In chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. The term aqueous solution is when one of the solvents is water. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. 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 assumes the phase of the solvent when the solvent is the larger fraction of the mixture, as is commonly the case. The concentration of a solute in a solution is the mass of that solute expressed as a percentage of the mass of the whole solution.
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.
If the solvent is a gas, only gases 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 molecules play almost no role, dilute gases form rather trivial solutions. In part of the literature, they are not even classified as solutions, but addressed as mixtures.
If the solvent is a liquid, then almost all gases, liquids, and solids can be dissolved. Here are some examples:
Body fluids are examples for 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.
If the solvent is a solid, then gases, liquids and solids can be dissolved.
The ability of one compound to dissolve in another compound is called solubility. 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.
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).
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.
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 with each other, while being incompatible with water.
An example for 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.
It is common practice in laboratories to make a solution directly from its constituent ingredients. There are three cases in practical calculation:
In the following equations, A is solvent, B is solute, and C is concentration. Solute volume contribution is considered through ideal solution model.
Example: Make 2 g/100mL of NaCl solution with 1 L water Water (properties). The density of resulting solution is considered to be equal to that of water, statement holding especially for dilute solutions, so the density information is not required.
An acid is a molecule or ion capable of donating a hydron (proton or hydrogen ion H+), or, alternatively, capable of forming a covalent bond with an electron pair (a Lewis acid).The first category of acids is the proton donors or Brønsted acids. In the special case of aqueous solutions, proton donors form the hydronium ion H3O+ and are known as Arrhenius acids. Brønsted and Lowry generalized the Arrhenius theory to include non-aqueous solvents. A Brønsted or Arrhenius acid usually contains a hydrogen atom bonded to a chemical structure that is still energetically favorable after loss of H+.
Aqueous Arrhenius acids have characteristic properties which provide a practical description of an acid. Acids form aqueous solutions with a sour taste, can turn blue litmus red, and react with bases and certain metals (like calcium) to form salts. The word acid is derived from the Latin acidus/acēre meaning sour. An aqueous solution of an acid has a pH less than 7 and is colloquially also referred to as 'acid' (as in 'dissolved in acid'), while the strict definition refers only to the solute. A lower pH means a higher acidity, and thus a higher concentration of positive hydrogen ions in the solution. Chemicals or substances having the property of an acid are said to be acidic.
Common aqueous acids include hydrochloric acid (a solution of hydrogen chloride which is found in gastric acid in the stomach and activates digestive enzymes), acetic acid (vinegar is a dilute aqueous solution of this liquid), sulfuric acid (used in car batteries), and citric acid (found in citrus fruits). As these examples show, acids (in the colloquial sense) can be solutions or pure substances, and can be derived from acids (in the strict sense) that are solids, liquids, or gases. Strong acids and some concentrated weak acids are corrosive, but there are exceptions such as carboranes and boric acid.
The second category of acids are Lewis acids, which form a covalent bond with an electron pair. An example is boron trifluoride (BF3), whose boron atom has a vacant orbital which can form a covalent bond by sharing a lone pair of electrons on an atom in a base, for example the nitrogen atom in ammonia (NH3). Lewis considered this as a generalization of the Brønsted definition, so that an acid is a chemical species that accepts electron pairs either directly or by releasing protons (H+) into the solution, which then accept electron pairs. However, hydrogen chloride, acetic acid, and most other Brønsted-Lowry acids cannot form a covalent bond with an electron pair and are therefore not Lewis acids. Conversely, many Lewis acids are not Arrhenius or Brønsted-Lowry acids. In modern terminology, an acid is implicitly a Brønsted acid and not a Lewis acid, since chemists almost always refer to a Lewis acid explicitly as a Lewis acid.Ammonia
