Partial Molar Volume of Water based on Solution Diffusion Model Calculator

✖Mass Water flux is defined as the rate of movement of water across a surface or through a medium.ⓘ Mass Water Flux [J_wm]			+10% -10%
✖Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness.ⓘ Temperature [T]			+10% -10%
✖Membrane Layer Thickness is the distance between the two outer surfaces of a membrane. It is typically measured in nanometers (nm), which are billionths of a meter.ⓘ Membrane Layer Thickness [l_m]			+10% -10%
✖Membrane water diffusivity is the rate at which water molecules diffuse across a membrane. It is typically measured in square meters per second (m^2/s).ⓘ Membrane Water Diffusivity [D_w]			+10% -10%
✖Membrane water concentration (MWC) is the concentration of water in a membrane. It is typically measured in moles per cubic meter (kg/m^3).ⓘ Membrane Water Concentration [C_w]			+10% -10%
✖Membrane pressure drop is the difference in pressure between the inlet and outlet of a membrane system, housing (pressure vessel), or element.ⓘ Membrane Pressure Drop [ΔP_atm]			+10% -10%
✖Osmotic pressure is the minimum pressure that must be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane.ⓘ Osmotic Pressure [Δπ]			+10% -10%

✖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.ⓘ Partial Molar Volume of Water based on Solution Diffusion Model [V_l]

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Formula

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Partial Molar Volume of Water based on Solution Diffusion Model

Formula

`"V"_{"l"} = ("J"_{"wm"}*"[R]"*"T"*"l"_{"m"})/("D"_{"w"}*"C"_{"w"}*("ΔP"_{"atm"}-"Δπ"))`

Example

`"0.018001m³/kmol"=("0.000063kg/s/m²"*"[R]"*"298K"*"0.000013m")/("0.0000000001762m²/s"*"156kg/m³"*("81.32at"-"39.5at"))`

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Partial Molar Volume of Water based on Solution Diffusion Model Solution

STEP 0: Pre-Calculation Summary

Formula Used

Partial Molar Volume = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure))
V_l = (J_wm*[R]*T*l_m)/(D_w*C_w*(ΔP_atm-Δπ))
This formula uses 1 Constants, 8 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Variables Used

Partial Molar Volume - (Measured in Cubic Meter per Mole) - 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.
Mass Water Flux - (Measured in Kilogram per Second per Square Meter) - Mass Water flux is defined as the rate of movement of water across a surface or through a medium.
Temperature - (Measured in Kelvin) - Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness.
Membrane Layer Thickness - (Measured in Meter) - Membrane Layer Thickness is the distance between the two outer surfaces of a membrane. It is typically measured in nanometers (nm), which are billionths of a meter.
Membrane Water Diffusivity - (Measured in Square Meter per Second) - Membrane water diffusivity is the rate at which water molecules diffuse across a membrane. It is typically measured in square meters per second (m^2/s).
Membrane Water Concentration - (Measured in Kilogram per Cubic Meter) - Membrane water concentration (MWC) is the concentration of water in a membrane. It is typically measured in moles per cubic meter (kg/m^3).
Membrane Pressure Drop - (Measured in Pascal) - Membrane pressure drop is the difference in pressure between the inlet and outlet of a membrane system, housing (pressure vessel), or element.
Osmotic Pressure - (Measured in Pascal) - Osmotic pressure is the minimum pressure that must be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane.

STEP 1: Convert Input(s) to Base Unit

Mass Water Flux: 6.3E-05 Kilogram per Second per Square Meter --> 6.3E-05 Kilogram per Second per Square Meter No Conversion Required
Temperature: 298 Kelvin --> 298 Kelvin No Conversion Required
Membrane Layer Thickness: 1.3E-05 Meter --> 1.3E-05 Meter No Conversion Required
Membrane Water Diffusivity: 1.762E-10 Square Meter per Second --> 1.762E-10 Square Meter per Second No Conversion Required
Membrane Water Concentration: 156 Kilogram per Cubic Meter --> 156 Kilogram per Cubic Meter No Conversion Required
Membrane Pressure Drop: 81.32 Atmosphere Technical --> 7974767.78 Pascal (Check conversion here)
Osmotic Pressure: 39.5 Atmosphere Technical --> 3873626.75 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_l = (J_wm*[R]*T*l_m)/(D_w*C_w*(ΔP_atm-Δπ)) --> (6.3E-05*[R]*298*1.3E-05)/(1.762E-10*156*(7974767.78-3873626.75))

Evaluating ... ...

V_l = 1.80011041407572E-05

STEP 3: Convert Result to Output's Unit

1.80011041407572E-05 Cubic Meter per Mole -->0.0180011041407572 Cubic Meter per Kilomole (Check conversion here)

FINAL ANSWER

0.0180011041407572 ≈ 0.018001 Cubic Meter per Kilomole <-- Partial Molar Volume

(Calculation completed in 00.004 seconds)

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Home » Engineering » Chemical Engineering » Mass Transfer Operations » Membrane Separation » Basics of Membrane Separation Processes » Partial Molar Volume of Water based on Solution Diffusion Model

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< 16 Basics of Membrane Separation Processes Calculators

Concentration of Mass at Membrane Surface

Go Solute Concentration at Membrane Surface = exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)/((Solute Rejection+(1-Solute Rejection)*exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)))*Bulk Concentration

Partial Molar Volume of Water based on Solution Diffusion Model

Go Partial Molar Volume = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure))

Water Permeability based on Initial flux

Go Water Permeability Through Membrane = Volumetric Water Flux Through Membrane/(Applied Pressure Driving Force*(1-(([R]*Temperature*Molecular Weight)/(Initial Volume*Applied Pressure Driving Force))))

