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Saturday, March 16, 2024

Apparent molar property

From Wikipedia, the free encyclopedia

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

where is the volume of the pure solvent before adding the solute and its molar volume (at the same temperature and pressure as the solution), is the number of moles of solvent, is the apparent molar volume of the solute, and 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 . 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. 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 is described only as an apparent value.

An apparent molar quantity can be similarly defined for the component identified as solvent . 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.

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

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

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 bT:

,

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.

,

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

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

Relation to partial (molar) quantities

Note the contrasting definitions between partial molar quantity and apparent molar quantity: in the case of partial molar volumes , defined by partial derivatives

,

one can write , and so always holds. In contrast, in the definition of apparent molar volume, the molar volume of the pure solvent, , is used instead, which can be written as

,

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 ,

,

the term is attributed to the pure solvent, while the "leftover" excess volume, , is considered to originate from the solute. At high dilution with , we have , and so the apparent molar volume and partial molar volume of the solute also converge: .

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,

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

The ratio ra 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 of the electrolyte and its solvation shell number h:

,

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 , 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 .)

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

,

where is the solution volume and the volume of pure water. This method can be extended for mixtures with more than 3 components.

,

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.

,

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

and

The apparent molar volume of the solvent is:

However, this is an unsatisfactory description of volumetric properties.

The apparent molar volume of two components or solutes considered as one pseudocomponent or is not to be confused with volumes of partial binary mixtures with one common component Vij, Vjk which mixed in a certain mixing ratio form a certain ternary mixture V or Vijk.

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:

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.

Citric acid

From Wikipedia, the free encyclopedia

Properties
C6H8O7
Molar mass 192.123 g/mol (anhydrous), 210.14 g/mol (monohydrate)[2]
Appearance white solid
Odor Odorless
Density 1.665 g/cm3 (anhydrous)
1.542 g/cm3 (18 °C, monohydrate)
Melting point 156 °C (313 °F; 429 K)
Boiling point 310 °C (590 °F; 583 K) decomposes from 175 °C[3]
54% w/w (10 °C)
59.2% w/w (20 °C)
64.3% w/w (30 °C)
68.6% w/w (40 °C)
70.9% w/w (50 °C)
73.5% w/w (60 °C)
76.2% w/w (70 °C)
78.8% w/w (80 °C)
81.4% w/w (90 °C)
84% w/w (100 °C)
Solubility Soluble in acetone, alcohol, ether, ethyl acetate, DMSO
Insoluble in C
6
H
6
, CHCl3, CS2, toluene
Solubility in ethanol 62 g/100 g (25 °C)
Solubility in amyl acetate 4.41 g/100 g (25 °C)
Solubility in diethyl ether 1.05 g/100 g (25 °C)
Solubility in 1,4-dioxane 35.9 g/100 g (25 °C)
log P −1.64
Acidity (pKa) pKa1 = 3.13
pKa2 = 4.76
pKa3 = 6.39, 6.40
pKa4 = 14.4
1.493–1.509 (20 °C)
1.46 (150 °C)
Viscosity 6.5 cP (50% aq. sol.)
Structure
Monoclinic
Thermochemistry
226.51 J/(mol·K) (26.85 °C)
252.1 J/(mol·K)
−1543.8 kJ/mol
1985.3 kJ/mol (474.5 kcal/mol, 2.47 kcal/g), 1960.6 kJ/mol
1972.34 kJ/mol (471.4 kcal/mol, 2.24 kcal/g) (monohydrate)
Pharmacology
A09AB04 (WHO)
Hazards
Occupational safety and health (OHS/OSH):
Main hazards
Skin and eye irritant
GHS labelling:
GHS05: CorrosiveGHS07: Exclamation mark
Warning
H290, H319, H315
P305+P351+P338
NFPA 704 (fire diamond)
NFPA 704 four-colored diamondHealth 2: Intense or continued but not chronic exposure could cause temporary incapacitation or possible residual injury. E.g. chloroformFlammability 1: Must be pre-heated before ignition can occur. Flash point over 93 °C (200 °F). E.g. canola oilInstability 0: Normally stable, even under fire exposure conditions, and is not reactive with water. E.g. liquid nitrogenSpecial hazards (white): no code
2
1
0
Flash point 155 °C (311 °F; 428 K)
345 °C (653 °F; 618 K)
Explosive limits 8%
Lethal dose or concentration (LD, LC):
3000 mg/kg (rats, oral)
Safety data sheet (SDS) HMDB
Except where otherwise noted, data are given for materials in their standard state (at 25 °C [77 °F], 100 kPa).
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Citric acid is an organic compound with the chemical formula HOC(CO2H)(CH2CO2H)2. It is a colorless weak organic acid. It occurs naturally in citrus fruits. In biochemistry, it is an intermediate in the citric acid cycle, which occurs in the metabolism of all aerobic organisms.

