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When a material (solute) is dissolved in a liquid (solvent), the physical properties of the solvent change.

In the presence of a semipermeable membrane that allows the solvent to pass through but retains the solute, osmotic pressure is generated. This phenomenon results in a reduction of the effective pressure in the solvent.

Additionally, the dissolution affects the liquid's phase transition temperatures. Specifically, it lowers the freezing point and raises the boiling point, altering its thermal behavior.

>Model

ID:(1675, 0)

Iframe

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ID:(15290, 0)

Image

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In a phase diagram of a solution, the boundaries between phases shift in such a way that, at the same pressure, the melting point decreases while the boiling point increases:

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>Top

Parameters

$N_A$

N_A

Avogadro's number

-

$T_b$

T_b

Boiling temperature

K

$T_{bs}$

T_bs

Boiling temperature with solute

K

$l_V$

l_V

Calor latente molar del cambio de fase liquido vapor

J/mol

$l_S$

l_S

Calor latente molar del cambio de fase solido liquido

J/mol

$\mu_L$

mu_L

Chemical potential of the liquid

J

$\mu_S$

mu_S

Chemical potential of the solid

J

$\mu_V$

mu_V

Chemical vapor potential

J

$T_{fs}$

T_fs

Freezing temperature with solute

K

$M$

M

Mass

kg

$M_s$

M_s

Mass of solute

kg

$s_L$

s_L

Molar entropy of the liquid

J/K mol

$s_S$

s_S

Molar entropy of the solid

J/K mol

$s_V$

s_V

Molar entropy of vapor

J/K mol

$M_m$

M_m

Molar Mass

kg/mol

$M_{ms}$

M_ms

Molar mass of the solute

kg/mol

$N_s$

N_s

Number of ions

-

$n$

n

Número de Moles

mol

$T_f$

T_f

Temperatura de fusión

K

$R$

R

Universal gas constant

J/mol K

Variables

$n_s$

n_s

Number of moles of the solute

mol

$N$

N

Number of particles

-

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:(15348, 0)

Equation

>Top, >Model

The chemical vapor potential ($\mu_V$), together with the avogadro's number ($N_A$), is equal to the molar entropy of vapor ($s_V$) multiplied by the difference between the absolute temperature ($T$) and the steam reference temperature ($T_V$), expressed as:

$\mu_V N_A = s_V ( T_{bs} - T_b )$

$\mu_V N_A = s_V ( T - T_V )$

Conditions

Variables

$T$

$T_{bs}$

Boiling temperature with solute

$K$

9862

$N_A$

Avogadro's number

6.02e+23

$-$

9860

$\mu_V$

Chemical vapor potential

$J$

9851

$s_V$

Molar entropy of vapor

$J/mol K$

9854

$T_V$

$T_b$

Boiling temperature

$K$

9861

Relation

ID:(12815, 0)

Equation

>Top, >Model

The chemical potential of the solid ($\mu_S$), together with the avogadro's number ($N_A$), is equivalent to the molar entropy of the solid ($s_S$) multiplied by the difference between the absolute temperature ($T$) and the solid reference temperature ($T_S$), represented as:

$\mu_S N_A = s_S ( T_{fs} - T_f )$

$\mu_S N_A = s_S ( T - T_S )$

Conditions

Variables

$T$

$T_{fs}$

Freezing temperature with solute

$K$

9863

$N_A$

Avogadro's number

6.02e+23

$-$

9860

$\mu_S$

Chemical potential of the solid

$J$

9853

$s_S$

Molar entropy of the solid

$J/mol K$

9856

$T_S$

$T_f$

Temperatura de fusión

$K$

9498

Relation

ID:(12816, 0)

Equation

>Top, >Model

The chemical potential of the liquid ($\mu_L$), together with the avogadro's number ($N_A$), is equal to the molar entropy of the liquid ($s_L$) multiplied by the difference between the absolute temperature ($T$) and the liquid reference temperature ($T_L$), in addition to the effect of osmotic pressure, which depends on the number of ions ($N_s$), the number of particles ($N$), the absolute temperature ($T$), and the universal gas constant ($R$), represented as:

