Understanding the Calculation of Tonicity: Hypotonic, Isotonic, and Hypertonic Solutions

Tonicity calculation determines the osmotic pressure gradient between two solutions. It classifies solutions as hypotonic, isotonic, or hypertonic based on solute concentration differences.

This article explores detailed formulas, common values, and real-world applications for calculating tonicity in biological and chemical contexts.

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Calculate tonicity of a 0.9% NaCl solution compared to blood plasma.
Determine if a 5% glucose solution is hypotonic, isotonic, or hypertonic relative to intracellular fluid.
Calculate osmolarity and tonicity of a solution containing 150 mM NaCl and 50 mM urea.
Evaluate the tonicity of a 3% saline solution for intravenous administration.

Comprehensive Tables of Common Values for Tonicity Calculation

Solution	Concentration (w/v or mM)	Osmolarity (mOsm/L)	Effective Osmolarity (mOsm/L)	Tonicity Classification	Typical Use/Application
0.9% NaCl (Normal Saline)	154 mM Na⁺, 154 mM Cl^–	308	308	Isotonic	Intravenous fluid replacement
5% Dextrose (Glucose)	278 mM Glucose	278	0	Hypotonic	Energy source, fluid replacement
3% NaCl	513 mM Na⁺, 513 mM Cl^–	1026	1026	Hypertonic	Treatment of hyponatremia
Intracellular Fluid (ICF)	~140 mM K⁺, 10 mM Na⁺, 140 mM organic solutes	~300	~300	Reference	Cellular environment
Plasma	140 mM Na⁺, 4 mM K⁺, 100 mM proteins (effective)	~290	~290	Isotonic	Physiological reference
10% Mannitol	555 mM Mannitol	555	555	Hypertonic	Osmotic diuretic
0.45% NaCl (Half Normal Saline)	77 mM Na⁺, 77 mM Cl^–	154	154	Hypotonic	Fluid replacement with free water
Urea 150 mM	150 mM Urea	150	0	Hypotonic (ineffective osmole)	Renal function tests

Fundamental Formulas for Calculating Tonicity

Tonicity is a measure of the effective osmotic pressure gradient caused by solutes that cannot freely cross a semipermeable membrane. It differs from osmolarity, which includes all solutes regardless of membrane permeability.

Osmolarity Calculation

The osmolarity (Osm) of a solution is calculated by summing the molar concentrations of all solutes multiplied by their dissociation factors:

Osmolarity = Σ (Ci × ni)

Where:

Ci = molar concentration of solute i (mol/L)

ni = number of particles into which solute i dissociates (van’t Hoff factor)

For example, NaCl dissociates into Na⁺ and Cl^–, so n = 2. Glucose does not dissociate, so n = 1.

Effective Osmolarity (Osmolality) or Tonicity

Effective osmolarity considers only solutes that do not freely cross the membrane (impermeant solutes). It is calculated as:

Effective Osmolarity = Σ (Ci × ni) for impermeant solutes only

Solutes like urea and ethanol are permeant and do not contribute to tonicity.

Classification of Solutions Based on Tonicity

Hypotonic: Effective osmolarity of solution < intracellular fluid (~280-300 mOsm/L). Cells swell due to water influx.
Isotonic: Effective osmolarity of solution ≈ intracellular fluid. No net water movement.
Hypertonic: Effective osmolarity of solution > intracellular fluid. Cells shrink due to water efflux.

Calculating Tonicity Relative to Intracellular Fluid

To determine tonicity, compare the effective osmolarity of the extracellular solution (Osm_ext) to the intracellular fluid (Osm_int):

If Osmext < Osmint → Hypotonic

If Osmext ≈ Osmint → Isotonic

If Osmext > Osmint → Hypertonic

Example: Calculating Osmolarity of NaCl Solution

Given a 0.9% NaCl solution:

Mass of NaCl = 0.9 g/100 mL = 9 g/L
Molar mass of NaCl = 58.44 g/mol
Molarity (C) = 9 g/L ÷ 58.44 g/mol ≈ 0.154 mol/L (154 mM)
NaCl dissociates into 2 particles (Na⁺ and Cl^–), so n = 2
Osmolarity = 0.154 × 2 = 0.308 Osm/L = 308 mOsm/L

This matches physiological osmolarity, so 0.9% NaCl is isotonic.

Detailed Explanation of Variables in Tonicity Formulas

C_i (Concentration): Molar concentration of each solute, typically in mol/L or mM. Common physiological concentrations range from 1 mM (e.g., K⁺) to 150 mM (e.g., Na⁺).
n_i (van’t Hoff factor): Number of particles a solute dissociates into. For example, NaCl dissociates into 2 ions, so n=2; glucose does not dissociate, so n=1.
Osmolarity: Total concentration of all solute particles in solution, including permeant and impermeant solutes.
Effective Osmolarity (Tonicity): Concentration of only impermeant solutes that exert osmotic pressure across membranes.
Membrane Permeability: Determines which solutes contribute to tonicity. Impermeant solutes cause water movement; permeant solutes equilibrate and do not.

Real-World Applications and Case Studies

Case 1: Intravenous Fluid Selection for a Dehydrated Patient

A patient presents with dehydration and low blood sodium (hyponatremia). The clinician must select an appropriate IV fluid to restore volume without causing cellular damage.

Given options:

0.45% NaCl (hypotonic)
0.9% NaCl (isotonic)
3% NaCl (hypertonic)

Calculations:

0.45% NaCl: 77 mM NaCl → Osmolarity = 77 × 2 = 154 mOsm/L (hypotonic)
0.9% NaCl: 154 mM NaCl → Osmolarity = 308 mOsm/L (isotonic)
3% NaCl: 513 mM NaCl → Osmolarity = 1026 mOsm/L (hypertonic)

Since the patient is hyponatremic, administering hypotonic fluid (0.45%) risks further lowering plasma sodium, worsening cerebral edema. Isotonic saline (0.9%) is safer for volume replacement. In severe hyponatremia, hypertonic saline (3%) may be used cautiously to raise plasma sodium.

Case 2: Evaluating Tonicity of a Mixed Solute Solution

A laboratory solution contains 150 mM NaCl and 50 mM urea. Determine its tonicity relative to intracellular fluid (~300 mOsm/L).

Step 1: Calculate total osmolarity

NaCl dissociates into 2 particles: 150 mM × 2 = 300 mOsm/L
Urea is permeant, so it contributes to osmolarity but not tonicity: 50 mM × 1 = 50 mOsm/L
Total osmolarity = 300 + 50 = 350 mOsm/L

Step 2: Calculate effective osmolarity (tonicity)

Only impermeant solutes count: NaCl = 300 mOsm/L
Urea excluded (permeant)
Effective osmolarity = 300 mOsm/L

Step 3: Compare to intracellular fluid

Effective osmolarity (300) ≈ intracellular fluid (300)
Solution is isotonic despite higher total osmolarity

This example highlights the importance of distinguishing osmolarity from tonicity in clinical and laboratory settings.

Additional Considerations in Tonicity Calculations

Temperature and Pressure: Osmolarity calculations assume standard conditions; physiological variations can slightly alter values.
Non-ideal Solutions: Interactions between solutes can affect dissociation and activity coefficients, impacting osmolarity.
Membrane Selectivity: Different cell types have varying permeability to solutes, influencing effective tonicity.
Clinical Implications: Incorrect tonicity can cause cell lysis (hypotonic) or crenation (hypertonic), critical in IV fluid therapy.

Calculation of Tonicity (hypotonic, isotonic, hypertonic)