Osmolarity and tonicity
This calculator estimates osmolarity from solute concentration and the van ’t Hoff factor, supports mixtures
by summation, and classifies tonicity (hypotonic / isotonic / hypertonic) by comparing inside vs outside
effective osmolarity (nonpermeable solutes).
Important distinction: osmolarity counts particles in solution. tonicity predicts
water movement across a membrane and depends mainly on solutes that do not cross the membrane easily.
1) Osmolarity model used
For a single solute with molar concentration \(C\) and van ’t Hoff factor \(i\) (number of dissolved particles
per formula unit), the model is:
\[
\text{Osmolarity} = i \cdot C
\]
Variables and units
- \(C\): concentration (typically in \(\text{mol}/\text{L}\) = M, or \(\text{mmol}/\text{L}\) = mM)
- \(i\): van ’t Hoff factor (dimensionless; ideal particle count)
- Osmolarity output: \(\text{Osm}/\text{L}\) or \(\text{mOsm}/\text{L}\)
Common conversions
- \(1\ \text{mM} = 10^{-3}\ \text{M}\)
- \(1\ \text{Osm}/\text{L} = 1000\ \text{mOsm}/\text{L}\)
Ideal vs real: \(i\) can be lower than the “integer” value at higher concentrations due to ion pairing
and non-ideal behavior. This tool uses the simple classroom model \(i\cdot C\).
2) Mixtures (multi-solute solutions)
For a solution containing multiple solutes, total osmolarity is the sum of each solute’s contribution:
\[
\text{Total osmolarity} = \sum_{k=1}^{n} i_k \cdot C_k
\]
In the calculator, each table row corresponds to a term \(i_k \cdot C_k\). The “Contribution table”
shows these terms and the final sum.
3) Effective osmolarity and tonicity
Tonicity is governed mainly by solutes that are nonpermeable (or effectively nonpenetrating) for the membrane
you care about. The calculator can compute an “effective osmolarity” by summing only nonpermeable contributions:
\[
\text{Effective osmolarity} = \sum_{k\in \text{nonpermeable}} i_k \cdot C_k
\]
Classification rule (outside vs inside)
- Isotonic: \(\text{eff}_{out} \approx \text{eff}_{in}\)
- Outside hypertonic: \(\text{eff}_{out} > \text{eff}_{in}\) → water tends to move out
- Outside hypotonic: \(\text{eff}_{out} < \text{eff}_{in}\) → water tends to move in
Why permeability matters
- Permeable solutes can cross the membrane and reduce sustained osmotic gradients.
- Nonpermeable solutes remain separated and maintain an osmotic driving force for water movement.
The tool’s “isotonic tolerance” treats very small differences as isotonic (useful because real measurements and
biological systems have variation).
4) Step-by-step examples
Example A: single-solute osmolarity
Suppose NaCl is \(150\ \text{mM}\) and we use \(i \approx 2\).
\[
C = 150\ \text{mM} = 0.150\ \text{M}
\]
\[
\text{Osm} = i\cdot C = 2 \cdot 0.150 = 0.300\ \text{Osm}/\text{L} = 300\ \text{mOsm}/\text{L}
\]
Example B: mixture osmolarity
A mixture with NaCl \(100\ \text{mM}\) (\(i=2\)) and glucose \(10\ \text{mM}\) (\(i=1\)):
\[
\text{Total} = (2\cdot 0.100) + (1\cdot 0.010)
= 0.200 + 0.010
= 0.210\ \text{Osm}/\text{L}
= 210\ \text{mOsm}/\text{L}
\]
Example C: tonicity by effective osmolarity
Inside effective osmolarity: \(290\ \text{mOsm}/\text{L}\). Outside effective osmolarity: \(320\ \text{mOsm}/\text{L}\).
Since \(\text{eff}_{out} > \text{eff}_{in}\), outside is hypertonic and water tends to leave the cell.
\[
\Delta = \text{eff}_{out} - \text{eff}_{in} = 320 - 290 = 30\ \text{mOsm}/\text{L}
\]
5) Quick reference: typical \(i\) presets
These are common classroom approximations for dilute solutions:
Best practice for tonicity: decide permeability for the specific membrane/system, then compute
effective osmolarity using only the nonpermeable solutes.
6) Interpretation and limitations
- Osmolarity vs osmolality: this calculator uses osmolarity (\(\text{Osm}/\text{L}\)). Osmolality (\(\text{Osm}/\text{kg}\)) is used in some lab settings and is close for dilute aqueous solutions.
- van ’t Hoff factor is approximate: real solutions may deviate due to non-ideal behavior.
- Tonicity depends on time: a solute that is “effectively nonpermeable” over minutes might become permeable over hours.
- Biology context matters: the same solute can behave differently depending on channels/transporters present.