$\mu_L N_A = s_L ( T_{fs} - T_f ) - \displaystyle\frac{ N_s }{ N } R T_{fs}$

$\mu_L N_A = s_L ( T - T_L ) - \displaystyle\frac{ N_s }{ N } R T$

Conditions

Variables

$T$

$T_{fs}$

Freezing temperature with solute

$K$

9863

$N_A$

Avogadro's number

6.02e+23

$-$

9860

$\mu_L$

Chemical potential of the liquid

$J$

9852

$T_L$

$T_f$

Temperatura de fusión

$K$

9498

$s_L$

Molar entropy of the liquid

$J/mol K$

9855

$N_s$

Number of ions

$-$

9850

$N$

Number of particles

$-$

6080

$R$

Universal gas constant

8.4135

$J/mol K$

4957

Relation

ID:(12817, 1)

Equation

>Top, >Model

The chemical potential of the liquid ($\mu_L$), together with the avogadro's number ($N_A$), is equal to the molar entropy of the liquid ($s_L$) multiplied by the difference between the absolute temperature ($T$) and the liquid reference temperature ($T_L$), in addition to the effect of osmotic pressure, which depends on the number of ions ($N_s$), the number of particles ($N$), the absolute temperature ($T$), and the universal gas constant ($R$), represented as:

$\mu_L N_A = s_L ( T_{bs} - T_b ) - \displaystyle\frac{ N_s }{ N } R T_{bs}$

$\mu_L N_A = s_L ( T - T_L ) - \displaystyle\frac{ N_s }{ N } R T$

Conditions

Variables

$T$

$T_{bs}$

Boiling temperature with solute

$K$

9862

$N_A$

Avogadro's number

6.02e+23

$-$

9860

$\mu_L$

Chemical potential of the liquid

$J$

9852

$T_L$

$T_b$

Boiling temperature

$K$

9861

$s_L$

Molar entropy of the liquid

$J/mol K$

9855

$N_s$

Number of ions

$-$

9850

$N$

Number of particles

$-$

6080

$R$

Universal gas constant

8.4135

$J/mol K$

4957

Relation

ID:(12817, 2)

Equation

>Top, >Model

If the temperatura de fusión ($T_f$) represents the boiling temperature, the molar entropy of the liquid ($s_L$) corresponds to the molar entropy of the liquid, and the molar entropy of the solid ($s_S$) to that of the solid, then the enthalpy of evaporation the calor latente molar del cambio de fase solido liquido ($l_S$) is calculated using the following formula:

$l_S = T_f ( s_L - s_S )$

Conditions

Variables

$l_S$

Calor latente molar del cambio de fase solido liquido

$J/mol$

9497

$s_L$

Molar entropy of the liquid

$J/mol K$

9855

$s_S$

Molar entropy of the solid

$J/mol K$

9856

$T_f$

Temperatura de fusión

$K$

9498

Relation

ID:(9051, 0)

Equation

>Top, >Model

If the boiling temperature ($T_b$) is the boiling temperature, the molar entropy of vapor ($s_V$) represents the molar entropy of the vapor, and the molar entropy of the liquid ($s_L$) represents that of the liquid, then the enthalpy of evaporation the calor latente molar del cambio de fase liquido vapor ($l_V$) is calculated using the following expression:

$l_V = T_b ( s_V - s_L )$

Conditions

Variables

$T_b$

Boiling temperature

$K$

9861

$l_V$

Calor latente molar del cambio de fase liquido vapor

$J/mol$

9501

$s_L$

Molar entropy of the liquid

$J/mol K$

9855

$s_V$

Molar entropy of vapor

$J/mol K$

9854

Relation

ID:(9050, 0)

Equation

>Top, >Model

Another effect that varies in solutions is the boiling point. When a solvent boils at a temperature $T$ and pressure $p$ in its pure state, the chemical potential of the liquid phase must equal the chemical potential of the vapor phase.

However, due to the reduction in vapor pressure caused by the presence of a solute, an increase in temperature is required to achieve this equilibrium. As a result, the boiling point of a solution is higher than that of the pure solvent.