Ammonia is a compound of nitrogen and hydrogen with the formula NH3. The simplest pnictogen hydride, ammonia is a colourless gas with a characteristic pungent smell. It is a common nitrogenous waste, particularly among aquatic organisms, and it contributes significantly to the nutritional needs of terrestrial organisms by serving as a precursor to food and fertilizers. Ammonia, either directly or indirectly, is also a building block for the synthesis of many pharmaceutical products and is used in many commercial cleaning products. It is mainly collected by downward displacement of both air and water. Ammonia is named for the Ammonians, worshipers of the Egyptian god Amun, who used ammonium chloride in their rituals.Although common in nature and in wide use, ammonia is both caustic and hazardous in its concentrated form. It is classified as an extremely hazardous substance in the United States, and is subject to strict reporting requirements by facilities which produce, store, or use it in significant quantities.The global industrial production of ammonia in 2014 was 176 million tonnes, a 16% increase over the 2006 global industrial production of 152 million tonnes. Industrial ammonia is sold either as ammonia liquor (usually 28% ammonia in water) or as pressurized or refrigerated anhydrous liquid ammonia transported in tank cars or cylinders.NH3 boils at −33.34 °C (−28.012 °F) at a pressure of one atmosphere, so the liquid must be stored under pressure or at low temperature. Household ammonia or ammonium hydroxide is a solution of NH3 in water. The concentration of such solutions is measured in units of the Baumé scale (density), with 26 degrees baumé (about 30% (by weight) ammonia at 15.5 °C or 59.9 °F) being the typical high-concentration commercial product.Aqueous solution
An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be represented as Na+(aq) + Cl−(aq). The word aqueous (comes from aqua) means pertaining to, related to, similar to, or dissolved in, water. As water is an excellent solvent and is also naturally abundant, it is a ubiquitous solvent in chemistry. Aqueous solution is water with a pH of 7.0 where the hydrogen ions (H+) and hydroxide ions (OH-) are in Arrhenius balance (10-7).
A non-aqueous solution is a solution in which the solvent is a liquid, but is not water.Substances that are hydrophobic ('water-fearing') often do not dissolve well in water, whereas those that are hydrophilic ('water-friendly') do. An example of a hydrophilic substance is sodium chloride. Acids and bases are aqueous solutions, as part of their Arrhenius definitions.
The ability of a substance to dissolve in water is determined by whether the substance can match or exceed the strong attractive forces that water molecules generate between themselves. If the substance lacks the ability to dissolve in water the molecules form a precipitate.
Reactions in aqueous solutions are usually metathesis reactions. Metathesis reactions are another term for double-displacement; that is, when a cation displaces to form an ionic bond with the other anion. The cation bonded with the latter anion will dissociate and bond with the other anion.
Aqueous solutions that conduct electric current efficiently contain strong electrolytes, while ones that conduct poorly are considered to have weak electrolytes. Those strong electrolytes are substances that are completely ionized in water, whereas the weak electrolytes exhibit only a small degree of ionization in water.
Nonelectrolytes are substances that dissolve in water yet maintain their molecular integrity (do not dissociate into ions). Examples include sugar, urea, glycerol, and methylsulfonylmethane (MSM).
When writing the equations of aqueous reactions, it is essential to determine the precipitate. To determine the precipitate, one must consult a chart of solubility. Soluble compounds are aqueous, while insoluble compounds are the precipitate. There may not always be a precipitate.
When performing calculations regarding the reacting of one or more aqueous solutions, in general one must know the concentration, or molarity, of the aqueous solutions. Solution concentration is given in terms of the form of the solute prior to it dissolving.
Aqueous solutions may contain, especially in alcaline zone or subjected to radiolysis, hydrated atomic hydrogen an hydrated electron.Brine
Brine is a high-concentration solution of salt (usually sodium chloride) in water. In different contexts, brine may refer to salt solutions ranging from about 3.5% (a typical concentration of seawater, on the lower end of solutions used for brining foods) up to about 26% (a typical saturated solution, depending on temperature). Lower levels of concentration are called by different names: fresh water, brackish water, and saline water.
