Information about Raoult's Law
Raoult's law states that
Once the components in the solution have reached chemical equilibrium, the total vapor pressure of the solution is:
and the individual vapor pressure for each component is
where
Consequently, as the number of components in a solution increases, the individual vapor pressures decrease, since the mole fraction of each component decreases with each additional component. If a pure solute which has zero vapor pressure (it will not evaporate) is dissolved in a solvent, the vapor pressure of the final solution will be lower than that of the pure solvent.
This law is strictly valid only under the assumption that the chemical interactions between the two liquids is equal to the bonding within the liquids: the conditions of an ideal solution. Therefore, comparing actual measured vapor pressures to predicted values from Raoult's law allows information about the relative strength of bonding between liquids to be obtained. If the measured value of vapor pressure is less than the predicted value, fewer molecules have left the solution than expected. This is put down to the strength of bonding between the liquids being greater than the bonding within the individual liquids, so fewer molecules have enough energy to leave the solution. Conversely, if the vapor pressure is greater than the predicted value more molecules have left the solution than expected, due to the bonding between the liquids being less strong than the bonding within each.
is:
where the reference state is the pure substance.
If the system is at equilibrium, then the chemical potential of the component must be the same in the liquid solution and in the vapor above it. That is,
Assuming the liquid is an ideal solution, and using the formula for the chemical potential of a gas, gives:
where
If we study the component in its pure state, we have:
where * indicates that we study a pure component.
But now,
= 1, so
Subtracting both equations gives us
which can be written as
or
This equation is valid for the ideal solution.
Now, suppose the vapor of the solution behaves as an ideal gas. In this case, fugacity and pressure are identical, and we get
At equilibrium we have
= 0, and then
Finally,
This last equality is what is known as Raoult’s Law.
This is always negative, so mixing is spontaneous. However the expression is -apart from a factor -T- equal to the entropy of mixing. This leaves no room at all for an enthalpy effect and implies that ΔHmix must be equal to zero and this can only be if the interactions U between the molecules are indifferent.
It can be shown using the Gibbs-Duhem equation that if Raoult's law holds over the entire concentration range x=0 to 1 in a binary solution that for the second component the same must hold.
If the deviations from ideality are not too strong, Raoult's law will still be valid in a narrow concentration range when approaching x=1 for the majority phase (the solvent). The solute will also show a linear limiting law but with a different coefficient. This law is known as Henry's law.
The presence of these limited linear regimes has been experimentally verified in a great number of cases.
). The second, the activity coefficient (
), is a correction for interactions in the liquid phase between the different molecules.
This modified or extended Raoult's law is then written:
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- The vapor pressure of an ideal solution is dependent on the vapor pressure of each chemical component and the mole fraction of the component present in the solution [1].
Once the components in the solution have reached chemical equilibrium, the total vapor pressure of the solution is:
and the individual vapor pressure for each component is
where
is the vapor pressure of the pure component
is the mole fraction of the component in solution
Consequently, as the number of components in a solution increases, the individual vapor pressures decrease, since the mole fraction of each component decreases with each additional component. If a pure solute which has zero vapor pressure (it will not evaporate) is dissolved in a solvent, the vapor pressure of the final solution will be lower than that of the pure solvent.
This law is strictly valid only under the assumption that the chemical interactions between the two liquids is equal to the bonding within the liquids: the conditions of an ideal solution. Therefore, comparing actual measured vapor pressures to predicted values from Raoult's law allows information about the relative strength of bonding between liquids to be obtained. If the measured value of vapor pressure is less than the predicted value, fewer molecules have left the solution than expected. This is put down to the strength of bonding between the liquids being greater than the bonding within the individual liquids, so fewer molecules have enough energy to leave the solution. Conversely, if the vapor pressure is greater than the predicted value more molecules have left the solution than expected, due to the bonding between the liquids being less strong than the bonding within each.
