Solution (chemistry)

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https://en.wikipedia.org/wiki/Solution_(chemistry)

Making a saline water solution by dissolving table salt (NaCl) in water. The salt is the solute and the water the solvent.

In chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. If the attractive forces between the solvent and solute particles are greater than the attractive forces holding the solute particles together, the solvent particles pull the solute particles apart and surround them. These surrounded solute particles then move away from the solid solute and out into the solution. The mixing process of a solution happens at a scale where the effects of chemical polarity are involved, resulting in interactions that are specific to solvation. The solution usually has the state of the solvent when the solvent is the larger fraction of the mixture, as is commonly the case. One important parameter of a solution is the concentration, which is a measure of the amount of solute in a given amount of solution or solvent. The term "aqueous solution" is used when one of the solvents is water.

Characteristics

• A solution is a homogeneous mixture of two or more substances.
• The particles of solute in a solution cannot be seen by the naked eye. By contrast, particles may be visible in a suspension.
• A solution does not cause beams of light to scatter. By contrast, the particles in a suspension or colloid can cause Tyndall scattering or Rayleigh scattering.
• A solution is stable, and solutes will not precipitate unless added in excess of the mixture's solubility, at which point the excess would remain in its solid phase. A solution containing more dissolved solutes than at equilibrium is referred to as supersaturated.
• The solutes and solvents in a solution cannot be separated by filtration (or mechanically).
• It is composed of only one phase.

Types

Homogeneous means that the components of the mixture form a single phase. Heterogeneous means that the components of the mixture are of different phase. The properties of the mixture (such as concentration, temperature, and density) can be uniformly distributed through the volume but only in absence of diffusion phenomena or after their completion. Usually, the substance present in the greatest amount is considered the solvent. Solvents can be gases, liquids, or solids. One or more components present in the solution other than the solvent are called solutes. The solution has the same physical state as the solvent.

Gaseous mixtures

If the solvent is a gas, only gases (non-condensable) or vapors (condensable) are dissolved under a given set of conditions. An example of a gaseous solution is air (oxygen and other gases dissolved in nitrogen). Since interactions between gaseous molecules play almost no role, non-condensable gases form rather trivial solutions. In the literature, they are not even classified as solutions, but simply addressed as homogeneous mixtures of gases. The Brownian motion and the permanent molecular agitation of gas molecules guarantee the homogeneity of the gaseous systems. Non-condensable gases mixtures (e.g., air/CO₂, or air/xenon) do not spontaneously demix, nor sediment, as distinctly stratified and separate gas layers as a function of their relative density. Diffusion forces efficiently counteract gravitation forces under normal conditions prevailing on Earth. The case of condensable vapors is different: once the saturation vapor pressure at a given temperature is reached, vapor excess condenses into the liquid state.

Liquid solutions

If the solvent is a liquid, then almost all gases, liquids, and solids can be dissolved. Here are some examples:

• Gas in liquid:
  • Oxygen in water
  • Carbon dioxide in water – a less simple example, because the solution is accompanied by a chemical reaction (formation of ions). The visible bubbles in carbonated water are not the dissolved gas, but only an effervescence of carbon dioxide that has come out of solution; the dissolved gas itself is not visible since it is dissolved on a molecular level.
• Liquid in liquid:
  • The mixing of two or more substances of the same chemistry but different concentrations to form a constant. (Homogenization of solutions)
  • Alcoholic beverages are basically solutions of ethanol in water.
• Solid in liquid:
  • Sucrose (table sugar) in water
  • Sodium chloride (NaCl) (table salt) or any other salt in water, which forms an electrolyte: When dissolving, salt dissociates into ions.
• Solutions in water are especially common, and are called aqueous solutions.
• Non-aqueous solutions are when the liquid solvent involved is not water.

Counterexamples are provided by liquid mixtures that are not homogeneous: colloids, suspensions, emulsions are not considered solutions.

