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Osmotic pressure is generated in a solution when a semipermeable membrane is present. This membrane allows the solvent to pass through while retaining the solute on one side, creating a pressure imbalance. As a result, there is a reduction in pressure on the solvent side, driving the solvent to move through the membrane toward the side containing the solute.

This process continues until the pressure on the solute side increases enough to balance the initial pressure reduction or until the solute becomes diluted enough that the pressure difference is eliminated, reaching osmotic equilibrium.

>Model

ID:(660, 0)

Iframe

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ID:(15287, 0)

Image

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When a semipermeable membrane is placed at the bottom of a U-shaped tube and water is added, it can be observed that adding dissolved material causes the column with the solute to rise:

This phenomenon is due to the negative pressure generated by osmotic pressure.

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Parameters

$p_0$

p_0

Atmospheric pressure

Pa

$N_A$

N_A

Avogadro's number

-

$g$

g

Gravitational Acceleration

m/s^2

$\rho_w$

rho_w

Liquid density

kg/m^3

$M$

M

Mass

kg

$M_m$

M_m

Molar Mass

kg/mol

$N_s$

N_s

Number of ions

-

$n$

n

Número de Moles

mol

$\Psi$

Psi

Osmotic pressure

Pa

$R$

R

Universal gas constant

J/mol K

$\Delta p$

Dp

Variación de la Presión

Pa

Variables

$T$

T

Absolute temperature

K

$\Delta h$

Dh

Height of liquid column

m

$h_1$

h_1

Height or depth 1

m

$h_2$

h_2

Height or depth 2

m

$p_1$

p_1

Pressure in column 1

Pa

$p_2$

p_2

Pressure in column 2

Pa

$V$

V

Volume

m^3

Calculations

• Alternative method
• Traditional method
• Strategy
• 2D
• 3D

Equation

Number

First, select the equation: to , then, select the variable: to

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Calculations

Symbol

Equation

Solved

Translated

Calculations

Symbol

Equation

Solved

Translated

Variable Given Calculate Target : Equation To be used

Equations

ID:(15634, 0)

Equation

>Top, >Model

The osmotic pressure ($\Psi$) behaves like the pressure of an ideal gas of the number of ions ($N_s$) in the volume ($V$) at the absolute temperature ($T$), using the universal gas constant ($R$) as described by:

$\Psi =\displaystyle\frac{ N_s }{ V } R T$

Conditions

Variables

$T$

Absolute temperature

$K$

5177

$N_s$

Number of ions

$-$

9850

$\Psi$

Osmotic pressure

$Pa$

6608

$R$

Universal gas constant

8.4135

$J/mol K$

4957

$V$

Volume

$m^3$

5226

Relation

Development

Como la energía molar libre de Gibbs es

$dg = - s dT + v dp + \mu dN$

se tiene que para el equilibrio entre un sistema con y sin material disuelto (dg=0) e igual temperatura (dT=0) que

$\displaystyle\frac{V}{N_A}dp=\displaystyle\frac{V}{N_A}(p - \Phi)=\mu dN=\mu (N-N_s)$

Como sin material disuelto se debe asumir que el vapor satisface la ecuación de los gases se tiene que

$\mu\sim \displaystyle\frac{R}{N_A} T$

con lo que se obtiene que

$\Psi =\displaystyle\frac{ N_s }{ V } R T$

ID:(12820, 0)

Equation

>Top, >Model

If two columns of water are separated at their base by a semipermeable membrane that allows water to pass through but blocks the solute present in one of them, the columns will exhibit different heights. This is because the presence of a solute reduces the osmotic pressure, leading to an adjustment in the height of the column to balance the pressure difference.

If the pressure in the first column is the pressure in column 1 ($p_1$), the pressure in the second column (without solute) is the pressure in column 2 ($p_2$), and the osmotic pressure is the osmotic pressure ($\Psi$), we can express the relationship as follows:

$p_1 = p_2 - \Psi$

Conditions

Variables

$\Psi$

Osmotic pressure

$Pa$

6608

$p_1$

Pressure in column 1

$Pa$

6261

$p_2$

Pressure in column 2

$Pa$

6262

Relation

ID:(12827, 0)

Equation

>Top, >Model

The height difference, denoted by the height difference ($\Delta h$), implies that the pressure in both columns is distinct. In particular, the pressure difference ($\Delta p$) is a function of the liquid density ($\rho_w$), the gravitational Acceleration ($g$), and the height difference ($\Delta h$), as follows:

$\Delta p = \rho_w g \Delta h$

Conditions

Variables

$g$

Gravitational Acceleration

9.8

$m/s^2$

5310

$\Delta h$

Height of liquid column

$m$

5819

$\rho_w$

Liquid density

$kg/m^3$

5407

$\Delta p$

Variación de la Presión

$Pa$

6673

Relation

Development

If there is the pressure difference ($\Delta p$) between two points, as determined by the equation:

