1. When ions are added to water, the resulting salt
solution has a lower vapor pressure. To evaporate
the solution, ions must be pushed out of the region
– only then can water molecules escape. The
work per volume to push the ions out is the
osmotic pressure, π.
Theory Results
Acknowledgements
Introduction
Methods
Measuring the Size of Aqueous Ions with Osmometry
Nigel Rambhujun1, Scott Milner2, Astha Garg2
1Department of Chemistry, Hartwick College, NY
2Department of Chemical Engineering, Pennsylvania State University, PA
Soft Materials REU
The osmotic pressure of a salt solution depends
on the two factors: the charge and size of its ions.
1) Oppositely charged ions tend to move together,
reducing osmotic pressure relative to an ideal gas.
Debye-Huckel Theory & Mean-Spherical
Approximation (MSA) Theory
2) Ions have a finite size (including “hydration
shells”), which increases osmotic pressure at high
concentrations.
Motivation
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
0 1 2 3 4 5 6 7
Osmoticcoefficient
Molality (mol/kg)
NaClIon effect
Crowding effect
𝜙 =
𝜋
𝜋0
=
𝜋
𝑐𝑅𝑇
At low concentrations, ϕ decreases from unity
with corrections of order c1/2, predicted by DH
theory.
At high concentrations, ϕ increases as hard-core
interactions dominate, predicted by MSA.
Freezing point Osmometer &
Dew point Osmometer
Single Size Fit vs. Double Size Fit
0.5 1.0 1.5 2.0
0.94
0.96
0.98
1.00
Molality (mol/kg)
Osmoticcoefficient
Monodisperse
Bidisperse
Na+
2.04Å
Cl-
3.62Å
D1
2.85 ± 0.47Å
Single size
3.57Å
D2
4.14 ± 0.35Å
The higher the concentration of a salt solution,
the greater the freezing point depression.
Pure liquid solvent
Solvent + Ions
Pure solid
solvent
Temperature, T
ChemicalPotential,μ
Freezing point
depression
Tm0Tm’
When ions are added to the solvent, the chemical
potential decreases, lowering the freezing point
(salt on ice).
• NSF DMR-Award # 1156960
• Daniel Dewey, Keating Research Group
• Dan Ye, Maranas Research Group
• Yuexiao Shen, Kumar Research Group
Standard
values of
crystal
ionic
diameters
0.90
0.92
0.94
0.96
0.98
1.00
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Osmoticcoefficient
Molality (mol/kg)
NaCl
To measure the
freezing point, the
FPO supercools the
sample and then
reaches a liquid-
solid equilibrium.
The DPO measures
the vapor pressure,
which decreases as
the solution gets
more concentrated.
Hamer W., Wu Y. (1972)
Conclusions
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.94
0.96
0.98
1.00
1.02
1.04
CH3SO3
-
5.54 ± 0.40Å
NaCH3SO3
Ions in solutions act in many ways like a gas. As
concentration increases (pressure for a gas), the
system deviates from ideality, and the particles
start behaving like hard spheres.
This affects the colligative properties of the
solution: freezing point and vapor pressure. By
measuring these properties versus concentration,
the osmotic coefficient is found; by comparing to
theories, the ion sizes can be obtained.
1) We can infer the hard-sphere size of the ions
by applying MSA theory to osmometry data.
2) The resulting ion sizes are slightly larger than
those obtained from spacings in ionic crystals,
which may result from hydration shell effects.
The data obtained with FPO (red) for NaCl was
consistent with literature data (black).
FPO was used to measure the osmotic coefficient
of NaCH3SO3 for which data is not available.
Molality (mol/kg)
Osmoticcoefficient
The ion size inferred is relatively close to the size
of the space-filling model.
Osmotic coefficient,
Δ𝑇 = −𝑇 𝑚0
𝜋𝑉
Δ𝐻𝑓
𝜙 =
𝜋
𝜋0
=
Δ𝑇
1.86𝑐