Body fluids are examples of complex liquid solutions, containing many solutes. Many of these are electrolytes since they contain solute ions, such as potassium. Furthermore, they contain solute molecules like sugar and urea. Oxygen and carbon dioxide are also essential components of blood chemistry, where significant changes in their concentrations may be a sign of severe illness or injury.

Solid solutions

If the solvent is a solid, then gases, liquids, and solids can be dissolved.

• Gas in solids:
  • Hydrogen dissolves rather well in metals, especially in palladium; this is studied as a means of hydrogen storage.
• Liquid in solid:
  • Mercury in gold, forming an amalgam
  • Water in solid salt or sugar, forming moist solids
  • Hexane in paraffin wax
  • Polymers containing plasticizers such as phthalate (liquid) in PVC (solid)
• Solid in solid:
  • Steel, basically a solution of carbon atoms in a crystalline matrix of iron atoms
  • Alloys like bronze and many others
  • Radium sulfate dissolved in barium sulfate: a true solid solution of Ra in BaSO₄

Solubility

Main articles: Solubility and Solvation

The ability of one compound to dissolve in another compound is called solubility.^{[clarification needed]} When a liquid can completely dissolve in another liquid the two liquids are miscible. Two substances that can never mix to form a solution are said to be immiscible.

All solutions have a positive entropy of mixing. The interactions between different molecules or ions may be energetically favored or not. If interactions are unfavorable, then the free energy decreases with increasing solute concentration. At some point, the energy loss outweighs the entropy gain, and no more solute particles can be dissolved; the solution is said to be saturated. However, the point at which a solution can become saturated can change significantly with different environmental factors, such as temperature, pressure, and contamination. For some solute-solvent combinations, a supersaturated solution can be prepared by raising the solubility (for example by increasing the temperature) to dissolve more solute and then lowering it (for example by cooling).

Usually, the greater the temperature of the solvent, the more of a given solid solute it can dissolve. However, most gases and some compounds exhibit solubilities that decrease with increased temperature. Such behavior is a result of an exothermic enthalpy of solution. Some surfactants exhibit this behaviour. The solubility of liquids in liquids is generally less temperature-sensitive than that of solids or gases.

Properties

The physical properties of compounds such as melting point and boiling point change when other compounds are added. Together they are called colligative properties. There are several ways to quantify the amount of one compound dissolved in the other compounds collectively called concentration. Examples include molarity, volume fraction, and mole fraction.

The properties of ideal solutions can be calculated by the linear combination of the properties of its components. If both solute and solvent exist in equal quantities (such as in a 50% ethanol, 50% water solution), the concepts of "solute" and "solvent" become less relevant, but the substance that is more often used as a solvent is normally designated as the solvent (in this example, water).

Liquid solution characteristics

See also: Solvent § Solvent classifications

In principle, all types of liquids can behave as solvents: liquid noble gases, molten metals, molten salts, molten covalent networks, and molecular liquids. In the practice of chemistry and biochemistry, most solvents are molecular liquids. They can be classified into polar and non-polar, according to whether their molecules possess a permanent electric dipole moment. Another distinction is whether their molecules can form hydrogen bonds (protic and aprotic solvents). Water, the most commonly used solvent, is both polar and sustains hydrogen bonds.

Water is a good solvent because the molecules are polar and capable of forming hydrogen bonds (1).

Salts dissolve in polar solvents, forming positive and negative ions that are attracted to the negative and positive ends of the solvent molecule, respectively. If the solvent is water, hydration occurs when the charged solute ions become surrounded by water molecules. A standard example is aqueous saltwater. Such solutions are called electrolytes. Whenever salt dissolves in water ion association has to be taken into account.

Polar solutes dissolve in polar solvents, forming polar bonds or hydrogen bonds. As an example, all alcoholic beverages are aqueous solutions of ethanol. On the other hand, non-polar solutes dissolve better in non-polar solvents. Examples are hydrocarbons such as oil and grease that easily mix, while being incompatible with water.

An example of the immiscibility of oil and water is a leak of petroleum from a damaged tanker, that does not dissolve in the ocean water but rather floats on the surface.