$\Delta p = p_2 - p_1$

we can utilize the water column pressure ($p$), which is defined as:

$p_t = p_0 + \rho_w g h$

This results in:

$\Delta p=p_2-p_1=p_0+\rho_wh_2g-p_0-\rho_wh_1g=\rho_w(h_2-h_1)g$

As the height difference ($\Delta h$) is:

$\Delta h = h_2 - h_1$

the pressure difference ($\Delta p$) can be expressed as:

$\Delta p = \rho_w g \Delta h$

ID:(4345, 0)

Equation

>Top, >Model

When two liquid columns are connected with the height of liquid column 1 ($h_1$) and the height of liquid column 2 ($h_2$), a the height difference ($\Delta h$) is formed, which is calculated as follows:

$\Delta h = h_2 - h_1$

Conditions

Variables

$\Delta h$

Height of liquid column

$m$

5819

$h_1$

Height or depth 1

$m$

6259

$h_2$

Height or depth 2

$m$

6260

Relation

the height difference ($\Delta h$) will generate the pressure difference that will cause the liquid to flow from the higher column to the lower one.

ID:(4251, 0)

Equation

>Top, >Model

When two liquid columns are connected with the pressure in column 1 ($p_1$) and the pressure in column 2 ($p_2$), a the pressure difference ($\Delta p$) is formed, which is calculated according to the following formula:

$\Delta p = p_2 - p_1$

Conditions

Variables

$p_1$

Pressure in column 1

$Pa$

6261

$p_2$

Pressure in column 2

$Pa$

6262

$\Delta p$

Variación de la Presión

$Pa$

6673

Relation

the pressure difference ($\Delta p$) represents the pressure difference that will cause the liquid to flow from the taller column to the shorter one.

ID:(4252, 0)

Equation

>Top, >Model

The number of moles ($n$) corresponds to the number of particles ($N$) divided by the avogadro's number ($N_A$):

$n \equiv\displaystyle\frac{ N_s }{ N_A }$

$n \equiv\displaystyle\frac{ N }{ N_A }$

Conditions

Variables

$N_A$

Avogadro's number

6.02e+23

$-$

9860

$N$

$N_s$

Number of ions

$-$

9850

$n$

Número de Moles

$mol$

6679

Relation

ID:(3748, 0)

Equation

>Top, >Model

The number of moles ($n$) is determined by dividing the mass ($M$) of a substance by its the molar Mass ($M_m$), which corresponds to the weight of one mole of the substance.

Therefore, the following relationship can be established:

$n = \displaystyle\frac{ M }{ M_m }$

Conditions

Variables

$M$

Mass

$kg$

5183

$M_m$

Molar Mass

$kg/mol$

6212

$n$

Número de Moles

$mol$

6679

Relation

Development

The number of moles ($n$) corresponds to the number of particles ($N$) divided by the avogadro's number ($N_A$):

$n \equiv\displaystyle\frac{ N_s }{ N_A }$

If we multiply both the numerator and the denominator by the particle mass ($m$), we obtain:

$n=\displaystyle\frac{N}{N_A}=\displaystyle\frac{Nm}{N_Am}=\displaystyle\frac{M}{M_m}$

So it is:

$n = \displaystyle\frac{ M }{ M_m }$

The molar mass is expressed in grams per mole (g/mol).

ID:(4854, 0)

Equation

>Top, >Model

The water column pressure ($p$) is with the liquid density ($\rho_w$), the column height ($h$), the gravitational Acceleration ($g$) and the atmospheric pressure ($p_0$) equal to:

$p_1 = p_0 + \rho_w g h_1$

$p_t = p_0 + \rho_w g h$

Conditions

Variables

$p_0$

Atmospheric pressure

$Pa$

5817

$h$

$h_1$

Height or depth 1

$m$

6259

$g$

Gravitational Acceleration

9.8

$m/s^2$

5310

$\rho_w$

Liquid density

$kg/m^3$

5407

$p_t$

$p_1$

Pressure in column 1

$Pa$

6261

Relation

ID:(4250, 1)

Equation

>Top, >Model

The water column pressure ($p$) is with the liquid density ($\rho_w$), the column height ($h$), the gravitational Acceleration ($g$) and the atmospheric pressure ($p_0$) equal to:

$p_2 = p_0 + \rho_w g h_2$

$p_t = p_0 + \rho_w g h$

Conditions

Variables

$p_0$

Atmospheric pressure

$Pa$

5817

$h$

$h_2$

Height or depth 2

$m$

6260

$g$

Gravitational Acceleration

9.8

$m/s^2$

5310

$\rho_w$

Liquid density

$kg/m^3$

5407

$p_t$

$p_2$

Pressure in column 2

$Pa$

6262

Relation

ID:(4250, 2)