Therefore, the boiling temperature with solute ($T_{bs}$), together with the boiling temperature ($T_b$), the number of ions ($N_s$), the number of particles ($N$), the calor latente molar del cambio de fase liquido vapor ($l_V$), and the universal gas constant ($R$), is equal to:

$T_{bs} = T_b +\displaystyle\frac{ N_s }{ N }\displaystyle\frac{ R T_b ^2}{ l_V }$

Conditions

Variables

$T_b$

Boiling temperature

$K$

9861

$T_{bs}$

Boiling temperature with solute

$K$

9862

$l_V$

Calor latente molar del cambio de fase liquido vapor

$J/mol$

9501

$N_s$

Number of ions

$-$

9850

$N$

Number of particles

$-$

6080

$R$

Universal gas constant

8.4135

$J/mol K$

4957

Relation

Development

Si se considera como temperatura de referencia T_0 la del punto de ebullición del liquido T_b, el potencial químico de la solución es

$\mu_L N_A = s_L ( T - T_L ) - \displaystyle\frac{ N_s }{ N } R T$

y el del vapor

$\mu_V N_A = s_V ( T_{bs} - T_b )$

se tiene que la temperatura de ebullición de la solución T_s estará definida por

$s_L (T_s-T_b)-\displaystyle\frac{N_s}{N}RT_s= s_V (T_s-T_b)$

Con

$l_V = T_b ( s_V - s_L )$

se tiene que con

$T_{bs} = T_b +\displaystyle\frac{ N_s }{ N }\displaystyle\frac{ R T_b ^2}{ l_V }$

ID:(12819, 0)

Equation

>Top, >Model

Another effect that varies in solutions is the freezing point. When a solvent freezes at a temperature $T$ and pressure $p$ in its pure state, the chemical potential of the solid phase must equal that of the liquid phase.

Due to the reduction in vapor pressure caused by the presence of a solute, the temperature must be lowered to achieve this equilibrium. As a result, the freezing point of the solvent decreases in a solution.

Thus, the freezing temperature with solute ($T_{fs}$), together with the freezing temperature ($T_f$), the number of ions ($N_s$), the number of particles ($N$), the calor latente molar del cambio de fase solido liquido ($l_S$), and the universal gas constant ($R$), is equal to:

$T_{fs} = T_f - \displaystyle\frac{ N_s }{ N }\displaystyle\frac{ R T_f ^2}{ l_S }$

Conditions

Variables

$l_S$

Calor latente molar del cambio de fase solido liquido

$J/mol$

9497

$T_{fs}$

Freezing temperature with solute

$K$

9863

$N_s$

Number of ions

$-$

9850

$N$

Number of particles

$-$

6080

$T_f$

Temperatura de fusión

$K$

9498

$R$

Universal gas constant

8.4135

$J/mol K$

4957

Relation

Development

Si se considera como temperatura de referencia T_0 la del punto de ebullición del liquido T_b, el potencial químico de la solución es

$\mu_L N_A = s_L ( T - T_L ) - \displaystyle\frac{ N_s }{ N } R T$

y el del solido

$\mu_S N_A = s_S ( T_{fs} - T_f )$

se tiene que la temperatura de ebullición de la solución T_s estara definida por

$s_S (T_s-T_b)= s_L (T_s-T_b)-\displaystyle\frac{N_s}{N}RT_s$

Con

$l_S = T_f ( s_L - s_S )$

se tiene que con

$T_{fs} = T_f - \displaystyle\frac{ N_s }{ N }\displaystyle\frac{ R T_f ^2}{ l_S }$

ID:(12818, 0)

Equation

>Top, >Model

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

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

Conditions

Variables

$N_A$

Avogadro's number

6.02e+23

$-$

9860

$N$

Number of particles

$-$

6080

$n$

Número de Moles

$mol$

6679

Relation

ID:(3748, 1)

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 ($N_A$):

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

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, 1)

Equation

>Top, >Model

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

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

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

Conditions

Variables

$N_A$

Avogadro's number

6.02e+23

$-$

9860

$N$

$N_s$

Number of ions

$-$

9850

$n$

$n_s$

Number of moles of the solute

$mol$

10505

Relation

ID:(3748, 2)

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:

$n_s = \displaystyle\frac{ M_s }{ M_{ms} }$

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

Conditions

Variables

$M$

$M_s$

Mass of solute

$kg$

10506

$M_m$

$M_{ms}$

Molar mass of the solute

$kg/mol$

10507

$n$

$n_s$

Number of moles of the solute

$mol$

10505

Relation

Development

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

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

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, 2)