Ideal Activity Example¶

Demonstrates using ActivityIdealMolar to compute activity from mass concentrations using Raoult's Law.

What This Example Shows¶

• Creating an ideal molar activity strategy
• Computing activity from mass concentrations
• Computing partial pressures from pure vapor pressures
• Verifying that activity equals mole fraction for ideal mixing

In [ ]:

import numpy as np
import particula as par

import numpy as np import particula as par

1. Create Ideal Activity Strategy¶

Define molar masses for a two-component system: water and an organic compound.

In [ ]:

# Molar masses for water and an organic compound
strategy = par.particles.ActivityIdealMolar(
    molar_mass=np.array([18.015e-3, 200.0e-3]),  # kg/mol: water, organic
)

print(f"Strategy: {type(strategy).__name__}")
print(f"Molar masses: {strategy.molar_mass * 1e3} g/mol")

# Molar masses for water and an organic compound strategy = par.particles.ActivityIdealMolar( molar_mass=np.array([18.015e-3, 200.0e-3]), # kg/mol: water, organic ) print(f"Strategy: {type(strategy).__name__}") print(f"Molar masses: {strategy.molar_mass * 1e3} g/mol")

2. Define Mass Concentrations and Compute Activity¶

Use equal mass of water and organic (50/50 by mass) and compute activity. For ideal mixing, activity equals mole fraction.

In [ ]:

# Equal mass of water and organic (50/50 by mass)
mass = np.array([0.5e-9, 0.5e-9])  # kg/m^3

# Compute activity (mole fraction based for ideal mixing)
activity = strategy.activity(mass_concentration=mass)

print("=== Ideal Activity (Raoult's Law) ===")
print(f"Mass concentrations: {mass * 1e9} ng/m^3")
print(f"Activity values: {activity}")

# Equal mass of water and organic (50/50 by mass) mass = np.array([0.5e-9, 0.5e-9]) # kg/m^3 # Compute activity (mole fraction based for ideal mixing) activity = strategy.activity(mass_concentration=mass) print("=== Ideal Activity (Raoult's Law) ===") print(f"Mass concentrations: {mass * 1e9} ng/m^3") print(f"Activity values: {activity}")

3. Compute Partial Pressures¶

Partial pressure is calculated as activity times pure vapor pressure: $p_i = a_i \cdot p_i^{\circ}$

In [ ]:

# Pure vapor pressures at 298 K (example values)
pure_pressure = np.array([3169.0, 1e-3])  # Pa: water, organic
partial_pressure = strategy.partial_pressure(
    pure_vapor_pressure=pure_pressure,
    mass_concentration=mass,
)

print(f"Pure vapor pressures: {pure_pressure} Pa")
print(f"Partial pressures: {partial_pressure} Pa")

# Pure vapor pressures at 298 K (example values) pure_pressure = np.array([3169.0, 1e-3]) # Pa: water, organic partial_pressure = strategy.partial_pressure( pure_vapor_pressure=pure_pressure, mass_concentration=mass, ) print(f"Pure vapor pressures: {pure_pressure} Pa") print(f"Partial pressures: {partial_pressure} Pa")

4. Verify Activity Equals Mole Fraction¶

For ideal mixing (Raoult's Law), activity equals mole fraction. Let's calculate mole fractions directly to verify.

In [ ]:

# Calculate mole fractions directly for comparison
moles = mass / strategy.molar_mass
mole_fractions = moles / np.sum(moles)
print(f"Mole fractions: {mole_fractions}")
print(
    f"Activity = mole fraction (ideal): {np.allclose(activity, mole_fractions)}"
)

# Calculate mole fractions directly for comparison moles = mass / strategy.molar_mass mole_fractions = moles / np.sum(moles) print(f"Mole fractions: {mole_fractions}") print( f"Activity = mole fraction (ideal): {np.allclose(activity, mole_fractions)}" )