Electrolyte Solutions and the Debye-Huckel Limiting Law
Ions in solution do not behave independently because each one gathers an atmosphere of opposite charge around it. That atmosphere lowers the effective concentration, and the limiting law predicts by how much.
What a learner can do afterwards
- Calculates ionic strength for a mixed electrolyte and explains why charge is squared in it
- Applies the limiting law to obtain a mean activity coefficient and states its range of validity
- Explains why a measured pH drifts from the calculated value as salt is added
- Says why single-ion activities cannot be measured and what is quoted instead
1 · Read
Ions in solution gather a cloud of opposite charge, the ionic atmosphere, which shields each ion. Ionic strength measures how crowded that world is: halve the sum of concentration times charge squared. Charge enters squared because an ion's charge both builds its atmosphere and feels it, so a doubly charged ion counts four times as much as a singly charged one.
For 0.10 M sodium chloride both charges are 1, so I is half of (0.10 + 0.10), which is 0.10 M. For 0.10 M magnesium sulphate both charges are 2, so I is half of (0.10 x 4 + 0.10 x 4), which is 0.40 M.
The Debye-Huckel limiting law gives the mean activity coefficient: log10 of gamma equals -0.509 times |z+ z-| times the square root of I, for water at 25 C. For 0.010 M sodium chloride, log gamma is -0.0509, so gamma is about 0.89. It holds only in very dilute solutions. Extra salt reshapes every ion cloud, so a measured pH drifts even when no acid or base was added.
No experiment can isolate one ion type, so single-ion activities cannot be measured. Tables quote mean coefficients for the whole salt instead.
Charge squared sets the strength, the cloud lowers the activity, and only whole-salt means ever reach print.
The rewritten readings were written for this dataset. Reading '11.2: Electrolytes' remains adapted from OpenStax Chemistry 2e (CC BY-NC-SA 4.0), openstax.org.
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.