Preparation from constituent ingredients

It is common practice in laboratories to make a solution directly from its constituent ingredients. There are three cases in practical calculation:

• Case 1: amount of solvent volume is given.
• Case 2: amount of solute mass is given.
• Case 3: amount of final solution volume is given.

In the following equations, A is solvent, B is solute, and C is concentration. Solute volume contribution is considered through the ideal solution model.

• Case 1: amount (mL) of solvent volume V_A is given. Solute mass m_B = C V_A d_A /(100-C/d_B)
• Case 2: amount of solute mass m_B is given. Solvent volume V_A = m_B (100/C-1/ d_B )
• Case 3: amount (mL) of final solution volume Vt is given. Solute mass m_B = C Vt /100; Solvent volume V_A=(100/C-1/ d_B) m_B
• Case 2: solute mass is known, V_A = m_B 100/C
• Case 3: total solution volume is known, same equation as case 1. V_A=Vt; m_B = C V_A /100

Example: Make 2 g/100mL of NaCl solution with 1 L water. The density of the resulting solution is considered to be equal to that of water, statement holding especially for dilute solutions, so the density information is not required.

m_B = C V_A = ( 2 / 100 ) g/mL × 1000 mL = 20 g

Chemists often make concentrated stock solutions that may then be diluted as needed for laboratory applications. Standard solutions are those where concentrations of solutes are accurately and precisely known.

Apparent molar property

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Apparent_molar_property 

In thermodynamics, an apparent molar property of a solution component in a mixture or solution is a quantity defined with the purpose of isolating the contribution of each component to the non-ideality of the mixture. It shows the change in the corresponding solution property (for example, volume) per mole of that component added, when all of that component is added to the solution. It is described as apparent because it appears to represent the molar property of that component in solution, provided that the properties of the other solution components are assumed to remain constant during the addition. However this assumption is often not justified, since the values of apparent molar properties of a component may be quite different from its molar properties in the pure state.

For instance, the volume of a solution containing two components identified as solvent and solute is given by

${\displaystyle V=V_0+{}^{\varphi }{V}_1={\tilde{V}}_0{n}_0+{}^{\varphi }{\tilde{V}}_1{n}_1}$

where ${\displaystyle V_0}$ is the volume of the pure solvent before adding the solute and ${\displaystyle {\tilde{V}}_0}$ its molar volume (at the same temperature and pressure as the solution), ${\displaystyle n_0}$ is the number of moles of solvent, ${\displaystyle {}^{\varphi }{\tilde{V}}_1}$ is the apparent molar volume of the solute, and ${\displaystyle n_1}$ is the number of moles of the solute in the solution. By dividing this relation to the molar amount of one component a relation between the apparent molar property of a component and the mixing ratio of components can be obtained.

This equation serves as the definition of ${\displaystyle {}^{\varphi }{\tilde{V}}_1}$. The first term is equal to the volume of the same quantity of solvent with no solute, and the second term is the change of volume on addition of the solute. ${\displaystyle {}^{\varphi }{\tilde{V}}_1}$ may then be considered as the molar volume of the solute if it is assumed that the molar volume of the solvent is unchanged by the addition of solute. However this assumption must often be considered unrealistic as shown in the examples below, so that ${\displaystyle {}^{\varphi }{\tilde{V}}_1}$ is described only as an apparent value.

An apparent molar quantity can be similarly defined for the component identified as solvent ${\displaystyle {}^{\varphi }{\tilde{V}}_0}$. Some authors have reported apparent molar volumes of both (liquid) components of the same solution. This procedure can be extended to ternary and multicomponent mixtures.

Apparent quantities can also be expressed using mass instead of number of moles. This expression produces apparent specific quantities, like the apparent specific volume.

${\displaystyle V=V_0+{}^{\varphi }{V}_1=v_0{m}_0+{}^{\varphi }{v}_1{m}_1}$

where the specific quantities are denoted with small letters.

Apparent (molar) properties are not constants (even at a given temperature), but are functions of the composition. At infinite dilution, an apparent molar property and the corresponding partial molar property become equal.