Brine naturally occurs on the Earth's surface (salt lakes), crust, and within brine pools on ocean bottom. High-concentration brine lakes typically emerge due to evaporation of ground saline water on high ambient temperatures. Brine is used for food processing and cooking (pickling and brining), for de-icing of roads and other structures, and in a number of technological processes. It is also a by-product of many industrial processes, such as desalination, and may pose an environmental risk due to its corrosive and toxic effects, so it requires wastewater treatment for proper disposal.Buffer solution
A buffer solution (more precisely, pH buffer or hydrogen ion buffer) is an aqueous solution consisting of a mixture of a weak acid and its conjugate base, or vice versa. Its pH changes very little when a small amount of strong acid or base is added to it. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical applications. In nature, there are many systems that use buffering for pH regulation. For example, the bicarbonate buffering system is used to regulate the pH of blood.Clotrimazole
Clotrimazole, sold under the brand name Canesten among others, is an antifungal medication. It is used to treat vaginal yeast infections, oral thrush, diaper rash, pityriasis versicolor, and types of ringworm including athlete's foot and jock itch. It can be taken by mouth or applied as a cream to the skin or in the vagina.Common side effects when taken by mouth include nausea and itchiness. When applied to the skin common side effects include redness and burning. In pregnancy, use on the skin or in the vagina is believed to be safe. There is no evidence of harm when used by mouth during pregnancy but this has been less well studied. When used by mouth, greater care should be taken in those with liver problems. It is in the azole class of medications and works by disrupting the cell membrane.Clotrimazole was discovered in 1969. It is on the World Health Organization's List of Essential Medicines, the most effective and safe medicines needed in a health system. It is available as a generic medication. The wholesale cost in the developing world as of 2014 is 0.20–0.86 USD per 20 gram tube of cream. In the United States a course of treatment typically costs less than 25 USD.E-commerce
E-commerce is the activity of buying or selling of products on online services or over the Internet. Electronic commerce draws on technologies such as mobile commerce, electronic funds transfer, supply chain management, Internet marketing, online transaction processing, electronic data interchange (EDI), inventory management systems, and automated data collection systems.
Modern electronic commerce typically uses the World Wide Web for at least one part of the transaction's life cycle although it may also use other technologies such as e-mail. Typical e-commerce transactions include the purchase of online books (such as Amazon) and music purchases (music download in the form of digital distribution such as iTunes Store), and to a less extent, customized/personalized online liquor store inventory services. There are three areas of e-commerce: online retailing, electric markets, and online auctions. E-commerce is supported by electronic business.E-commerce businesses may also employ some or all of the followings:
Online shopping for retail sales direct to consumers via Web sites and mobile apps, and conversational commerce via live chat, chatbots, and voice assistants
Providing or participating in online marketplaces, which process third-party business-to-consumer or consumer-to-consumer sales
Business-to-business buying and selling;
Gathering and using demographic data through web contacts and social media
Business-to-business (B2B) electronic data interchange
Marketing to prospective and established customers by e-mail or fax (for example, with newsletters)
Engaging in pretail for launching new products and services
Online financial exchanges for currency exchanges or trading purposes.Electrolyte
An electrolyte is a substance that produces an electrically conducting solution when dissolved in a polar solvent, such as water. The dissolved electrolyte separates into cations and anions, which disperse uniformly through the solvent. Electrically, such a solution is neutral. If an electric potential is applied to such a solution, the cations of the solution are drawn to the electrode that has an abundance of electrons, while the anions are drawn to the electrode that has a deficit of electrons. The movement of anions and cations in opposite directions within the solution amounts to a current. This includes most soluble salts, acids, and bases. Some gases, such as hydrogen chloride, under conditions of high temperature or low pressure can also function as electrolytes. Electrolyte solutions can also result from the dissolution of some biological (e.g., DNA, polypeptides) and synthetic polymers (e.g., polystyrene sulfonate), termed "polyelectrolytes", which contain charged functional groups. A substance that dissociates into ions in solution acquires the capacity to conduct electricity. Sodium, potassium, chloride, calcium, magnesium, and phosphate are examples of electrolytes.