More than two million tons of citric acid are manufactured every year. It is used widely as an acidifier, as a flavoring, and a chelating agent.

A citrate is a derivative of citric acid; that is, the salts, esters, and the polyatomic anion found in solution. An example of the former, a salt is trisodium citrate; an ester is triethyl citrate. When part of a salt, the formula of the citrate anion is written as C
6
H
5
O3−
7
or C
3
H
5
O(COO)3−
3
.

Natural occurrence and industrial production

Lemons, oranges, limes, and other citrus fruits contain high concentrations of citric acid.

Citric acid occurs in a variety of fruits and vegetables, most notably citrus fruits. Lemons and limes have particularly high concentrations of the acid; it can constitute as much as 8% of the dry weight of these fruits (about 47 g/L in the juices[12]). The concentrations of citric acid in citrus fruits range from 0.005 mol/L for oranges and grapefruits to 0.30 mol/L in lemons and limes; these values vary within species depending upon the cultivar and the circumstances under which the fruit was grown.

Citric acid was first isolated in 1784 by the chemist Carl Wilhelm Scheele, who crystallized it from lemon juice.

Industrial-scale citric acid production first began in 1890 based on the Italian citrus fruit industry, where the juice was treated with hydrated lime (calcium hydroxide) to precipitate calcium citrate, which was isolated and converted back to the acid using diluted sulfuric acid. In 1893, C. Wehmer discovered Penicillium mold could produce citric acid from sugar. However, microbial production of citric acid did not become industrially important until World War I disrupted Italian citrus exports.

In 1917, American food chemist James Currie discovered that certain strains of the mold Aspergillus niger could be efficient citric acid producers, and the pharmaceutical company Pfizer began industrial-level production using this technique two years later, followed by Citrique Belge in 1929. In this production technique, which is still the major industrial route to citric acid used today, cultures of Aspergillus niger are fed on a sucrose or glucose-containing medium to produce citric acid. The source of sugar is corn steep liquor, molasses, hydrolyzed corn starch, or other inexpensive, carbohydrate solution. After the mold is filtered out of the resulting suspension, citric acid is isolated by precipitating it with calcium hydroxide to yield calcium citrate salt, from which citric acid is regenerated by treatment with sulfuric acid, as in the direct extraction from citrus fruit juice.

In 1977, a patent was granted to Lever Brothers for the chemical synthesis of citric acid starting either from aconitic or isocitrate (also called alloisocitrate) calcium salts under high pressure conditions; this produced citric acid in near quantitative conversion under what appeared to be a reverse, non-enzymatic Krebs cycle reaction.

Global production was in excess of 2,000,000 tons in 2018. More than 50% of this volume was produced in China. More than 50% was used as an acidity regulator in beverages, some 20% in other food applications, 20% for detergent applications, and 10% for applications other than food, such as cosmetics, pharmaceuticals, and in the chemical industry.

Chemical characteristics

Speciation diagram for a 10-millimolar solution of citric acid

Citric acid can be obtained as an anhydrous (water-free) form or as a monohydrate. The anhydrous form crystallizes from hot water, while the monohydrate forms when citric acid is crystallized from cold water. The monohydrate can be converted to the anhydrous form at about 78 °C. Citric acid also dissolves in absolute (anhydrous) ethanol (76 parts of citric acid per 100 parts of ethanol) at 15 °C. It decomposes with loss of carbon dioxide above about 175 °C.

Citric acid is a tribasic acid, with pKa values, extrapolated to zero ionic strength, of 3.128, 4.761, and 6.396 at 25 °C. The pKa of the hydroxyl group has been found, by means of 13C NMR spectroscopy, to be 14.4. The speciation diagram shows that solutions of citric acid are buffer solutions between about pH 2 and pH 8. In biological systems around pH 7, the two species present are the citrate ion and mono-hydrogen citrate ion. The SSC 20X hybridization buffer is an example in common use. Tables compiled for biochemical studies are available.