Some apparent molar properties that are commonly used are apparent molar enthalpy, apparent molar heat capacity, and apparent molar volume.

Relation to molality

The apparent (molal) volume of a solute can be expressed as a function of the molality b of that solute (and of the densities of the solution and solvent). The volume of solution per mole of solute is

${\displaystyle \frac{1}{\rho }\left(\frac{1}{b}+M_1\right).}$

Subtracting the volume of pure solvent per mole of solute gives the apparent molal volume:

${\displaystyle {}^{\varphi }{\tilde{V}}_1=\frac{V-V_0}{n_1}=\left(\frac{m}{\rho }-\frac{m_0}{{\rho }_0^0}\right)\frac{1}{n_1}=\left(\frac{m_1+m_0}{\rho }-\frac{m_0}{{\rho }_0^0}\right)\frac{1}{n_1}=\left(\frac{m_0}{\rho }-\frac{m_0}{{\rho }_0^0}\right)\frac{1}{n_1}+\frac{m_1}{\rho n_1}}$

${\displaystyle {}^{\varphi }{\tilde{V}}_1=\frac{1}{b}\left(\frac{1}{\rho }-\frac{1}{{\rho }_0^0}\right)+\frac{M_1}{\rho }}$

For more solutes the above equality is modified with the mean molar mass of the solutes as if they were a single solute with molality b_T:

${\displaystyle {}^{\varphi }{\tilde{V}}_{\mathrm{12..}}=\frac{1}{b_T}\left(\frac{1}{\rho }-\frac{1}{{\rho }_0^0}\right)+\frac{M}{\rho }}$, ${\displaystyle M=\sum y_i{M}_i}$

The sum of products molalities – apparent molar volumes of solutes in their binary solutions equals the product between the sum of molalities of solutes and apparent molar volume in ternary of multicomponent solution mentioned above.

${\displaystyle {}^{\varphi }{\tilde{V}}_{\mathrm{123..}}(b_1+b_2+b_3+...)=b_1{}^{\varphi }{\tilde{V}}_1+b_2{}^{\varphi }{\tilde{V}}_2+b_3{}^{\varphi }{\tilde{V}}_3+...}$,

Relation to mixing ratio

A relation between the apparent molar of a component of a mixture and molar mixing ratio can be obtained by dividing the definition relation

${\displaystyle V=V_0+{}^{\varphi }{V}_1={\tilde{V}}_0{n}_0+{}^{\varphi }{\tilde{V}}_1{n}_1}$

to the number of moles of one component. This gives the following relation:

${\displaystyle {}^{\varphi }{\tilde{V}}_1=\frac{V}{n_1}-{\tilde{V}}_0\frac{n_0}{n_1}=\frac{V}{n_1}-{\tilde{V}}_0{r}_{01}}$

Relation to partial (molar) quantities

Note the contrasting definitions between partial molar quantity and apparent molar quantity: in the case of partial molar volumes ${\displaystyle \overline{V_0},\overline{V_1}}$, defined by partial derivatives

${\displaystyle \overline{V_0}=(\frac{\mathrm{\partial }V}{\mathrm{\partial }{n}_0}{)}_{T,p,n_1},\overline{V_1}=(\frac{\mathrm{\partial }V}{\mathrm{\partial }{n}_1}{)}_{T,p,n_0}}$,

one can write ${\displaystyle dV=\overline{V_0}d{n}_0+\overline{V_1}d{n}_1}$, and so ${\displaystyle V=\overline{V_0}{n}_0+\overline{V_1}{n}_1}$ always holds. In contrast, in the definition of apparent molar volume, the molar volume of the pure solvent, ${\displaystyle {\tilde{V}}_0}$, is used instead, which can be written as

${\displaystyle \widetilde{V_0}=(\frac{\mathrm{\partial }V}{\mathrm{\partial }{n}_0}{)}_{T,p,n_1=0}}$,

for comparison. In other words, we assume that the volume of the solvent does not change, and we use the partial molar volume where the number of moles of the solute is exactly zero ("the molar volume"). Thus, in the defining expression for apparent molar volume ${\displaystyle {}^{\varphi }{\tilde{V}}_1}$,

