Explain lattice-energy magnitude from charge and radius
Compare ionic attractions using charge and distance, then predict how lattice-energy magnitude changes.
Section 23 · Chemical energetics
A Level; Cambridge International Chemistry 9701, 2028–2030 syllabus, Topic 23. Use the syllabus sign convention for lattice enthalpy (gaseous ions forming the ionic solid); state phases, signs, units and temperature. Written practice is self-checked
Before you begin
- Use AS enthalpy changes and Hess's law, formulae for ions, balanced equations, and temperature in kelvins.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What happens to electrostatic attraction when the same charges are brought closer together?
What you will learn
- Relate lattice-energy magnitude to ionic charge
- Relate lattice-energy magnitude to ionic radius
- Compare compounds without confusing magnitude and sign
Charge density controls electrostatic attraction
Lattice-energy magnitude increases when oppositely charged ions attract more strongly. Higher ionic charges produce stronger electrostatic attraction; smaller ionic radii bring the ion centres closer and also increase attraction.
For example, a 2+/2− ionic solid generally has a larger lattice-energy magnitude than a comparable 1+/1− solid. Across ions with the same charges, the smaller ion usually gives the larger magnitude.
State whether you mean magnitude or signed value
Lattice formation enthalpy is negative. A larger magnitude means a more negative formation value, such as −2500 kJ mol⁻¹ having a greater magnitude than −700 kJ mol⁻¹.
When comparing real salts, consider both ion charges and sizes. Do not attribute a difference to radius if the charges also change, unless the question holds charge constant or supplies enough information to compare both factors.
Pause and explain
For the same ionic charges, which pair tends to give the larger lattice-energy magnitude?
Worked example
Which is expected to have the larger lattice-energy magnitude, MgO or NaCl? Explain using charge.
Show the worked solution
- MgO contains Mg²⁺ and O²⁻.
- NaCl contains Na⁺ and Cl⁻.
- The larger charge product in MgO strengthens electrostatic attraction.
Answer MgO is expected to have the larger lattice-energy magnitude because its 2+ and 2− ions attract more strongly than the 1+ and 1− ions in NaCl. Its lattice-formation enthalpy is expected to be more negative.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Compare the expected lattice-energy magnitudes of NaCl and MgO using both charge and likely sign.
Give me a hint
Compare the charge products, then translate magnitude into a signed formation enthalpy.
Compare my reasoning
- NaCl uses 1+ and 1− ions.
- MgO uses 2+ and 2− ions.
- Stronger attraction means a greater magnitude and a more negative formation value.
MgO is expected to have the larger magnitude because of its higher ionic charges; its lattice-formation enthalpy is more negative than NaCl's, all else considered qualitatively.
Look for these in your work
- Charges compared
- Magnitude direction correct
- Negative sign interpreted
For two salts with ions of equal charges, salt A has smaller ions than salt B. Which has the larger lattice-energy magnitude?
Give me a hint
Hold charge constant and compare ion-centre separation.
Compare my reasoning
- Both have equal charge products.
- Smaller ions bring the centres closer.
- Closer centres strengthen attraction.
Salt A tends to have the larger lattice-energy magnitude because its smaller ions have stronger electrostatic attraction at shorter separation.
Look for these in your work
- Controlled comparison identified
- Radius effect correct
- Magnitude stated
A learner says, ‘−2400 is a smaller lattice energy than −900, so the first salt has weaker attraction.’ Correct the comparison.
Give me a hint
Separate signed numerical order from absolute magnitude and physical attraction.
Compare my reasoning
- Compare absolute values 2400 and 900.
- The magnitude 2400 is larger.
- Formation is more exothermic and the attraction stronger for the first salt.
The first value has the larger magnitude: |−2400| > |−900|. Its lattice formation is more exothermic, consistent with stronger ionic attraction.
Look for these in your work
- Magnitude calculated
- Sign handled correctly
- Attraction interpretation stated
Common mistakes
- Calling a more negative lattice enthalpy a smaller magnitude
- Comparing radius without checking charge
- Saying larger ions attract more strongly at the same charge
- Treating a qualitative trend as an exact numerical prediction
What can you explain now?
What happens to electrostatic attraction when the same charges are brought closer together?
Compare with the explanation
It becomes stronger
A shorter separation increases Coulombic attraction.
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Make it stick
How do charge and radius affect lattice-energy magnitude, and what does that mean for its negative formation sign?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.