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Osmotic pressure
Storyboard

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)


Gas phase, water vapor
Concept

The gaseous phase, which in our case corresponds to water vapor, is the phase in which atoms can move relatively freely.

In this phase, there is only minimal interaction that can affect the behavior of atoms without significantly confining them.

ID:(15142, 0)


Liquid phase, water
Concept

The liquid phase, which in our case corresponds to water, is the phase in which atoms can move relatively freely while maintaining their unity and adapting to the shape that contains them.

In this phase, no specific structure is observed.

ID:(15140, 0)


Mechanisms
Concept


ID:(15287, 0)


Model
Concept


ID:(15634, 0)


Phase diagram of water
Concept

One of the most relevant phase diagrams for our planet is that of water. This diagram exhibits the three classical phases: solid, liquid, and gas, along with several phases featuring different crystalline structures of ice.

The significant distinction compared to other materials is that within a pressure range spanning from 611 Pa to 209.9 MPa, the solid phase occupies a greater volume than the liquid phase. This characteristic is reflected in the phase diagram as a negative slope along the boundary line separating the solid phase (hexagonal ice) and the liquid phase (water).

ID:(836, 0)


Solid phase, ice
Concept

The solid phase, which in our case corresponds to ice, is the phase in which atoms cannot move relatively and can only oscillate around their equilibrium point.

In this phase, one can observe a structure that is often crystalline and, therefore, regular.

ID:(15141, 0)


Osmotic pressure
Model

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.

Variables
Symbol
Text
Variable
Value
Units
Calculate
MKS Value
MKS Units
$T$
T
Absolute temperature
K
$p_0$
p_0
Atmospheric pressure
Pa
$h$
h
Column height
m
$\Delta h$
Dh
Height of liquid column
m
$h_1$
h_1
Height or depth 1
m
$h_2$
h_2
Height or depth 2
m
$\rho_w$
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
$p_1$
p_1
Pressure in column 1
Pa
$p_2$
p_2
Pressure in column 2
Pa
$p_t$
p_t
Total pressure
Pa
$\Delta p$
Dp
Variación de la Presión
Pa
$V$
V
Volume
m^3

Calculations

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Symbol
Equation
Solved
Translated

Calculations

Symbol
Equation
Solved
Translated

 Variable   Given   Calculate   Target :   Equation   To be used


Equations

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

$ dp = p - p_0 $



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)

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 }$

(ID 4854)

Como la energ a 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 ecuaci n 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_C } R T $

(ID 12820)

Examples


(ID 15287)

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.

(ID 2024)


(ID 15634)

ID:(660, 0)