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Partial Molar Volume of Water based on Solution Diffusion Model Formula

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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. Check FAQs

V l = \frac{J wm \cdot [R] \cdot T \cdot l m}{D w \cdot C w \cdot (ΔP atm - Δπ)}

V_l - Partial Molar Volume?J_wm - Mass Water Flux?T - Temperature?l_m - Membrane Layer Thickness?D_w - Membrane Water Diffusivity?C_w - Membrane Water Concentration?ΔP_atm - Membrane Pressure Drop?Δπ - Osmotic Pressure?[R] - Universal gas constant?

Partial Molar Volume of Water based on Solution Diffusion Model Example

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Here is how the Partial Molar Volume of Water based on Solution Diffusion Model equation looks like with Values.

Here is how the Partial Molar Volume of Water based on Solution Diffusion Model equation looks like with Units.

Here is how the Partial Molar Volume of Water based on Solution Diffusion Model equation looks like.

0.018 = \frac{6.3E-5 \cdot 8.3145 \cdot 298 \cdot 1.3E-5}{1.8E-10 \cdot 156 \cdot (81.32 - 39.5)}

0.018m³/kmol = \frac{6.3E-5kg/s/m² \cdot 8.3145 \cdot 298K \cdot 1.3E-5m}{1.8E-10m²/s \cdot 156kg/m³ \cdot (81.32at - 39.5at)}

0.018 = \frac{6.3E-5 \cdot 8.3145 \cdot 298 \cdot 1.3E-5}{1.8E-10 \cdot 156 \cdot (81.32 - 39.5)}

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Partial Molar Volume of Water based on Solution Diffusion Model Solution

Follow our step by step solution on how to calculate Partial Molar Volume of Water based on Solution Diffusion Model?

FIRST Step Consider the formula

V l = \frac{J wm \cdot [R] \cdot T \cdot l m}{D w \cdot C w \cdot (ΔP atm - Δπ)}

Next Step Substitute values of Variables

∴

V l = \frac{6.3E-5kg/s/m² \cdot [R] \cdot 298K \cdot 1.3E-5m}{1.8E-10m²/s \cdot 156kg/m³ \cdot (81.32at - 39.5at)}

Next Step Substitute values of Constants

∴

V l = \frac{6.3E-5kg/s/m² \cdot 8.3145 \cdot 298K \cdot 1.3E-5m}{1.8E-10m²/s \cdot 156kg/m³ \cdot (81.32at - 39.5at)}

Next Step Convert Units

∴

V l = \frac{6.3E-5kg/s/m² \cdot 8.3145 \cdot 298K \cdot 1.3E-5m}{1.8E-10m²/s \cdot 156kg/m³ \cdot (8E+6Pa - 3.9E+6Pa)}

Next Step Prepare to Evaluate

∴

V l = \frac{6.3E-5 \cdot 8.3145 \cdot 298 \cdot 1.3E-5}{1.8E-10 \cdot 156 \cdot (8E+6 - 3.9E+6)}

Next Step Evaluate

∴

V l = 1.80011041407572E-05m³/mol

Next Step Convert to Output's Unit

∴

V l = 0.0180011041407572m³/kmol

LAST Step Rounding Answer

∴

V l = 0.018m³/kmol

Partial Molar Volume of Water based on Solution Diffusion Model Formula Elements

Variables

Constants

Partial Molar Volume

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.

Symbol: V_l

Measurement: Molar VolumeUnit: m³/kmol

Note: Value should be greater than 0.

Formulas to find Partial Molar Volume

Mass Water Flux

Mass Water flux is defined as the rate of movement of water across a surface or through a medium.

Symbol: J_wm

Measurement: Mass FluxUnit: kg/s/m²

Note: Value should be greater than 0.

Formulas to find Mass Water Flux

Temperature

Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness.

Symbol: T

Measurement: TemperatureUnit: K

Note: Value should be greater than 274.15.

Formulas to find Temperature

Membrane Layer Thickness

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.

Symbol: l_m

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Membrane Layer Thickness

Membrane Water Diffusivity

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).

Symbol: D_w

Measurement: Kinematic ViscosityUnit: m²/s

Note: Value should be greater than 0.

Formulas to find Membrane Water Diffusivity

Membrane Water Concentration

Membrane water concentration (MWC) is the concentration of water in a membrane. It is typically measured in moles per cubic meter (kg/m^3).

Symbol: C_w

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Membrane Water Concentration

Membrane Pressure Drop

Membrane pressure drop is the difference in pressure between the inlet and outlet of a membrane system, housing (pressure vessel), or element.

Symbol: ΔP_atm

Measurement: PressureUnit: at

Note: Value should be greater than 0.

Formulas to find Membrane Pressure Drop

Osmotic Pressure

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.

Symbol: Δπ

Measurement: PressureUnit: at

Note: Value should be greater than 0.

Formulas to find Osmotic Pressure

Universal gas constant

Universal gas constant is a fundamental physical constant that appears in the ideal gas law, relating the pressure, volume, and temperature of an ideal gas.

Symbol: [R]

Value: 8.31446261815324

Other formulas in Basics of Membrane Separation Processes category

Go Hagen Poiseuille Based Flux for Membrane Separation

J wM = \frac{ε \cdot d^{2} \cdot ΔP m}{32 \cdot μ \cdot Τ \cdot l mt}

Go Resistance to flow in Membranes

R m = \frac{ΔP m}{μ \cdot J wM}

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

Partial Molar Volume of Water based on Solution Diffusion Model evaluator uses Partial Molar Volume = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure)) to evaluate 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 evaluate Partial Molar Volume of Water based on Solution Diffusion Model using this online evaluator? To use this online evaluator 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.

FAQs on Partial Molar Volume of Water based on Solution Diffusion Model

What is the formula to find Partial Molar Volume of Water based on Solution Diffusion Model?

The formula of Partial Molar Volume of Water based on Solution Diffusion Model is expressed as Partial Molar Volume = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure)). Here is an example- 18.58781 = (6.3E-05*[R]*298*1.3E-05)/(1.762E-10*156*(7974767.78-3873626.75)).

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

With 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) we can find Partial Molar Volume of Water based on Solution Diffusion Model using the formula - Partial Molar Volume = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure)). This formula also uses Universal gas constant .

Can the Partial Molar Volume of Water based on Solution Diffusion Model be negative?

Yes, the Partial Molar Volume of Water based on Solution Diffusion Model, measured in Molar Volume can be negative.

Which unit is used to measure Partial Molar Volume of Water based on Solution Diffusion Model?

Partial Molar Volume of Water based on Solution Diffusion Model is usually measured using the Cubic Meter per Kilomole[m³/kmol] for Molar Volume. Cubic Meter per Mole[m³/kmol] are the few other units in which Partial Molar Volume of Water based on Solution Diffusion Model can be measured.

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Partial Molar Volume of Water based on Solution Diffusion Model Formula

Partial Molar Volume of Water based on Solution Diffusion Model Example

Partial Molar Volume of Water based on Solution Diffusion Model Solution

Partial Molar Volume of Water based on Solution Diffusion Model Formula Elements

Other formulas in Basics of Membrane Separation Processes category

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

FAQs on Partial Molar Volume of Water based on Solution Diffusion Model

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