In medicine, electrolyte replacement is needed when a person has prolonged vomiting or diarrhea, and as a response to strenuous athletic activity. Commercial electrolyte solutions are available, particularly for sick children (such as oral rehydration solution, Suero Oral, or Pedialyte) and athletes (sports drinks). Electrolyte monitoring is important in the treatment of anorexia and bulimia.Final Solution
The Final Solution (German: Endlösung) or the Final Solution to the Jewish Question (German: die Endlösung der Judenfrage, pronounced [diː ˈɛntˌløːzʊŋ deːɐ̯ ˈjuːdn̩ˌfʁaːɡə]) was a Nazi plan for the genocide of Jews during World War II. The "Final Solution of the Jewish Question" was the official code name for the murder of all Jews within reach, which was not restricted to the European continent. This policy of deliberate and systematic genocide starting across German-occupied Europe was formulated in procedural and geo-political terms by Nazi leadership in January 1942 at the Wannsee Conference held near Berlin, and culminated in the Holocaust, which saw the killing of 90% of Polish Jews, and two thirds of the Jewish population of Europe.The nature and timing of the decisions that led to the Final Solution is an intensely researched and debated aspect of the Holocaust. The program evolved during the first 25 months of war leading to the attempt at "murdering every last Jew in the German grasp". Most historians agree, wrote Christopher Browning, that the Final Solution cannot be attributed to a single decision made at one particular point in time. "It is generally accepted the decision-making process was prolonged and incremental." In 1940, following the Fall of France, Adolf Eichmann devised the Madagascar Plan to move Europe's Jewish population to the French colony, but the plan was abandoned for logistical reasons, mainly a naval blockade. There were also preliminary plans to deport Jews to Palestine and Siberia. In 1941, wrote Raul Hilberg, in the first phase of the mass murder of Jews, the mobile killing units began to pursue their victims across occupied eastern territories; in the second phase, stretching across all of German-occupied Europe, the Jewish victims were sent on death trains to centralized extermination camps built for the purpose of systematic implementation of the Final Solution.Glucose
Glucose (also called dextrose) is a simple sugar with the molecular formula C6H12O6. Glucose is the most abundant monosaccharide, a subcategory of carbohydrates. Glucose is mainly made by plants and most algae during photosynthesis from water and carbon dioxide, using energy from sunlight. There it is used to make cellulose in cell walls, which is the most abundant carbohydrate. In energy metabolism, glucose is the most important source of energy in all organisms. Glucose for metabolism is partially stored as a polymer, in plants mainly as starch and amylopectin and in animals as glycogen. Glucose circulates in the blood of animals as blood sugar. The naturally occurring form of glucose is D-glucose, while L-glucose is produced synthetically in comparably small amounts and is of lesser importance.
Glucose, as intravenous sugar solution, is on the World Health Organization's List of Essential Medicines, the most important medications needed in a basic health system. The name glucose derives through the French from the Greek γλυκός, which means "sweet," in reference to must, the sweet, first press of grapes in the making of wine. The suffix "-ose" is a chemical classifier, denoting a sugar.Hydroponics
Hydroponics is a subset of hydroculture, which is a method of growing plants without soil by using mineral nutrient solutions in a water solvent. Terrestrial plants may be grown with only their roots exposed to the mineral solution, or the roots may be supported by an inert medium, such as perlite or gravel.
The nutrients used in hydroponic systems can come from an array of different sources; these can include, but are not limited to, byproduct from fish waste, duck manure, or purchased chemical fertilisers.Molar concentration
Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solution. In chemistry, the most commonly used unit for molarity is the number of moles per litre, having the unit symbol mol/L. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M.PH
In chemistry, pH () is a scale used to specify how acidic or basic a water-based solution is. Acidic solutions have a lower pH, basic solutions have a higher pH. At room temperature, pure water is neither acidic nor basic and has a pH of 7.
The scale is logarithmic. It is approximately the negative of the base 10 logarithm of the molar concentration (measured in units of moles per liter) of hydrogen ions. More precisely it is the negative of the base 10 logarithm of the activity of the hydrogen ion. At 25 °C, solutions with a pH less than 7 are acidic and solutions with a pH greater than 7 are basic. The neutral value of the pH depends on the temperature, being lower than 7 if the temperature increases. Pure water is neutral (pH 7) at 25 °C. Contrary to popular belief, the pH value can be less than 0 or greater than 14 for very strong acids and bases respectively.Measurements of pH are important in agronomy, medicine, chemistry, water treatment, and many other applications.
