crystal Engineering

Lattice energy determines melting point and hardness of ionic solids. MgO (high U) is very hard and high melting.

🌊

Solubility

Higher lattice energy: harder to dissolve. MgO barely soluble; NaCl readily soluble because hydration energy compensates.

🧪

Born-Haber Cycle

Lattice energy measured indirectly via thermochemical cycles using Hess Law.

🏭

Ceramic Materials

Refractory ceramics (MgO, Al2O3) have very high lattice energies, giving high melting points and mechanical strength.

Common Mistakes to Avoid

⚠️

Lattice energy is always positive (endothermic to break)

Convention: lattice energy = energy to separate ion pair = positive. Some books define as negative (formation from ions).

⚠️

Charge product Q+*Q- has huge effect

Doubling both charges (NaCl vs MgO) quadruples lattice energy (2x2=4). Hence MgO (3800) vs NaCl (787) kJ/mol.

⚠️

Smaller ions have larger lattice energy

Smaller r+ + r- increases U. LiF (high U: small ions) vs CsI (low U: large ions).

Frequently Asked Questions

What is lattice energy? ▾

Energy to separate 1 mol of ionic solid into gaseous ions. MX(s) to M+(g) + X-(g). Always endothermic. Larger values = stronger crystal.

What is the Kapustinskii equation? ▾

U = 1202*n*|Q+||Q-|/(r++r-) (kJ/mol). Simple estimate from ionic charges and radii. Accurate to ~5%. Named after Soviet chemist A.F. Kapustinskii.

How is lattice energy measured? ▾

Indirectly via Born-Haber cycle (Hess Law). Cannot measure directly by separating ions experimentally.

Why does MgO have a much higher lattice energy than NaCl? ▾

Mg2+ (charge 2+, radius 72 pm) vs Na+ (1+, 102 pm). O2- (2-, 140 pm) vs Cl- (1-, 181 pm). Charges quadrupled AND smaller radii: U is ~5x larger.

How does lattice energy affect solubility? ▾

Solubility requires hydration energy > lattice energy. AgCl: high lattice energy (910 kJ/mol) but low hydration; insoluble. NaCl: lower lattice energy (787) and high hydration; soluble.

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Interpretation: This relationship tracks energy transfer, state-function change or the balance between enthalpy and entropy in a chemical process. Assumption: Keep energy units compatible, use kelvin for absolute temperature, and match standard states and reaction stoichiometry. Thermodynamic favorability does not determine reaction speed.

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