Deriving Raoult's Law (Raoult's Equation)
We define an ideal solution as a solution for which the chemical potential of component is:
,
where the reference state is the pure substance.
If the system is at equilibrium, then the chemical potential of the component
must be the same in the liquid solution and in the vapor above it. That is,
Assuming the liquid is an ideal solution, and using the formula for the chemical potential of a gas, gives:
(1)
where
is the If we study the component
in its pure state, we have:
where * indicates that we study a pure component.
But now,
= 1, so
Subtracting both equations gives us
which can be written as
or
This equation is valid for the ideal solution.
Now, suppose the vapor of the solution behaves as an ideal gas. In this case, fugacity and pressure are identical, and we get
At equilibrium we have
= 0, and then
Finally,
This last equality is what is known as Raoult’s Law.
Ideal mixing
An ideal solution can be said to follow Raoult's Law but it must be kept in mind that in the strict sense ideal solutions do not exist. The fact that the vapor is taken to be ideal is the least of our worries. Interactions between gas molecules are typically quite small especially if the vapor pressures are low. The interactions in a liquid however are very strong. For a solution to be ideal we must assume that it does not matter whether a molecule A has another A as neighbor or a B molecule. This is only approximately true if the two species are almost identical chemically. We can see that from considering the Gibbs free energy change of mixing:
This is always negative, so mixing is spontaneous. However the expression is -apart from a factor -T- equal to the entropy of mixing. This leaves no room at all for an enthalpy effect and implies that ΔHmix must be equal to zero and this can only be if the interactions U between the molecules are indifferent.
It can be shown using the Gibbs-Duhem equation that if Raoult's law holds over the entire concentration range x=0 to 1 in a binary solution that for the second component the same must hold.
If the deviations from ideality are not too strong, Raoult's law will still be valid in a narrow concentration range when approaching x=1 for the majority phase (the solvent). The solute will also show a linear limiting law but with a different coefficient. This law is known as Henry's law.
The presence of these limited linear regimes has been experimentally verified in a great number of cases.
Non-ideal mixing
Raoult's Law may be adapted to non-ideal solutions by incorporating two factors that will account for the interactions between molecules of different substances. The first factor is a correction for gas non-ideality, or deviations from the ideal-gas law. It is called the fugacity coefficient (). The second, the activity coefficient (), is a correction for interactions in the liquid phase between the different molecules.
This modified or extended Raoult's law is then written:
See also
References
Concepts in distillation | |
|---|---|
| Principles | Raoult's law, Dalton's law, Reflux, Fenske equation, McCabe-Thiele method, Theoretical plate |
| Industrial processes | Batch distillation, Continuous distillation, Fractionating column |
| Laboratory methods | Rotary evaporator, Kugelrohr, Spinning band distillation |
| Techniques | Fractional distillation, Vacuum distillation, Extractive distillation, Reactive distillation, Dry distillation, Destructive distillation, Azeotropic distillation, Steam distillation |
Vapor pressure, also known as vapour pressure, is the pressure of a vapor in equilibrium with its non-vapor phases. All liquids and solids have a tendency to evaporate to a gaseous form, and all gases have a tendency to condense back into their orignal form (either liquid
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In chemistry, an ideal solution or ideal mixture is a solution in which the enthalpy of solution is zero [1]. The closer to zero the enthalpy of solution is, the more "ideal" the solution becomes.
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In chemistry, the mole fraction of a component in a mixture is the relative proportion of molecules belonging to the component to those in the mixture, by number of molecules. It is one way of measuring concentration.
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chemical equilibrium is the state in which the chemical activities or concentrations of the reactants and products have no net change over time. Usually, this state results when the forward chemical process proceeds at the same rate as their reverse reaction.
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Vapor pressure, also known as vapour pressure, is the pressure of a vapor in equilibrium with its non-vapor phases. All liquids and solids have a tendency to evaporate to a gaseous form, and all gases have a tendency to condense back into their orignal form (either liquid
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In chemistry, the mole fraction of a component in a mixture is the relative proportion of molecules belonging to the component to those in the mixture, by number of molecules. It is one way of measuring concentration.