The pH scale is traceable to a set of standard solutions whose pH is established by international agreement.
Primary pH standard values are determined using a concentration cell with transference, by measuring the potential difference between a hydrogen electrode and a standard electrode such as the silver chloride electrode.
The pH of aqueous solutions can be measured with a glass electrode and a pH meter, or an indicator.
There are three current theories used to describe acid–base reactions: Arrhenius, Bronsted-Lowry and Lewis when determining pH.Quadratic equation
In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form
where x represents an unknown, and a, b, and c represent known numbers, with a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no term. The numbers a, b, and c are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.
The values of x that satisfy the equation are called solutions, roots of zeros of the equation or its left-hand side. A quadratic equation has at most two solutions. If there is no real solution, there are two complex solutions. If there is only one solution, one says that it is a double root. So a quadratic equation has always two roots, if complex roots are considered, and if a double root is counted for two. If the two solutions are denoted r and s (possibly equal), one has
Thus, the process of solving a quadratic equation is also called factorizing or factoring. Completing the square is the standard method for that, which results in the quadratic formula, which express the solutions in terms of a, b, and c. Graphing may also be used for getting an approximate value of the solutions. Solutions to problems that may be expressed in terms of quadratic equations were known as early as 2000 BC.
Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation only contains powers of x that are non-negative integers, and therefore it is a polynomial equation. In particular, it is a second-degree polynomial equation, since the greatest power is two.Saline (medicine)
Saline, also known as saline solution, is a mixture of sodium chloride in water and has a number of uses in medicine. Applied to the affected area it is used to clean wounds, help remove contact lenses, and help with dry eyes. By injection into a vein it is used to treat dehydration such as from gastroenteritis and diabetic ketoacidosis. It is also used to dilute other medications to be given by injection.Large amounts may result in fluid overload, swelling, acidosis, and high blood sodium. In those with long-standing low blood sodium, excessive use may result in osmotic demyelination syndrome. Saline is in the crystalloid family of medications. It is most commonly used as a sterile 9 g of salt per litre (0.9%) solution, known as normal saline. Higher and lower concentrations may also occasionally be used. Saline has a pH of 5.5 making it acidic.The medical use of saline began around 1831. It is on the World Health Organization's List of Essential Medicines, the most effective and safe medicines needed in a health system. The wholesale cost in the developing world is about US$0.60–4.20 per liter of normal saline.Sodium hydroxide
Sodium hydroxide, also known as lye and caustic soda, is an inorganic compound with the formula NaOH. It is a white solid ionic compound consisting of sodium cations Na+ and hydroxide anions OH−.
Sodium hydroxide is a highly caustic base and alkali that decomposes proteins at ordinary ambient temperatures and may cause severe chemical burns. It is highly soluble in water, and readily absorbs moisture and carbon dioxide from the air. It forms a series of hydrates NaOH·nH2O. The monohydrate NaOH·H2O crystallizes from water solutions between 12.3 and 61.8 °C. The commercially available "sodium hydroxide" is often this monohydrate, and published data may refer to it instead of the anhydrous compound. As one of the simplest hydroxides, it is frequently utilized alongside neutral water and acidic hydrochloric acid to demonstrate the pH scale to chemistry students.Sodium hydroxide is used in many industries: in the manufacture of pulp and paper, textiles, drinking water, soaps and detergents, and as a drain cleaner. Worldwide production in 2004 was approximately 60 million tonnes, while demand was 51 million tonnes.Solubility
Solubility is the property of a solid, liquid or gaseous chemical substance called solute to dissolve in a solid, liquid or gaseous solvent. The solubility of a substance fundamentally depends on the physical and chemical properties of the solute and solvent as well as on temperature, pressure and presence of other chemicals (including changes to the pH) of the solution. The extent of the solubility of a substance in a specific solvent is measured as the saturation concentration, where adding more solute does not increase the concentration of the solution and begins to precipitate the excess amount of solute.
Insolubility is the inability to dissolve in a solid, liquid or gaseous solvent.
Most often, the solvent is a liquid, which can be a pure substance or a mixture. One may also speak of solid solution, but rarely of solution in a gas (see vapor–liquid equilibrium instead).