${\displaystyle V=V_0+{}^{\varphi }{V}_1={\tilde{V}}_0{n}_0+{}^{\varphi }{\tilde{V}}_1{n}_1}$,

the term ${\displaystyle V_0}$ is attributed to the pure solvent, while the "leftover" excess volume, ${\displaystyle {}^{\varphi }{V}_1}$, is considered to originate from the solute. At high dilution with ${\displaystyle n_0\gg n_1\approx 0}$, we have ${\displaystyle \widetilde{V_0}\approx \overline{V_0}}$, and so the apparent molar volume and partial molar volume of the solute also converge: ${\displaystyle {}^{\varphi }{\tilde{V}}_1\approx {\overline{V}}_1}$.

Quantitatively, the relation between partial molar properties and the apparent ones can be derived from the definition of the apparent quantities and of the molality. For volume,

${\displaystyle \overline{V_1}={}^{\varphi }{\tilde{V}}_1+b\frac{\mathrm{\partial }{}^{\varphi }{\tilde{V}}_1}{\mathrm{\partial }b}.}$

Relation to the activity coefficient of an electrolyte and its solvation shell number

The ratio r_a between the apparent molar volume of a dissolved electrolyte in a concentrated solution and the molar volume of the solvent (water) can be linked to the statistical component of the activity coefficient ${\displaystyle {\gamma }_s}$ of the electrolyte and its solvation shell number h:

${\displaystyle \ln {\gamma }_s=\frac{h-\nu }{\nu }\ln (1+\frac{b{r}_a}{55.5})-\frac{h}{\nu }\ln (1-\frac{b{r}_a}{55.5})+\frac{b{r}_a(r_a+h-\nu )}{55.5(1+\frac{b{r}_a}{55.5})}}$,

where ν is the number of ions due to dissociation of the electrolyte, and b is the molality as above.

Examples

Everyday example: when sand is mixed with water, the bulk volume of the mixture is smaller than the sum of the individual volumes, as the water can lodge in the spaces between the sand grains. A similar situation with a different mechanism occurs when ethanol is mixed with water.

Electrolytes

The apparent molar volume of salt is usually less than the molar volume of the solid salt. For instance, solid NaCl has a volume of 27 cm³ per mole, but the apparent molar volume at low concentrations is only 16.6 cc/mole. In fact, some aqueous electrolytes have negative apparent molar volumes: NaOH −6.7, LiOH −6.0, and Na₂CO₃ −6.7 cm³/mole. This means that their solutions in a given amount of water have a smaller volume than the same amount of pure water. (The effect is small, however.) The physical reason is that nearby water molecules are strongly attracted to the ions so that they occupy less space.

Alcohol

Excess volume of a mixture of ethanol and water

Another example of the apparent molar volume of the second component is less than its molar volume as a pure substance is the case of ethanol in water. For example, at 20 mass percents ethanol, the solution has a volume of 1.0326 liters per kg at 20 °C, while pure water is 1.0018 L/kg (1.0018 cc/g). The apparent volume of the added ethanol is 1.0326 L – 0.8 kg x 1.0018 L/kg = 0.2317 L. The number of moles of ethanol is 0.2 kg / (0.04607 kg/mol) = 4.341 mol, so that the apparent molar volume is 0.2317 L / 4.341 mol = 0.0532 L / mol = 53.2 cc/mole (1.16 cc/g). However pure ethanol has a molar volume at this temperature of 58.4 cc/mole (1.27 cc/g).

If the solution were ideal, its volume would be the sum of the unmixed components. The volume of 0.2 kg pure ethanol is 0.2 kg x 1.27 L/kg = 0.254 L, and the volume of 0.8 kg pure water is 0.8 kg x 1.0018 L/kg = 0.80144 L, so the ideal solution volume would be 0.254 L + 0.80144 L = 1.055 L. The nonideality of the solution is reflected by a slight decrease (roughly 2.2%, 1.0326 rather than 1.055 L/kg) in the volume of the combined system upon mixing. As the percent ethanol goes up toward 100%, the apparent molar volume rises to the molar volume of pure ethanol.