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Evaporation is the process by which molecules in a liquid state (e.g. water) spontaneously become gaseous (e.g. water vapor), without being heated to boiling point. It is the opposite of condensation.
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A chemical bond is the physical process responsible for the attractive interactions between atoms and molecules, and that which confers stability to diatomic and polyatomic chemical compounds.
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In chemistry, an ideal solution or ideal mixture is a solution in which the enthalpy of solution is zero [1]. The closer to zero the enthalpy of solution is, the more "ideal" the solution becomes.
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molecule is defined as a sufficiently stable electrically neutral group of at least two atoms in a definite arrangement held together by strong chemical bonds.[1][2] In organic chemistry and biochemistry, the term molecule
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In chemistry, an ideal solution or ideal mixture is a solution in which the enthalpy of solution is zero [1]. The closer to zero the enthalpy of solution is, the more "ideal" the solution becomes.
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This article is about chemical solutions. For other uses, see Solution (disambiguation).
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In thermodynamics and chemistry, chemical potential, symbolized by μ, is a term introduced in 1876 by the American mathematical physicist Willard Gibbs, which he defined as follows:
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chemical equilibrium is the state in which the chemical activities or concentrations of the reactants and products have no net change over time. Usually, this state results when the forward chemical process proceeds at the same rate as their reverse reaction.
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In thermodynamics and chemistry, chemical potential, symbolized by μ, is a term introduced in 1876 by the American mathematical physicist Willard Gibbs, which he defined as follows:
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Vapor or vapour (see spelling differences) is the gas phase component of another state of matter (e.g. liquid or solid) which does not completely fill its container. It is distinguished from the pure gas phase by the presence of the same substance in another state of matter.
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Fugacity is a measure of chemical potential in the form of 'adjusted pressure.' It directly relates to the tendency of a substance to prefer one phase (liquid, solid, gas) over another. At a fixed temperature and pressure, water will have a different fugacity for each phase.
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Vapor or vapour (see spelling differences) is the gas phase component of another state of matter (e.g. liquid or solid) which does not completely fill its container. It is distinguished from the pure gas phase by the presence of the same substance in another state of matter.
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Vapor or vapour (see spelling differences) is the gas phase component of another state of matter (e.g. liquid or solid) which does not completely fill its container. It is distinguished from the pure gas phase by the presence of the same substance in another state of matter.
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An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. Additionally, the constituent atoms or molecules undergo perfectly elastic collisions with the walls of the container.
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Fugacity is a measure of chemical potential in the form of 'adjusted pressure.' It directly relates to the tendency of a substance to prefer one phase (liquid, solid, gas) over another. At a fixed temperature and pressure, water will have a different fugacity for each phase.
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Pressure (symbol: p) is the force per unit area applied on a surface in a direction perpendicular to that surface.
Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.
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Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.
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The entropy of mixing (also known as configurational entropy) is the change in the entropy, an extensive thermodynamic quantity, when two different chemical substances or components are mixed.
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The Gibbs-Duhem equation in thermodynamics describes the relationship between changes in chemical potential for components in a thermodynamical system [1] :
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In chemistry, Henry's law is one of the gas laws, formulated by William Henry. It states that:
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- At a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in
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The gas laws are a set of laws that describe the relationship between thermodynamic temperature (T), pressure (P) and volume (V) of gases. They are a loose collection of rules developed between the late Renaissance and early 19th century.
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In chemistry, Henry's law is one of the gas laws, formulated by William Henry. It states that:
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- At a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in
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Dalton's law (also called Dalton's law of partial pressures) states that the total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each individual component in a gas mixture.
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Distillation is a method of separating chemical substances based on differences in their volatilities in a boiling liquid mixture. Distillation usually forms part of a larger chemical process, and is thus referred to as a unit operation.
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