Conversely, the pH of a 1 mM solution of citric acid will be about 3.2. The pH of fruit juices from citrus fruits like oranges and lemons depends on the citric acid concentration, with a higher concentration of citric acid resulting in a lower pH.

Acid salts of citric acid can be prepared by careful adjustment of the pH before crystallizing the compound. See, for example, sodium citrate.

The citrate ion forms complexes with metallic cations. The stability constants for the formation of these complexes are quite large because of the chelate effect. Consequently, it forms complexes even with alkali metal cations. However, when a chelate complex is formed using all three carboxylate groups, the chelate rings have 7 and 8 members, which are generally less stable thermodynamically than smaller chelate rings. In consequence, the hydroxyl group can be deprotonated, forming part of a more stable 5-membered ring, as in ammonium ferric citrate, (NH
4
)
5
Fe(C
6
H
4
O
7
)
2
·2H
2
O
.

Citric acid can be esterified at one or more of its three carboxylic acid groups to form any of a variety of mono-, di-, tri-, and mixed esters.

Biochemistry

Citric acid cycle

Citrate is an intermediate in the citric acid cycle, also known as the TCA (TriCarboxylic Acid) cycle or the Krebs cycle, a central metabolic pathway for animals, plants, and bacteria. Citrate synthase catalyzes the condensation of oxaloacetate with acetyl CoA to form citrate. Citrate then acts as the substrate for aconitase and is converted into aconitic acid. The cycle ends with regeneration of oxaloacetate. This series of chemical reactions is the source of two-thirds of the food-derived energy in higher organisms. Hans Adolf Krebs received the 1953 Nobel Prize in Physiology or Medicine for the discovery.

Some bacteria (notably E. coli) can produce and consume citrate internally as part of their TCA cycle, but are unable to use it as food, because they lack the enzymes required to import it into the cell. After tens of thousands of evolutions in a minimal glucose medium that also contained citrate during Richard Lenski's Long-Term Evolution Experiment, a variant E. coli evolved with the ability to grow aerobically on citrate. Zachary Blount, a student of Lenski's, and colleagues studied these "Cit+" E. coli as a model for how novel traits evolve. They found evidence that, in this case, the innovation was caused by a rare duplication mutation due to the accumulation of several prior "potentiating" mutations, the identity and effects of which are still under study. The evolution of the Cit+ trait has been considered a notable example of the role of historical contingency in evolution.

Other biological roles

Citrate can be transported out of the mitochondria and into the cytoplasm, then broken down into acetyl-CoA for fatty acid synthesis, and into oxaloacetate. Citrate is a positive modulator of this conversion, and allosterically regulates the enzyme acetyl-CoA carboxylase, which is the regulating enzyme in the conversion of acetyl-CoA into malonyl-CoA (the commitment step in fatty acid synthesis). In short, citrate is transported into the cytoplasm, converted into acetyl-CoA, which is then converted into malonyl-CoA by acetyl-CoA carboxylase, which is allosterically modulated by citrate.

High concentrations of cytosolic citrate can inhibit phosphofructokinase, the catalyst of a rate-limiting step of glycolysis. This effect is advantageous: high concentrations of citrate indicate that there is a large supply of biosynthetic precursor molecules, so there is no need for phosphofructokinase to continue to send molecules of its substrate, fructose 6-phosphate, into glycolysis. Citrate acts by augmenting the inhibitory effect of high concentrations of ATP, another sign that there is no need to carry out glycolysis.

Citrate is a vital component of bone, helping to regulate the size of apatite crystals.

Applications

Food and drink

Powdered citric acid being used to prepare lemon pepper seasoning

Because it is one of the stronger edible acids, the dominant use of citric acid is as a flavoring and preservative in food and beverages, especially soft drinks and candies. Within the European Union it is denoted by E number E330. Citrate salts of various metals are used to deliver those minerals in a biologically available form in many dietary supplements. Citric acid has 247 kcal per 100 g. In the United States the purity requirements for citric acid as a food additive are defined by the Food Chemicals Codex, which is published by the United States Pharmacopoeia (USP).