Electrolyte – non-electrolyte systems

Apparent quantities can underline interactions in electrolyte – non-electrolyte systems which show interactions like salting in and salting out, but also give insights in ion-ion interactions, especially by their dependence on temperature.

Multicomponent mixtures or solutions

For multicomponent solutions, apparent molar properties can be defined in several ways. For the volume of a ternary (3-component) solution with one solvent and two solutes as an example, there would still be only one equation ${\displaystyle (V={\tilde{V}}_0{n}_0+{}^{\varphi }{\tilde{V}}_1{n}_1+{}^{\varphi }{\tilde{V}}_2{n}_2)}$, which is insufficient to determine the two apparent volumes. (This is in contrast to partial molar properties, which are well-defined intensive properties of the materials and therefore unambiguously defined in multicomponent systems. For example, partial molar volume is defined for each component i as ${\displaystyle \overline{V_i}=(\mathrm{\partial }V/\mathrm{\partial }{n}_i{)}_{T,p,n_{j\ne i}}}$.)

One description of ternary aqueous solutions considers only the weighted mean apparent molar volume of the solutes, defined as

${\displaystyle {}^{\varphi }\tilde{V}(n_1,n_2)={}^{\varphi }{\tilde{V}}_{12}=\frac{V-V_0}{n_1+n_2}}$,

where ${\displaystyle V}$ is the solution volume and ${\displaystyle V_0}$ the volume of pure water. This method can be extended for mixtures with more than 3 components.

${\displaystyle {}^{\varphi }\tilde{V}(n_1,n_2,n_3,..)={}^{\varphi }{\tilde{V}}_{\mathrm{123..}}=\frac{V-V_0}{n_1+n_2+n_3+...}}$,

The sum of products molalities – apparent molar volumes of solutes in their binary solutions equals the product between the sum of molalities of solutes and apparent molar volume in ternary of multicomponent solution mentioned above.

${\displaystyle {}^{\varphi }{\tilde{V}}_{\mathrm{123..}}(b_1+b_2+b_3+...)=b_1{}^{\varphi }{\tilde{V}}_1+b_2{}^{\varphi }{\tilde{V}}_2+b_3{}^{\varphi }{\tilde{V}}_3+...}$,

Another method is to treat the ternary system as pseudobinary and define the apparent molar volume of each solute with reference to a binary system containing both other components: water and the other solute. The apparent molar volumes of each of the two solutes are then

${\displaystyle {}^{\varphi }{\tilde{V}}_1=\frac{V-V(solvent+solute2)}{n_1}}$ and ${\displaystyle {}^{\varphi }{\tilde{V}}_2=\frac{V-V(solvent+solute1)}{n_2}}$

The apparent molar volume of the solvent is:

${\displaystyle {}^{\varphi }{\tilde{V}}_0=\frac{V-V(solute1+solute2)}{n_0}}$

However, this is an unsatisfactory description of volumetric properties.

The apparent molar volume of two components or solutes considered as one pseudocomponent ${\displaystyle {}^{\varphi }{\tilde{V}}_{12}}$ or ${\displaystyle {}^{\varphi }{\tilde{V}}_{ij}}$ is not to be confused with volumes of partial binary mixtures with one common component V_ij, V_jk which mixed in a certain mixing ratio form a certain ternary mixture V or V_ijk.

Of course the complement volume of a component in respect to other components of the mixture can be defined as a difference between the volume of the mixture and the volume of a binary submixture of a given composition like:

${\displaystyle {}^c{\tilde{V}}_2=\frac{V-V_{01}}{n_2}}$

There are situations when there is no rigorous way to define which is solvent and which is solute like in the case of liquid mixtures (say water and ethanol) that can dissolve or not a solid like sugar or salt. In these cases apparent molar properties can and must be ascribed to all components of the mixture.