Time of Dialysis using Hollow Fiber Haemodialyser

Go Time of Dialysis = (Volume of blood/Volumetric Rate of Blood)*ln(Initial Concentration In Blood/Final Concentration In Blood)*((1-(e^-No of Transfer Units))^-1)

Hagen Poiseuille Based Flux for Membrane Separation

Go Flux through Membrane = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Tortuosity*Membrane Thickness)

Liquid Viscosity Based On Hagen Poiseuille Equation

Go Liquid Viscosity = (Pore Diameter^2*Membrane Porosity*Applied Pressure Driving Force)/(32*Flux through Membrane*Tortuosity*Membrane Thickness)

Tortuosity Factor of Pores

Go Tortuosity = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Flux through Membrane*Membrane Thickness)

Pressure Difference across Pore based on Poiseuille's Law

Go Pressure Difference Across Pore = (Liquid Flow through Pore*128*Viscosity of Liquid*Length of Pore)/(pi*(Membrane Pore Diameter)^(4))

Liquid Flow through Pore Based On Poiseuilles Law

Go Liquid Flow through Pore = ((pi*(Membrane Pore Diameter)^4)/(128*Viscosity of Liquid*Length of Pore))*Pressure Difference Across Pore

Liquid Viscosity based on Poiseuille's Law

Go Viscosity of Liquid = (Pressure Difference Across Pore*pi*(Membrane Pore Diameter)^(4))/(Liquid Flow through Pore*128*Length of Pore)

Liquid Viscosity based on Membrane Resistance

Go Liquid Viscosity = Applied Pressure Driving Force/(Membrane Flow Resistance of Unit Area*Flux through Membrane)

Membrane Flux Based on Resistance

Go Flux through Membrane = Applied Pressure Driving Force/(Membrane Flow Resistance of Unit Area*Liquid Viscosity)

Resistance to flow in Membranes

Go Membrane Flow Resistance of Unit Area = Applied Pressure Driving Force/(Liquid Viscosity*Flux through Membrane)

Applied Pressure Driving Force Based on Permeability of Membrane

Go Applied Pressure Driving Force = Flux through Membrane/Water Permeability Through Membrane

Water Permeability through Membrane

Go Water Permeability Through Membrane = Flux through Membrane/Applied Pressure Driving Force

Membrane Flux Based on Water Permeability

Go Flux through Membrane = Water Permeability Through Membrane*Applied Pressure

Partial Molar Volume of Water based on Solution Diffusion Model Formula

What are the Assumptions of Solution Diffusion Model?

Some of the key assumptions of the solution-diffusion model:

The membrane is non-porous.
The water and solutes dissolve in the membrane material.
The diffusion coefficient of the water and solutes in the membrane is constant.
The concentration gradient across the membrane is the driving force for transport.

How to Calculate Partial Molar Volume of Water based on Solution Diffusion Model?

Partial Molar Volume of Water based on Solution Diffusion Model calculator uses Partial Molar Volume = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure)) to calculate the Partial Molar Volume, Partial molar volume of water based on solution diffusion model in a solution is the volume occupied by one mole of water in the solution. Partial Molar Volume is denoted by V_l symbol.

How to calculate Partial Molar Volume of Water based on Solution Diffusion Model using this online calculator? To use this online calculator for Partial Molar Volume of Water based on Solution Diffusion Model, enter Mass Water Flux (J_wm), Temperature (T), Membrane Layer Thickness (l_m), Membrane Water Diffusivity (D_w), Membrane Water Concentration (C_w), Membrane Pressure Drop (ΔP_atm) & Osmotic Pressure (Δπ) and hit the calculate button. Here is how the Partial Molar Volume of Water based on Solution Diffusion Model calculation can be explained with given input values -> 18.58781 = (6.3E-05*[R]*298*1.3E-05)/(1.762E-10*156*(7974767.78-3873626.75)).

FAQ

What is Partial Molar Volume of Water based on Solution Diffusion Model?

Partial molar volume of water based on solution diffusion model in a solution is the volume occupied by one mole of water in the solution and is represented as V_l = (J_wm*[R]*T*l_m)/(D_w*C_w*(ΔP_atm-Δπ)) or Partial Molar Volume = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure)). Mass Water flux is defined as the rate of movement of water across a surface or through a medium, Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness, Membrane Layer Thickness is the distance between the two outer surfaces of a membrane. It is typically measured in nanometers (nm), which are billionths of a meter, Membrane water diffusivity is the rate at which water molecules diffuse across a membrane. It is typically measured in square meters per second (m^2/s), Membrane water concentration (MWC) is the concentration of water in a membrane. It is typically measured in moles per cubic meter (kg/m^3), Membrane pressure drop is the difference in pressure between the inlet and outlet of a membrane system, housing (pressure vessel), or element & Osmotic pressure is the minimum pressure that must be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane.

How to calculate Partial Molar Volume of Water based on Solution Diffusion Model?

Partial molar volume of water based on solution diffusion model in a solution is the volume occupied by one mole of water in the solution is calculated using Partial Molar Volume = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure)). To calculate Partial Molar Volume of Water based on Solution Diffusion Model, you need Mass Water Flux (J_wm), Temperature (T), Membrane Layer Thickness (l_m), Membrane Water Diffusivity (D_w), Membrane Water Concentration (C_w), Membrane Pressure Drop (ΔP_atm) & Osmotic Pressure (Δπ). With our tool, you need to enter the respective value for Mass Water Flux, Temperature, Membrane Layer Thickness, Membrane Water Diffusivity, Membrane Water Concentration, Membrane Pressure Drop & Osmotic Pressure and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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