Citric acid can be added to ice cream as an emulsifying agent to keep fats from separating, to caramel to prevent sucrose crystallization, or in recipes in place of fresh lemon juice. Citric acid is used with sodium bicarbonate in a wide range of effervescent formulae, both for ingestion (e.g., powders and tablets) and for personal care (e.g., bath salts, bath bombs, and cleaning of grease). Citric acid sold in a dry powdered form is commonly sold in markets and groceries as "sour salt", due to its physical resemblance to table salt. It has use in culinary applications, as an alternative to vinegar or lemon juice, where a pure acid is needed. Citric acid can be used in food coloring to balance the pH level of a normally basic dye.

Cleaning and chelating agent

Structure of an iron(III) citrate complex

Citric acid is an excellent chelating agent, binding metals by making them soluble. It is used to remove and discourage the buildup of limescale from boilers and evaporators. It can be used to treat water, which makes it useful in improving the effectiveness of soaps and laundry detergents. By chelating the metals in hard water, it lets these cleaners produce foam and work better without need for water softening. Citric acid is the active ingredient in some bathroom and kitchen cleaning solutions. A solution with a six percent concentration of citric acid will remove hard water stains from glass without scrubbing. Citric acid can be used in shampoo to wash out wax and coloring from the hair. Illustrative of its chelating abilities, citric acid was the first successful eluant used for total ion-exchange separation of the lanthanides, during the Manhattan Project in the 1940s. In the 1950s, it was replaced by the far more efficient EDTA.

In industry, it is used to dissolve rust from steel, and to passivate stainless steels.

Cosmetics, pharmaceuticals, dietary supplements, and foods

Citric acid is used as an acidulant in creams, gels, and liquids. Used in foods and dietary supplements, it may be classified as a processing aid if it was added for a technical or functional effect (e.g. acidulent, chelator, viscosifier, etc.). If it is still present in insignificant amounts, and the technical or functional effect is no longer present, it may be exempt from labeling.

Citric acid is an alpha hydroxy acid and is an active ingredient in chemical skin peels.

Citric acid is commonly used as a buffer to increase the solubility of brown heroin.

Citric acid is used as one of the active ingredients in the production of facial tissues with antiviral properties.

Other uses

The buffering properties of citrates are used to control pH in household cleaners and pharmaceuticals.

Citric acid is used as an odorless alternative to white vinegar for fabric dyeing with acid dyes.

Sodium citrate is a component of Benedict's reagent, used for both qualitative and quantitative identification of reducing sugars.

Citric acid can be used as an alternative to nitric acid in passivation of stainless steel.

Citric acid can be used as a lower-odor stop bath as part of the process for developing photographic film. Photographic developers are alkaline, so a mild acid is used to neutralize and stop their action quickly, but commonly used acetic acid leaves a strong vinegar odor in the darkroom.

Citric acid/potassium-sodium citrate can be used as a blood acid regulator. The citric acid is included to improve palatability

Citric acid is an excellent soldering flux, either dry or as a concentrated solution in water. It should be removed after soldering, especially with fine wires, as it is mildly corrosive. It dissolves and rinses quickly in hot water.

Alkali citrate can be used as an inhibitor of kidney stones by increasing urine citrate levels, useful for prevention of calcium stones, and increasing urine pH, useful for preventing uric acid and cystine stones.

Synthesis of other organic compounds

Citric acid is a versatile precursor to many other organic compounds. Dehydration routes give itaconic acid and its anhydride. Citraconic acid can be produced via thermal isomerization of itaconic acid anhydride. The required itaconic acid anhydride is obtained by dry distillation of citric acid. Aconitic acid can be synthesized by dehydration of citric acid using sulfuric acid:

(HO2CCH2)2C(OH)CO2H → HO2CCH=C(CO2H)CH2CO2H + H2O

Acetonedicarboxylic acid can also be prepared by decarboxylation of citric acid in fuming sulfuric acid.

Safety

Although a weak acid, exposure to pure citric acid can cause adverse effects. Inhalation may cause cough, shortness of breath, or sore throat. Over-ingestion may cause abdominal pain and sore throat. Exposure of concentrated solutions to skin and eyes can cause redness and pain. Long-term or repeated consumption may cause erosion of tooth enamel.

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