Colligative Properties: Ideal Solutions

Calculate ΔTb, ΔTf, Osmotic Pressure (π) and Vapor Pressure Lowering (Raoult & Antoine equation) for ideal dilute solutions with non-volatile solutes.

Solvent

Tb100

Kb0.512

P⁰23.69

Tf0

Kf1.86

ρ1

Solute

MM58.44 g/mol

Parameters

Solute Mass

Amount of solute to dissolve

01000

Solvent Amount

Amount of pure solvent

0.00110

Working Temperature

For osmotic pressure calculation

-50200

At concentrations above 0.1 mol/kg, the solution behavior deviates significantly from ideality. The actual Van't Hoff factor will be lower than the theoretical value. Results are approximate.

Intermediate Metrics

Solute Moles

0.1711

mol

Molality

0.3422

mol/kg

Mole Fraction (Solute)

0.006128

particles: 0.01218 (i=2)

Molarity (approx.)

0.3422

mol/L

* Since masses are input, the simulator approximates Molarity by assuming the volume contributed by the solute is negligible (V_solution ≈ V_solvent). This is a standard approximation for dilute solutions.

Results

Boiling Point

100.4

°C

ΔTb = +0.3504 °C

Freezing Point

-1.273

°C

ΔTf = −1.273 °C

Osmotic Pressure

16.75

atm

= 1697 kPa

Vapor Pressure

23.4

mmHg

ΔP = −0.2885 mmHg

Fundamentals & Explanation

What are Colligative Properties?

Colligative properties are physical properties of solutions that depend exclusively on the number of solute particles dissolved (molecules or ions), and not on their chemical identity. For an ideal solution with a non-volatile solute, these properties explain how the presence of the solute alters the thermodynamic behavior of the solvent.

Raoult's Law and the Antoine Equation

P_{\text{solution}} = X_{\text{solvent}} \cdot P^0_{\text{solvent}}

\log_{10}(P^0) = A - \frac{B}{T(^\circ\text{C}) + C}

Raoult's Law states that the vapor pressure of the solution decreases proportionally to the mole fraction of the solute ( $X_{\text{solute}}$ ). In this simulator, the vapor pressure of the pure solvent ( $P^0$ ) is not static; it is computed dynamically based on the temperature using the Antoine Equation, guaranteeing thermodynamic rigor even at elevated temperatures. For electrolytes, this mole fraction is evaluated over the particles actually present in solution: the Van't Hoff factor multiplies the moles of solute ( $X_{\text{solute}} = \frac{i \cdot n_{\text{solute}}}{i \cdot n_{\text{solute}} + n_{\text{solvent}}}$ ), so dissociation also intensifies the vapor-pressure lowering, consistent with $\Delta T_b$ , $\Delta T_f$ and $\pi$ .

Ebullioscopy and Cryoscopy

\Delta T_b = i \cdot K_b \cdot m \quad (\text{Boiling-Point Elevation})

\Delta T_f = i \cdot K_f \cdot m \quad (\text{Freezing-Point Depression})

As the vapor pressure decreases, the solvent's phase diagram shifts: a higher temperature is needed to reach boiling, and a lower one for freezing. The constants $K_b$ and $K_f$ are intrinsic to the solvent. The Van't Hoff factor ( $i$ ) corrects for the number of dissociated ions ( $i=2$ for NaCl).

Osmotic Pressure (π)

\Pi = i \cdot M \cdot R \cdot T

Osmotic pressure is the pressure required to stop the net flow of solvent across a semipermeable membrane. This Van't Hoff equation is analogous to the ideal gas law. It is fundamental in physiology to calculate the tonicity of intravenous fluids and in reverse osmosis.

Limitations of the Ideal Model

Dilution Assumption:

Colligative equations are limiting laws; they are accurate only in very dilute solutions ( $m < 0.1$ mol/kg). At high concentrations, ionic interactions (ion pairing) reduce the effective Van't Hoff factor below its theoretical integer value [1].

Molarity Approximation:

Since masses are input, the simulator approximates Molarity by assuming the volume contributed by the solute is negligible ( $V_{\text{solution}} \approx V_{\text{solvent}}$ ). This is a standard physical chemistry approximation for ideal dilute solutions.

Simulator Conditions

R = 0.08206 L·atm/(K·mol)

Solutes: Non-volatile

Equation: Antoine

Solute Vol: Negligible

Van't Hoff Factor (i)

Glucose: i = 1

NaCl: i = 2

CaCl₂: i = 3

Na₂SO₄: i = 3

Academic References

[1] Atkins, P. & de Paula, J. (2018). Atkins' Physical Chemistry (11th ed.). Oxford University Press. Ch. 5: Simple mixtures.
[2] Chang, R. & Goldsby, K. A. (2015). Chemistry (12th ed.). McGraw-Hill Education. Ch. 12: Physical Properties of Solutions.
[3] Yaws, C. L. (2015). The Yaws Handbook of Vapor Pressure: Antoine Coefficients (2nd ed.). Gulf Professional Publishing.
[4] CRC Handbook of Chemistry and Physics (104th ed., 2023–2024). CRC Press. Tables of ebullioscopic and cryoscopic constants.

Colligative Properties: Ideal Solutions

Parameters

Intermediate Metrics

Results

Fundamentals & Explanation

What are Colligative Properties?

Raoult's Law and the Antoine Equation

Ebullioscopy and Cryoscopy

Osmotic Pressure (π)

Limitations of the Ideal Model

Simulator Conditions

Van't Hoff Factor (i)

Academic References

You may also like:

What are Colligative Properties?

Raoult's Law and the Antoine Equation

Ebullioscopy and Cryoscopy

Osmotic Pressure (π)

Limitations of the Ideal Model

Simulator Conditions

Van't Hoff Factor (i)

Academic References