Under certain conditions, the equilibrium solubility can be exceeded to give a so-called supersaturated solution, which is metastable. Metastability of crystals can also lead to apparent differences in the amount of a chemical that dissolves depending on its crystalline form or particle size. A supersaturated solution generally crystallises when 'seed' crystals are introduced and rapid equilibration occurs. Phenylsalicylate is one such simple observable substance when fully melted and then cooled below its fusion point.
Solubility is not to be confused with the ability to 'dissolve' a substance, because the solution might also occur because of a chemical reaction. For example, zinc 'dissolves' (with effervescence) in hydrochloric acid as a result of a chemical reaction releasing hydrogen gas in a displacement reaction. The zinc ions are soluble in the acid.
The solubility of a substance is an entirely different property from the rate of solution, which is how fast it dissolves. The smaller a particle is, the faster it dissolves although there are many factors to add to this generalization.
Crucially solubility applies to all areas of chemistry, geochemistry, inorganic, physical, organic and biochemistry. In all cases it will depend on the physical conditions (temperature, pressure and concentration) and the enthalpy and entropy directly relating to the solvents and solutes concerned.
By far the most common solvent in chemistry is water which is a solvent for most ionic compounds as well as a wide range of organic substances. This is a crucial factor in acidity/alkalinity and much environmental and geochemical work.System of linear equations
In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables. For example,
is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by
since it makes all three equations valid. The word "system" indicates that the equations are to be considered collectively, rather than individually.
In mathematics, the theory of linear systems is the basis and a fundamental part of linear algebra, a subject which is used in most parts of modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, and play a prominent role in engineering, physics, chemistry, computer science, and economics. A system of non-linear equations can often be approximated by a linear system (see linearization), a helpful technique when making a mathematical model or computer simulation of a relatively complex system.
Very often, the coefficients of the equations are real or complex numbers and the solutions are searched in the same set of numbers, but the theory and the algorithms apply for coefficients and solutions in any field. For solutions in an integral domain like the ring of the integers, or in other algebraic structures, other theories have been developed, see Linear equation over a ring. Integer linear programming is a collection of methods for finding the "best" integer solution (when there are many). Gröbner basis theory provides algorithms when coefficients and unknowns are polynomials. Also tropical geometry is an example of linear algebra in a more exotic structure.Two-state solution
The two-state solution refers to a solution of the Israeli–Palestinian conflict which calls for "two states for two groups of people." The two-state solution envisages an independent State of Palestine alongside the State of Israel, west of the Jordan River. The boundary between the two states is still subject to dispute and negotiation, with Palestinian and Arab leadership insisting on the "1967 borders", which is not accepted by Israel. The territory of the former Mandate Palestine (including Jerusalem) which shall not form part of the Palestinian State, shall be part of Israeli territory.
For the Palestinian negotiators, though not all aspects being accepted by Israel, the framework of the solution is UN resolutions on the "Peaceful settlement of the question of Palestine", going back to 1974. The resolution calls for "two States, Israel and Palestine … side by side within secure and recognized borders" together with "a just resolution of the refugee question in conformity with UN resolution 194". The borders of the state of Palestine are "based on the pre-1967 borders". The latest resolution in November 2013 was passed 165 to 6, with 6 abstentions; with Israel and the United States voting against.The Palestinians have "shown serious interest" in a two-state solution since the mid-1970s, and its mainstream leadership has embraced the concept since the 1982 Arab Summit in Fez. Israel views moves by Palestinian leaders to obtain international recognition of a State of Palestine as being unilateral action by the Palestinians and inconsistent with a negotiated two-state solution.
Over the years, polls have consistently shown "respectable Israeli and Palestinian majorities in favor of a negotiated two-state settlement."There have been many diplomatic efforts to realize a two state solution, starting from the 1991 Madrid Conference. There followed the 1993 Oslo Accords and the failed 2000 Camp David Summit followed by the Taba negotiations in early 2001. In 2002, the Arab League proposed the Arab Peace Initiative. The latest initiative, which also failed, was the 2013–14 peace talks.
and related quantities