Partial Molar Volume of Water based on Solution Diffusion Model Calculator

Partial Molar Volume Formula:

\[ V_l = \frac{J_{wm} \cdot [R] \cdot T \cdot l_m}{D_w \cdot C_w \cdot (\Delta P_{atm} - \Delta \pi)} \]

Mass Water Flux (J_wm):

kg/(s·m²)

Temperature (T):

Membrane Thickness (l_m):

Water Diffusivity (D_w):

m²/s

Water Concentration (C_w):

kg/m³

Membrane Pressure Drop (ΔP_atm):

Osmotic Pressure (Δπ):

Partial Molar Volume (V_l):

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1. What is Partial Molar Volume of Water?

Definition: The partial molar volume of a substance in a mixture is the change in volume of the mixture per mole of that substance added, at constant temperature and pressure.

Purpose: This calculator determines the partial molar volume of water based on the solution-diffusion model, which is important in membrane science and chemical engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V_l = \frac{J_{wm} \cdot [R] \cdot T \cdot l_m}{D_w \cdot C_w \cdot (\Delta P_{atm} - \Delta \pi)} \]

Where:

\( V_l \) — Partial molar volume (m³/mol)
\( J_{wm} \) — Mass water flux (kg/(s·m²))
\( [R] \) — Universal gas constant (8.314 J/(mol·K))
\( T \) — Temperature (K)
\( l_m \) — Membrane thickness (m)
\( D_w \) — Water diffusivity (m²/s)
\( C_w \) — Water concentration (kg/m³)
\( \Delta P_{atm} \) — Membrane pressure drop (Pa)
\( \Delta \pi \) — Osmotic pressure (Pa)

Explanation: The formula relates water transport through a membrane to its partial molar volume under applied pressure and osmotic gradients.

3. Importance of Partial Molar Volume Calculation

Details: Understanding partial molar volumes is crucial for designing membrane separation processes, predicting solution behavior, and modeling transport phenomena in chemical and biological systems.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Default values are provided for typical conditions, but should be adjusted for specific systems.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for partial molar volume of water?
A: For water, partial molar volumes typically range from 1.8×10⁻⁵ to 2.0×10⁻⁵ m³/mol under normal conditions.

Q2: How does temperature affect the result?
A: Higher temperatures generally increase the partial molar volume due to thermal expansion effects.

Q3: What if my osmotic pressure is zero?
A: If there's no osmotic pressure difference (Δπ=0), the driving force is simply the applied pressure difference.

Q4: How accurate is this calculation?
A: The accuracy depends on the input parameters and assumes ideal solution behavior. For precise work, experimental validation is recommended.

Q5: What are common applications of this calculation?
A: This is particularly useful in reverse osmosis, nanofiltration, and other membrane separation processes.