Relate hydration enthalpy to charge density
Explain why ions with higher charge and smaller radius tend to have more exothermic hydration enthalpies.
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 interaction forms when gaseous ions hydrate?
What you will learn
- Relate hydration enthalpy magnitude to ionic charge
- Relate hydration enthalpy magnitude to ionic radius
- Distinguish greater magnitude from a more positive signed value
Water is attracted to charged ions
Hydration forms ion–dipole attractions between an ion and polar water molecules. An ion with greater charge density attracts water molecules more strongly, releasing more energy and producing a larger-magnitude, more negative hydration enthalpy.
For ions with the same charge, a smaller radius gives a larger charge density and generally more exothermic hydration. For similarly sized ions, a higher charge also tends to increase the magnitude.
Keep magnitude and sign separate
Hydration enthalpies are usually negative because attractions form. A change from −400 to −900 kJ mol⁻¹ is an increase in magnitude and is more exothermic, even though the signed number is numerically smaller.
Use the comparison conditions in the question. If both charge and size change, explain both influences before giving a qualitative prediction.
Pause and explain
For ions with equal charge, which usually has the more negative hydration enthalpy?
Worked example
Which ion is expected to have the more negative hydration enthalpy, Mg²⁺ or Na⁺? Explain.
Show the worked solution
- Both are small cations, but their charges differ.
- Mg²⁺ has a greater charge than Na⁺.
- Greater charge density strengthens ion–dipole attractions.
Answer Mg²⁺ is expected to have the more negative hydration enthalpy because its higher charge density attracts water molecules more strongly.
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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 hydration enthalpy magnitudes of Li⁺ and K⁺ and explain the trend.
Give me a hint
Both have charge +1; compare ionic radius and charge density.
Compare my reasoning
- Li⁺ is smaller than K⁺.
- Both have the same charge.
- The smaller Li⁺ gives stronger ion–dipole attraction.
Li⁺ generally has the larger hydration-enthalpy magnitude and more negative value because its smaller radius gives higher charge density than K⁺.
Look for these in your work
- Equal charge recognised
- Radius comparison correct
- Sign and magnitude stated
Explain why Mg²⁺ hydration is more exothermic than Na⁺ hydration using charge density.
Give me a hint
Compare the magnitude of charge and consider that both are small cations.
Compare my reasoning
- Mg²⁺ carries charge +2; Na⁺ carries +1.
- The greater charge density in Mg²⁺ strengthens attraction to polar water.
- More energy is released on hydration.
Mg²⁺ has higher charge density, so it attracts water molecules more strongly and releases more energy; its hydration enthalpy is more negative.
Look for these in your work
- Charges compared
- Ion–dipole attraction linked
- More negative sign stated
A dataset changes from ΔHhyd = −420 to −880 kJ mol⁻¹. Explain whether the hydration enthalpy has increased or decreased in magnitude.
Give me a hint
Compare absolute values and then describe the heat released.
Compare my reasoning
- The magnitudes are 420 and 880.
- 880 is larger.
- The second hydration is more exothermic.
The magnitude has increased from 420 to 880 kJ mol⁻¹. The second value is more negative and more exothermic.
Look for these in your work
- Absolute magnitudes compared
- Direction correct
- Signed interpretation correct
Common mistakes
- Saying a more negative enthalpy is a smaller magnitude
- Ignoring charge when comparing same-sized ions
- Ignoring size when comparing ions with the same charge
- Calling hydration endothermic because water molecules become ordered
What can you explain now?
What interaction forms when gaseous ions hydrate?
Compare with the explanation
Ion–dipole attractions
Polar water molecules orient around the charged ion.
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Make it stick
How do ionic charge and radius affect charge density, hydration magnitude and the negative sign?
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